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Optical signal processing for high-speed, reconfigurable fiber optic networks

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Optical signal processing for high-speed, reconfigurable fiber optic networks

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Content OPTICAL SIGNAL PROCESSING FOR HIGH-SPEED, RECONFIGURABLE FIBER OPTIC NETWORKS by Saurabh Kumar A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) December 2006 Copyright 2006 Saurabh Kumar ii Acknowledgements I would like to thank my advisor, Prof. Alan Willner for his invaluable guidance and support. His contagious enthusiasm for new ideas has been a critical ingredient in the research conducted as part of this dissertation. I am also deeply indebted to Prof. Daniel Dapkus and Prof. William Steier for always being available as members of my dissertation committee and often sharing their insights in various aspects of the field of photonics. Sincere thanks also go out to Prof. John O’Brien who was a member of my qualifying exam committee and guided me through the screening process in the early part of my graduate studies. I would also like to thank Prof. Eugene Bickers for joining my dissertation committee as an outside member. Special thanks to Dr. Edward Maby, who was kind enough to take me under his wing as a teaching assistant. Due to his faith in me, I never had to worry about financial issues during the school year. I will always remember his funny anecdotes and may take the liberty to borrow some, too. No acknowledgements can be complete without mentioning my colleagues at the optical communications laboratory. OCLAB, as we all call it, became a second home for me during these five years. In fact, I wouldn’t be lying if I said that I spent more time there than at home, something that would never have been possible without the friendly faces that make OCLAB a fun place to be. In particular, I should mention the selfless efforts of Dr. Deniz Gurkan and Dr. John McGeehan iii towards initiating me into the field of experimental fiber optics. I learnt the basics of PPLN waveguides and ‘SOA the great’ from them, two devices which later became the bread and butter of my research. The discussions on the happenings in the world of sports with John were the perfect way to start the day. Special thanks to Bo Zhang, for always being there to listen whether the results we were discussing were ‘rocking’ or ‘shocking’. Bo was an active collaborator in the development of devices models I used often and continue to use. Soon to be Dr. Poorya Saghari deserves special mention too for being a co-conspirator in several adventures during these five years. Our tenures at OCLAB coincided almost exactly and his support through all the highs and lows of graduate school is highly appreciated. Every single member of OCLAB has contributed to my stint here being a memorable one and I will always cherish the fun moments we shared together. My sincere thanks to the electrical engineering staff for taking care of all the paperwork and background protocol that we as graduate students never had to worry about. In particular, I wish to thank Ramona Gordon in EE-electrophysics and Milly Montenegro, Mayumi Thrasher, Gerrielyn Ramos and Diane Demetras in EE- systems for all their help. My close friends and family in the United States have played a special role in ensuring that graduate school never bogged me down and there was always time for fun and entertainment. My cousin, Hiram, his wife Nirmala and their twin sons iv Ayoosh and Rohin who live in Sunnyvale always offered a nice retreat where I could forget about work and let life slow down. Adit and Pavitra, two of my close friends who have guided me through all aspects of life in the US deserve special mention. Adit and I continue to frustrate our respective wives by taking off into heavy technical discussions at the most inopportune moments. None of this would have been possible without the love and support of my wonderful parents and my caring sister. It was my parents who instilled in me a respect for education and tirelessly motivated me through every stage of my academic career. This dissertation is the fruit of their sacrifices. My sister, being elder was primarily responsible for blazing the trail with her own wonderful accomplishments. Thankfully, she was always by my side to guide me through it, too. She has dreamt every dream of mine with me and has contributed in more ways than can be stated to realize them. Last, but not the least, I want to express my deep gratitude to my lovely wife, Dr. Shilpa Sambashivan. Shilpa and I have known each other for more than nine years, and I continue to be in awe of her. Her patience and understanding have no bound. From the undergrad days when she would wake me up before tests to post-marital days when she would stay awake with me while I worked into the wee hours of the morning, Shilpa’s contribution to my life cannot be described in words. Without her, I would not have made it through the ups and downs of graduate life. She has been v the one constant who I could turn to for advice, crib to whenever I was in the mood and share a laugh with when a tight corner was turned. Thanks, Shilpa for being by my side. vi Table of Contents Acknowledgements ii List of Figures viii Abstract xix Chapter 1: Introduction 1 1.1 Optical signal processing 3 1.2 Processing functions performed at a network router 6 1.3 Outline of the dissertation 8 Chapter 2: Nonlinear processes in semiconductor optical amplifiers and periodically poled lithium niobate waveguides 12 2.1 Cross-gain modulation 12 2.2 Cross-phase modulation 15 2.3 Cross-polarization modulation 17 2.4 Four-wave mixing 18 2.5 Second harmonic generation and difference frequency generation 20 Chapter 3: Digital optical modules based on SOAs and PPLN waveguides for network applications 25 3.1 All-optical XNOR gate using simultaneous XGM and FWM in an SOA 25 3.2 All-optical serial half adder using an SOA and a PPLN waveguide in an XOR-less configuration 34 3.3 All-optical hard-limiting using XGM in an SOA for alleviating the ‘near-far’ effect in O-CDMA networks 47 Chapter 4: Deleterious effects in differential mode wavelength converters and their compensation through optical signal processing techniques 58 4.1 Delayed-interference signal converter 58 4.2 Differential cross-phase modulation 60 4.3 Sub-pulses in a DISC 62 4.4 Data-pattern dependence in differential mode wavelength converters 65 4.5 Operational parameters and their interplay in DXPM wavelength converters 78 vii 4.6 Difference between DXPM and DISC configurations with respect to sensitivity to input signal extinction ratio 92 Chapter 5: Design and implementation of a 160 Gb/s optical time- division multiplexing system 95 5.1 Performance of the transmitter subsystem 98 5.2 Performance of the receiver subsystem 103 5.3 Demultiplexing of an 80 Gb/s signal using EAMs 111 5.4 Demultiplexing of a 160 Gb/s signal using EAMs 114 Chapter 6: Phase-reconstructive wavelength conversion of OTDM signals using an SOA MZI to generate high-speed coherent phase-correlated signals 116 6.1 Advanced modulation formats 117 6.2 Generation of high-speed phase-correlated signals 119 6.3 Coherent phase control through DXPM in an SOA-MZI 122 Bibliography 146 Appendix A: MATLAB code for simulating carrier dynamics in semiconductor optical amplifiers 159 viii List of Figures Figure 1-1: Is optics better than electronics? Optical signal processing may become economically more viable than electronic processing beyond a certain bit-rate. 2 Figure 1-2: Processing functions at a router node. The path taken by the packets that will be forwarded to the next node is highlighted in blue. 7 Figure 2-1: Cross gain modulation. An inverted copy of the data on the pump wavelength gets imprinted on the probe wavelength. 13 Figure 2-2: XGM-based wavelength conversion of RZ data. The gain exhibits slow recovery, which can lead to pattern dependence in the converted bits. 14 Figure 2-3: Cross phase modulation. Pump pulses cause refractive index variations in SOA1 which are converted into amplitude modulation by the MZI structure. 16 Figure 2-4: Four wave mixing. Pump and probe waves set up dynamic gain and refractive index gratings leading to new optical products. 18 Figure 2-5: Photograph of a periodically poled lithium niobate waveguide. 21 Figure 2-6: Second-harmonic generation followed by difference-frequency generation in a PPLN waveguide. The output wavelength is a “mirror-image” of the input wavelength relative to the pump wavelength. 21 Figure 2-7: Single-pump operation of a PPLN waveguide. Each input is individually wavelength-converted through the process of SHG:DFG. This switching behavior corresponds to a multi-pole single-throw switch. 22 Figure 2-8: Multi-pump operation of a PPLN waveguide. Each input is wavelength-converted to multiple outputs (governed by the pump wavelengths). This switching behavior corresponds to a multi-pole multi-throw switch. The specific example in the figure refers to a case of two inputs and two pumps. 23 ix Figure 3-1: Truth table of an XNOR gate. The XNOR is equivalent to performing an OR operation on the results obtained from a NOR operation and an AND operation. 27 Figure 3-2: Digital circuit for XNOR gate. Since the NOR and AND operations need to be performed in parallel, simultaneous nonlinear processes need to be employed. Four-wave mixing and cross-gain modulation in an SOA are two such simultaneous processes. 27 Figure 3-3: Optical equivalent circuit for XNOR gate. FWM in the SOA generates the AND output while the NOR is obtained using XGM. These two outputs are combined using a coupler to obtain the XNOR output. 28 Figure 3-4: AND gate performance of FWM in an SOA. The output on the new wavelength is ‘on’ only if both the inputs are ‘on’ simultaneously. 29 Figure 3-5: NOR operation based on XGM in an SOA. Only when both the signals are ‘off’, the corresponding pulse from the low power clock input emerges at the output. 29 Figure 3-6: Signal flow through the XNOR gate. FWM in the SOA generates the AND output while the NOR output is obtained from the XGM process. The two outputs are combined to generate the final XNOR signal. 30 Figure 3-7: Experimental setup for the all-optical XNOR gate. 31 Figure 3-8: (a) Inputs to the SOA. l 1 and l 2 are the signals and l p is the pulse train, (b) FWM spectrum for the SOA, (c) Output of the SOA: NOR output on l p and AND output on l a . 32 Figure 3-9: Bit patterns showing the XNOR gate’s performance. 32 Figure 3-10: Bit-error-rate curves for the XNOR gate. The NOR output suffers a power penalty of 0.5 dB for BER=1e-9, and an additional 1 dB penalty is incurred by the AND output. The final XNOR signal exhibits a power penalty of 2 dB. 33 Figure 3-11: Logic diagram and truth table for a half adder. The Carry output is ‘on’ only when both the inputs are ‘on’ and the Sum output is ‘on’ if and only if one of the two inputs is ‘on’. 36 x Figure 3-12: XOR-less equivalent circuit for the half adder. 37 Figure 3-13: Optical schematic for the half adder. DFG in a PPLN waveguide is used for the AND operation while cross-gain modulation in the SOA simulates the NOT and AND gates operating together to generate the XOR output. 38 Figure 3-14: Signal propagation through the half adder module. 38 Figure 3-15: Experimental setup for the all-optical half adder. 40 Figure 3-16: (a) Output spectrum of PPLN waveguide. Signal on l 2 =1548.53 nm is converted to l c =1551.76 nm only when the signal on l 1 =1550.15 nm is high (logic 1). (b) The converted signal is filtered and amplified to form the Carry output. 42 Figure 3-17: (a) Spectrum of the input to the SOA comprising of pulses on l 1 =1550.15 nm and l 2 =1548.53 nm. A reservoir CW channel, l cw =1539 nm is also coupled in to the SOA. (b) SOA output (Sum) spectrum after filtering. The Sum is comprised of pulses on both l 1 and l 2 , which are filtered together. 44 Figure 3-18: 5 Gb/s RZ bit patterns for the half adder. The Carry output is ‘on’ only when both the inputs are ‘on’. The SOA outputs on l 1 and l 2 are filtered together to obtain the Sum output. 44 Figure 3-19: BER measurements for the half adder, taken using a pre- programmed pattern of 2 7 bits. The Carry output exhibits <1 dB power penalty while the Sum output on a single wavelength shows <2 dB penalty. An excess 1.8 dB penalty is observed for the combined Sum output. 46 Figure 3-20: 2-D (time, wavelength) O-CDMA. 2D OCDMA allows more orthogonal codes for a given number of chip times. 48 Figure 3-21: Operation of a 2-D O-CDMA system. ‘1’ bits are encoded into a sequence of chips with predetermined temporal and spectral location. 50 Figure 3-22: Near-far problem: Interfering users located closer to the receiver than the user of interest can produce enough power in the autocorrelation position to cause ‘0’ bits to be detected as ‘1’s. 51 xi Figure 3-23: Missing Chip Detection: The auto correlation peak is re-spread and then the missing chips are detected using all-optical sampling. The presence of any missing chips indicates a ‘0’ bit. 52 Figure 3-24: Experimental setup. The chips in the autocorrelation peak are spectrally separated and re-spread to specific temporal positions. These positions are sampled by pulses from the mode-locked laser. 53 Figure 3-25: Experimental patterns for missing chip detection technique. Top patterns show the re-spread O-CDMA signal, with and without interference. Bottom patterns show the SOA output (missing chip indicators). 54 Figure 3-26: BER measurement for the worst case, tolerable MAI (6.9 dB interference to signal ratio). 56 Figure 3-27: Comparison of Missing Chip Detection and conventional receiver. MAI tolerance is increased by ~6 dB. 56 Figure 4-1: Structure of the delayed-interference signal converter. 59 Figure 4-2: Operating principle of the DISC. The input signal causes phase variation of the probe. This phase modulated signal is made to interfere with its own delayed copy using the AMZI, generating narrow output pulses and trailing sub-pulses. 59 Figure 4-3: Structure of the differential cross-phase modulation wavelength converter. 61 Figure 4-4: Operating principle of the DXPM wavelength converter. By adjusting the signal splitting ratio S split , the recovery of the phase in the two arms can be made to coincide, minimizing the deleterious sub-pulses. 61 Figure 4-5: (a) Output of the DISC showing small sub-pulses trailing the main pulses. (b) Temporal chirp profile of the wavelength converted output. The main pulses are red-shifted while the sub-pulses are blue-shifted. 63 Figure 4-6: Red-shifted filter detuning to suppress sub-pulses. Red-detuning the output filter leads to Q-factor improvement until the OSNR starts degrading. 64 xii Figure 4-7: Data-pattern dependence due to slow carrier recovery in SOA based wavelength converters. 65 Figure 4-8: Eye-closure penalty due to increasing bit-rate for differential mode wavelength converters. 66 Figure 4-9: Eye-closure penalty in cascades of differential mode wavelength converters. Pattern dependence-induced eye-closure grows rapidly. 67 Figure 4-10: Structure of the delayed-interference signal converter. 68 Figure 4-11: Operation of the DISC assuming only linear pattern dependence exists in the SOA. All pulses induce the same amount of phase- swing and the differential mode completely compensates for linear pattern dependence. 69 Figure 4-12: Operation of the DISC including nonlinear pattern dependence in the SOA. The amount of phase-swing induced by input pulses reduces in a long string of 1’s leading to a reduction in output pulse amplitudes. 70 Figure 4-13: Correspondence between gain suppression and pattern dependence. Output pulses that exhibit lower power correspond to larger gain saturation in the SOA. 71 Figure 4-14: Experimental setup to observe polarization state of DISC’s output for an input (pump) pulse train. As the pump power increases, the amount of gain saturation and polarization rotation increases. 73 Figure 4-15: Gain suppression and polarization rotation as a function of input optical signal power. Pulses that correspond to larger gain suppression undergo greater polarization rotation. 74 Figure 4-16: Experimental setup. The SOA and the 25 ps delay-interferometer form the DISC. The polarization controller and polarizer are added to control the pattern dependence of the output signal. 75 Figure 4-17: Principle of polarimetric pattern dependence reduction. The polarization controller and polarizer placed after the DISC are adjusted such that the pulses with larger amplitude are preferentially attenuated relative to the smaller pulses. 75 Figure 4-18: Reduction of pattern dependence in DISC. 76 xiii Figure 4-19: Bit-patterns and eye diagrams showing control over the pattern dependence. Through appropriate adjustment of the output polarization controller, the pattern dependence can be reduced from 3.3 dB to 0 dB or increased to >7 dB. 77 Figure 4-20: Bit-error-rate measurements showing 2.6 dB power penalty improvement at BER=1e-9. Eye opening is improved by more than 33%. 77 Figure 4-21: Structure of the DXPM wavelength converter and the various operational parameters that impact the device’s performance. 79 Figure 4-22: Ideal probe phase variations induced by a single pump pulse for the DXPM wavelength converter. The slow recovery in the bottom arm (blue) coincides with the recovery in the upper arm (red) leading to a high-quality switching window. 81 Figure 4-23: Deviations from the ideal condition for the DXPM wavelength converter. Relative amplitude changes, horizontal or vertical offsets between the phase variations in the two arms lead to degradation of the output signal. 82 Figure 4-24: Optimizing signal splitting ratio for the DXPM wavelength converter. 82 Figure 4-25: Deleterious effects of non-optimum signal splitting ratio. Less than optimum signal splitting ratio causes delayed-phase overshoots leading to sub-pulses while exceeding the optimum value causes pulse broadening. 83 Figure 4-26: Variation of optimum signal splitting ratio with differential delay. 84 Figure 4-27: Sensitivity to MZI phase-bias in DXPM wavelength converters. 85 Figure 4-28: Deleterious effects of non-optimum phase-bias in MZI. Deviation from optimum leads to a loss of extinction ratio. 86 Figure 4-29: Dependence of the phase of the probe carrier emerging from the two SOAs on the input signal extinction ratio. 88 Figure 4-30: Variation of optimum phase-bias with input signal extinction ratio. As the input signal extinction ratio increases, the optimum phase- bias asymptotically approaches a value close to ‘p’ radians. 89 xiv Figure 4-31: Sensitivity of output signal extinction ratio to MZI phase-bias for different values of input signal extinction ratio. 90 Figure 4-32: Enhancement of the regenerative window for DXPM wavelength converters. Maintaining the optimum phase-bias as the input signal’s extinction ratio changes improves the output extinction ratio by ~5 dB. 91 Figure 4-33: Sensitivity of output signal extinction ratio to MZI phase-bias for delayed-interference signal converters. If the sub-pulses are neglected, the optimum phase-bias remains at ‘p’ independent of the input signal extinction ratio. 93 Figure 4-34: Sensitivity of output signal extinction ratio to MZI phase-bias for delayed-interference signal converters if the sub-pulses are included. The optimum phase-bias moves away from ‘p’ as the input signal extinction ratio increases. 94 Figure 5-1: Block diagram of an optical time-division multiplexing system. 95 Figure 5-2: OTDM transmitter comprising of a short-pulse source, modulator and split-delay-combine multiplexer. 98 Figure 5-3: (a) 10 GHz short-pulse train from a mode-locked laser observed using a 40 GHz detector. (b) Autocorrelation trace of the pulses: pulse-width of 1.85 ps. 101 Figure 5-4: (a) Mode-locked spectrum of the 10 GHz short pulse train. (b) Close-up of the individual modes showing good spectral quality. 102 Figure 5-5: Autocorrelation traces of 40, 80 and 160 Gb/s signals. 103 Figure 5-6: Concept of time-domain demultiplexing of high-speed signals. The demultiplexer creates switching windows with width ~ line- rate bit-slot and base-rate repetition frequency. 104 Figure 5-7: Wavelength conversion spectrum of a 42.8 Gb/s -to- 10.7 Gb/s demultiplexer using a periodically-poled lithium niobate waveguide. 106 Figure 5-8: Eye diagram of the demultiplexed output channel. 106 xv Figure 5-9: Experimental setup for demultiplexing using electro-absorption modulators. A two-stage design is shown where the first stage switches out an intermediate rate channel which is demultiplexed down to base-rate in the second stage. 109 Figure 5-10: Autocorrelation trace of the switching windows in the first stage of the demultiplexer. The EAM generates a 42.944 GHz, 6.1 ps FWHM switching window. 110 Figure 5-11: Autocorrelation trace of the overall switching window of the two- stage demultiplexer. The cascaded EAMs generate a 10.736 GHz, 6.1 ps FWHM switching window. 111 Figure 5-12: Eye diagrams obtained after the first stage of the demultiplexer that performs 85.888 Gb/s -to- 21.472 Gb/s demultiplexing. The EAM is reverse biased at 3 V and driven with a 4 V p-p 21.472 GHz electrical clock. 112 Figure 5-13: Eye diagrams obtained after the second stage of the demultiplexer. The 21.472 Gb/s signals are stepped down to 10.736 Gb/s. The second EAM is reverse biased at 3.2 V and driven with a 5 V p-p 10.736 GHz electrical clock. 113 Figure 5-14: Bit patterns of all eight base-rate channels obtained after the two- stage demultiplexer. The line-rate signal at 85.888 Gb/s is stepped down to 10.736 Gb/s. 113 Figure 5-15: Bit-error-rate measurements of the 10.736 Gb/s channel demultiplexed from an 85.888 Gb/s signal. The best-case channel shows negligible penalty compared to a back-to-back measurement for a base-rate channel. 114 Figure 5-16: Eye diagrams obtained for single-stage demultiplexing of a 171.776 Gb/s signal down to eight 21.472 Gb/s signals. The EAM is reverse biased at 3 V and driven with a 4 V p-p 21.472 GHz electrical clock. The cross-talk observed is due to excessively broad switching windows. 115 Figure 6-1: Advanced modulation formats, their temporal-phase characteristics and their primary advantages. 117 Figure 6-2: Loss of bit-to-bit phase relationship in OTDM signals as observed through spectral instability. 119 xvi Figure 6-3: Multiplexing of OOK signals into a single phase-modulated signal. 122 Figure 6-4: (a) Destructive interference in the SOA-MZI. (b) Constructive interference with output phase ‘0’. (c) Constructive interference with output phase ‘p’. 123 Figure 6-5: Phase properties of the output signal generated through cross-phase modulation. A relative phase difference of ‘p’ exists between the two output carriers corresponding to XPM in the upper and lower arm, no matter how small the actual value of the phase-shift induced by the pump. 124 Figure 6-6: Conversion of 8X10 Gb/s RZ signals into an 80 Gb/s CSRZ signal. 127 Figure 6-7: Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent CSRZ output. 127 Figure 6-8: Spectrum of the 80 Gb/s coherent CSRZ output, obtained through simulations. The original carrier position is shown in blue. Tone spacing of 80 GHz is observed. 128 Figure 6-9: Intensity and phase variations for the 80 Gb/s coherent CSRZ output. Phase alternates between 0 and ‘p’ for adjacent bit-slots. 129 Figure 6-10: Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent PAP-CSRZ output. 130 Figure 6-11: Spectrum of the 80 Gb/s coherent PAP-CSRZ output, obtained through simulations. The original carrier position is shown in blue. Tone spacing of 40 GHz is observed. 130 Figure 6-12: Intensity and phase variations for the 80 Gb/s coherent PAP-CSRZ output. Phase alternates between 0 and ‘p’ for adjacent pairs of bit-slots. 131 Figure 6-13: Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent GAP-CSRZ output. 132 Figure 6-14: Spectrum of the 80 Gb/s coherent GAP-CSRZ output, obtained through simulations. The original carrier position is shown in blue. Tone spacing of 20 GHz is observed with alternate pairs of tones being suppressed. 132 xvii Figure 6-15: Intensity and phase variations for the 80 Gb/s coherent GAP-CSRZ output. Phase alternates between 0 and ‘p’ for adjacent sets of four bit-slots. 133 Figure 6-16: (a) Incoherently multiplexed 80 Gb/s OTDM DPSK signal. Adjacent bits possess random relative phase. (b) The random distribution of the carrier phase in the multiplexed 80 Gb/s data is highlighted using blue colored markers. 134 Figure 6-17: Unsuccessful demodulation of an incoherently multiplexed 80 Gb/s DPSK signal using an 80 GHz delay interferometer. The signals on the destructive and constructive ports do not exhibit well-defined on/off states, leading to eye closure. 135 Figure 6-18: Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent RZ-DPSK output. 136 Figure 6-19: Intensity and phase variations for the 80 Gb/s coherent RZ-DPSK output. Phase changes are determined by the pre-coded OTDM data stream that perturbs the SOA-MZI. The example is for an 8- bit input sequence ‘01001101’. 137 Figure 6-20: Successful demodulation of a coherent 80 Gb/s DPSK signal using an 80 GHz delay interferometer. The signals on the destructive and constructive ports exhibit well-defined on/off states and a clear eye opening is observed after balanced detection. 138 Figure 6-21: Spectrum of the 80 Gb/s coherent RZ-DPSK output, obtained through simulations. The original carrier position is shown in blue. 139 Figure 6-22: (a) Intensity and phase profiles of an 8 bit pattern of a coherent 80 Gb/s RZ-DPSK signal generated using the SOA-MZI scheme. (b) Intensity and phase profiles of the same 8 bits with the injection scheme altered to generate CSRZ-DPSK. Alternate bits exhibit a ‘p’ phase shift relative to the phase profile of the DPSK signal. 139 Figure 6-23: Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent AMI output. 141 Figure 6-24: Intensity and phase variations for the 80 Gb/s coherent AMI output. Phase changes by ‘p’ for every ‘1’ bit. 142 Figure 6-25: Spectrum of the 80 Gb/s coherent AMI output, obtained through simulations. The original carrier position is shown in blue. 142 xviii Figure 6-26: Output pulse-width control enabled through the differential delay in the DXPM process. The example shown here is for an 80 Gb/s RZ-DPSK signal. 143 Figure 6-27: Spectra of 80 Gb/s coherent phase modulated formats generated using the SOA-MZI. The pattern of injection of the low-rate RZ tributaries is used to reconfigure the output format. 144 xix Abstract The past decade has witnessed tremendous growth in telecommunication network traffic. The ever-increasing demand for bandwidth has been tackled primarily through wavelength-division-multiplexing technology. However, with the emergence of multimedia applications, the high-capacity transport capability offered by optical-fiber systems has started to move away from the network core towards the end users. This trend has led to diverse networks with critical interoperability needs. As single channel data rates increase and wavelength channel spacing continues to reduce in order to enable cost-effective, high spectral efficiency links, the work load on the conventional electronic signal processing elements in the network routers is building up. Signal processing in the optical domain can potentially alleviate this bottleneck if the properties unique to the optical domain are leveraged efficiently to assist conventional electronic processing methodologies. Ultra-high speed capability along with the potential for format-transparent and multi-channel operation make optical signal processing an attractive technology poised to make a big impact on future optical networks. At this juncture, exploration of optical signal processing techniques for applications in fiber optic network subsystems is a laudable goal. This dissertation investigates novel optical signal processing techniques through experimental demonstrations, xx identifies drawbacks and limitations of optical processing elements and proposes techniques to minimize the system-level penalties induced by them. The results described include the design and development of all-optical logic modules including an XNOR gate and a serial half adder. A digital module to implement all-optical hard-limiting in optical code-division-multiple-access networks to alleviate the ‘near-far’ effect is also presented. Non-idealities in semiconductor optical amplifier-based differential-mode wavelength converters are analyzed and experimental techniques to compensate for data pattern dependence and deleterious sub-pulses are demonstrated. Additionally, a 160 Gb/s optical time division multiplexing system has been constructed and nonlinear signal processing techniques have been proposed to extend its applicability to the generation of phase- correlated modulation formats that are starting to emerge as important candidates for future high spectral efficiency, robust transmission systems. 1 Chapter 1 Introduction Since its introduction into the realm of telecommunication, fiber optic technology has advanced tremendously and today it forms the backbone of most long distance terrestrial communication links and networks. Efforts are underway to achieve the long sought after goal of bringing ‘fiber to the home’ in order to provide large bandwidth directly to the consumer [91]. The opportunity to exploit the vast bandwidth offered by optical communication has led to extensive research by the industry and academia aimed at enhancing the capabilities of optical fiber as a transmission medium [52]. However, the role of optics in telecommunication networks remains confined under its original banner, “larger bandwidth, longer distance”. Practically all the control and processing functions in today’s networks are implemented through electronics. The optical signal received at a network router is converted into electronic bits, undergoes several processing steps implemented through electronic integrated circuits and is then converted back to optical form before being retransmitted to the next node. This time-consuming and inefficient optical-electronic-optical (OEO) conversion is a significant source of latency in networks. Furthermore, network architectures are developed keeping in view the capabilities/limitations of electronic 2 processing techniques. Several reasons can be cited for this division of roles in current networks: · The electronics industry is significantly more mature than its optical counterpart. · Several networking functions tend to be computation-driven, a field that has been mastered by electronic solutions. · Optical signal processing is in a nascent stage and even simple building blocks can represent a significant research challenge. Unfortunately, as bandwidth-hungry multimedia applications emerge and the consumer demand for speed and security increases, electronic processing techniques may not be able to keep pace with the operating speeds of fiber optic links. As shown in Fig. 1-1, a stage may come where it becomes economically more viable to explore and employ inherently high-speed optical techniques rather than expensive electronic solutions. Processing cost per bit (arb. units) Bit-rate (Gb/s) Electronic Processing Optical Processing Beyond what bit rate will optical processing be justified ? 40/100/160 Gb/s ? Fig. 1-1. Is optics better than electronics? Optical signal processing may become economically more viable than electronic processing beyond a certain bit-rate. 3 Future high-speed optical networks will probably utilize optics and electronics in a complementary fashion, leveraging their individual advantages to produce an efficient control and processing platform. Electronics may still handle computation- intensive tasks while optics may perform simpler “on-the-fly” processing, potentially operating on multiple wavelength channels simultaneously. The result could well be a reconfigurable core network that enables interconnection of a diverse set of local networks, operating on different bit-rates, modulation formats and protocols. 1.1 Optical signal processing The research in optical signal processing techniques follows a three-pronged approach · Identifying unique characteristics of optical domain processing and determining potential applications where the use of optical techniques to assist/replace electronic ones is justifiable. · Design and implementation of novel optical signal processing elements for development of advanced signal generation, processing, and detection subsystems. · Developing an understanding of deleterious effects of optical processing modules and the corresponding system penalties and implementing techniques to prevent or compensate for these effects. 4 As a starting step in identifying potential target areas for optical signal processing applications, an understanding of properties unique to the optical domain is required. Some of these features that are at the core of optical signal processing research are listed below · Ultra-high speed: Optical devices offer nonlinearities with recovery time- scales ranging from a few fs to low 100’s of ps. Techniques to alleviate effects of slow-recovering processes have also been developed. As a result, several processing functions have been demonstrated at bit-rates 320 Gb/s [90, 102], far exceeding those achievable through state-of-the-art electronic processors. · Multi-channel operation: Some optical devices, particularly ones that employ wave-mixing can potentially operate on multiple wavelength channels, simultaneously. Significant cost reduction may be realized if a single optical device can replace a large number of electronic modules operating independently on each channel. This property unique to the optical domain has been used for all-optical multicasting [18] and equalization [23]. · Preservation of optical domain properties: The process of detection converts optical intensity to electrical current and other properties of the optical carrier e.g. phase and polarization are lost. However, these properties add an additional dimension that carries information in the optical domain. Optical processing can be performed while preserving these properties enabling unique functionalities like mid-span spectral inversion [37] to mitigate fiber 5 degradations. Moreover, various fiber impairments can be isolated from each other and monitored [108] if all the properties of the optical signal are preserved. · Format and bit-rate transparency: Since most optical signal processing techniques do not employ bit-rate specific components, they are immune to changes in input signal bit-rates. Moreover, since optical properties e.g. phase can be preserved, certain functions can be implemented in a modulation format-transparent way. · Simultaneous nonlinear processes: Several nonlinear optical devices exhibit simultaneous nonlinear processes which can be exploited to perform more than one processing task on the input signals. This capability has been used to achieve diverse functions like clock-recovery and demultiplexing in a single device [15]. · Functional reconfigurability: Nonlinear optical devices possess the unique flexibility of electronic as well as optical biasing. With the additional degree of freedom offered by tunable optical filters, the processing function performed by a particular device can be dynamically reconfigured simply by changing its optical/electrical operating conditions. For example, reconfigurable optical logic gates based on a single semiconductor optical amplifier whose function can be changed from an XOR to an AND simply by changing the input signal powers and tuning the output filter have been demonstrated [53]. 6 · Functional integration: Unlike electronic integration which aims at squeezing together several components into a functional integrated circuit, optical signal processing may exploit the multitude of functionalities available through a single device. For example, electro-absorption modulators have been used for simultaneous clock recovery, demultiplexing and detection in a single device [38]. These properties in conjunction with attractive features of electronic processing, e.g. automatic regeneration are the key to building a synergistic signal processing platform aimed at developing hybrid subsystems to extract and process multi- dimensional information at ultra-high speed. 1.2 Processing functions performed at a network router As a potential target area, the various functions performed on incoming data packets at each router node within a packet-switched core network can be explored [40, 107]. Some of these functions are depicted in Fig. 1-2. The path of the data packets that are destined to be forwarded to the next node is highlighted in blue. To enhance throughput and reduce latency, the highlighted blocks should ideally not involve OEO conversion, and therefore represent the functions that will benefit greatly from all-optical implementations. Various wavelength channels need to be synchronized so that processing under a universal clock is possible. Based on 7 feedback signals obtained from a set of data-degradation monitors, compensation modules need to be controlled in order to regenerate the data. WDM input Demux S S Synchronization of all l 1 , …, l N Regeneration Monitoring Packet- start detection Header/label recognition Table look-up for switching decision Add/ drop switch Processing node for add/drop Header/label updating Buffer, l-shifter, bit-time compressor/ interleaver Contention detection & resolution decision To optical switch Path of data packets WDM input Demux S S Synchronization of all l 1 , …, l N Regeneration Monitoring Packet- start detection Header/label recognition Table look-up for switching decision Add/ drop switch Processing node for add/drop Header/label updating Buffer, l-shifter, bit-time compressor/ interleaver Contention detection & resolution decision To optical switch Path of data packets Fig. 1-2. Processing functions at a router node. The path taken by the packets that will be forwarded to the next node is highlighted in blue. Some of the traffic may be dropped and routed to the access networks and new packets added to the network core. The remaining packets that need to be forwarded to another node require modification of several fields in their headers (header updating) and finally any contention occurring at the output ports needs to be resolved through buffering, or wavelength conversion of the packets. There have been several demonstrations of all-optical subsystems that perform key processing tasks on data packets [5, 12, 45, 73], some of which [34, 35, 60] were precursors to the research described in this work. Two routing functions that represent broad classes of optical signal processing techniques are header updating and wavelength conversion. The former requires 8 modification of the contents of the optical signal while the latter involves modification of the carrier wavelength without affecting the contents of the signal. The non-idealities in the nonlinear processing techniques that are employed to realize these functions, almost always lead to unwanted effects. For example, header updating techniques typically convert the data to a new wavelength, while wavelength converters usually distort the signal. The successful commercialization of optical processing modules requires research on novel processing methodologies as well as the signal degradation caused by them. Understanding the limitations of such techniques and devising methods to enhance their performance is an essential facet of optical signal processing research. Moreover, optical methods may require re-thinking the problem and re-architecting the solution, rather than mimicking the currently used electronic methodology. 1.3 Outline of the dissertation As part of this work, both carrier-modification and content-modification related signal processing techniques have been investigated. Chapter 2 describes the various nonlinear optical processes that have been used to implement the modules described in this work. These include cross-gain modulation (XGM), cross-phase modulation (XPM), cross-polarization modulation (XpolM) and four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) as well as second harmonic generation (SHG) and difference frequency generation (DFG) in periodically-poled lithium niobate (PPLN) waveguides. 9 The two digital optical logic modules demonstrated as part of this work are described in Chapter 3. One is an all-optical XNOR gate that uses simultaneous XGM and FWM in an SOA and the other is a half-adder that uses an SOA and a PPLN waveguide in a simple XOR-less configuration. Chapter 3 also describes the use of XGM in an SOA to implement all-optical hard-limiting in order to increase the tolerance of optical code division multiple access (O-CDMA) systems to multiple- access interference (MAI), thereby alleviating the penalties due to the ‘near-far’ effect. Chapter 4 is dedicated to an extensive analysis of differential mode (DM) SOA- based wavelength converters that enable high-speed operation by compensating for slow carrier recovery effects. Two popular configurations of such wavelength converters, namely, the delayed-interference signal converter (DISC) and differential cross-phase modulation (DXPM) are analyzed through simulations. A model for the SOAs has also been developed in MATLAB to simulate accurate carrier dynamics. The model is interfaced with a commercial optical systems simulation package, OptSim which provides signal generation and visualization capabilities. The chirp induced on the output signal of DM wavelength converters is analyzed and a filtering technique is proposed to suppress deleterious sub-pulses that exist in the DISC’s output. An approach to reduction of data-pattern dependence in DM wavelength converters based on polarimetric filtering is also experimentally demonstrated for the 10 DISC. In the latter half of the chapter, the effect of various operational parameters of the DXPM configuration is studied through simulations and their impact on system- level performance is quantified. Design rules are proposed for optimizing the output signal quality by taking into account the interplay between the various operational parameters and input signal characteristics. The chapter concludes by pointing out some important differences between the DISC and DXPM configurations. In chapter 5, the design and construction of a 160 Gb/s optical time-division multiplexing (OTDM) system is described. The transmitter built around a 10 GHz short-pulse mode-locked laser and a split-delay-combine passive multiplexer is analyzed using high resolution spectrum analyzers and autocorrelators. A PPLN waveguide based demultiplexer for 40-to-10 Gb/s demultiplexing is demonstrated. For demultiplexing an 80 Gb/s signal down to its 10 Gb/s tributaries, a two-stage electro-absorption modulator (EAM)-based approach is implemented. Tradeoffs between switching window width and switching window extinction ratio that determine the optimum electrical drive conditions for the EAMs in order to perform demultiplexing of a 160 Gb/s signal are described. Conventional OTDM techniques cannot be used to generate high-speed phase- correlated signals due to the loss of bit-to-bit phase relationships in passive multiplexing. This problem is tackled in chapter 6 where a technique based on an SOA-based Mach Zehnder interferometer (MZI) is proposed to enable the generation 11 of 80 Gb/s phase-correlated signals, e.g. differential phase-shift keying (DPSK), carrier-suppressed return to zero (CSRZ) and its variants and alternate mark inversion (AMI). Simulations are performed to demonstrate the module’s functionalities and the generation of coherent 80 Gb/s signals is verified through unique format-specific spectral properties and intensity-phase temporal profiles. 12 Chapter 2 Nonlinear processes in semiconductor optical amplifiers and periodically-poled lithium niobate waveguides Semiconductor optical amplifiers (SOAs) have emerged as popular candidates for use as nonlinear elements in optical signal processing techniques [22, 28, 39, 59, 73]. They provide high nonlinearity in a small footprint, a key feature that enables nonlinear processing with fairly low optical powers. SOAs can also be integrated with various waveguide structures and are therefore well suited to stable interferometric processing techniques. Various nonlinearities in SOAs including cross-gain modulation, cross-phase modulation, cross-polarization modulation and four-wave mixing have been exploited for implementing all-optical processing modules. 2.1 Cross-gain modulation The gain of an SOA depends on the total number of carriers available to produce stimulated photons. Therefore, any variation in the carrier density of the semiconductor medium directly alters the gain seen by an optical wave propagating through the SOA [25]. If a high power modulated signal (called “pump”) and a low power CW beam (called “probe”) are coupled into an SOA, the modulation of the pump can be transferred to the probe, as shown in Fig. 2-1. 13 Gain Output power SOA gain saturates at high output powers SOA High power signal (pump) Low power CW (probe) Filter Inverted output on probe wavelength Fig. 2-1. Cross gain modulation. An inverted copy of the data on the pump wavelength gets imprinted on the probe wavelength. A high power pump pulse depletes the carriers in the SOA, leading to a suppression of the gain seen by the probe light. Thus the output power in the probe beam is reduced. When the pump signal goes low, the carriers in the SOA recover and the gain for the probe light returns to a high value, thereby increasing the output probe power. Thus an inverted copy of the pump signal gets imprinted on the probe wavelength. This process of transfer of modulated information via gain variations in of the SOA is called cross gain modulation (XGM) [74]. XGM has been utilized for various applications including wavelength conversion [25], optical logic [41], and clock recovery [2]. XGM has been studied extensively and various SOA models [19, 20, 92] have been developed to enable simulation of this phenomenon. The bandwidth of the XGM process is limited to low 10s of GHz due to the slow carrier recovery time [32]. This limitation presents itself as pattern dependence in the output signal. Fig. 2-2 shows experimental eye diagrams of RZ bits being wavelength converted via XGM. 14 Input XGM output Fig. 2-2. XGM-based wavelength conversion of RZ data. The gain exhibits slow recovery, which can lead to pattern dependence in the converted bits. A pump pulse that enters the SOA after a long string of 0s sees its unsaturated gain and induces greater XGM than a pulse that follows another pulse, if the gain doesn’t recover to its unsaturated value between the two pulses. As a result the high level of the output shows large variations with long tails for the inverted pulses. Such a signal suffers from eye-closure due to unequal pulse amplitudes. The recovery time can be reduced by operating the SOA in deep saturation (driving it with a higher bias current and injecting a higher CW probe power). Sometimes a third CW input, called a reservoir channel or assist light is also injected to reduce the recovery time [94]. Gain saturation is also accompanied by a shift of the SOA gain spectrum towards higher wavelengths. As a result wavelength up-conversion is not as efficient as down-conversion. The gain modulation also induces chirp on the output wavelength converted signal since the carrier density also determines the refractive index of the semiconductor medium. For the conventional inverting operation, a red-shift is observed at the falling edge of the output, while a blue chirp is present on the rising edge. This temporal relation between power and frequency- 15 shift is referred to as positive chirp and leads to quicker pulse broadening due to dispersion when the signal is transmitted over single mode fiber (positive dispersion). On the other hand, the chirping that leads to broadening of the probe spectrum can itself be utilized for wavelength conversion by selectively filtering the red-shifted part of the spectrum [10]. Since the red-shift is induced by fast carrier depletion and not the slow carrier recovery, it enables high speed wavelength conversion. Under special conditions XGM based wavelength conversion has been demonstrated up to 100 Gb/s [27]. Recent results on filtering-assisted XGM have enabled wavelength conversion up to 320 Gb/s [90]. 2.2 Cross-phase modulation The modulation of the carrier density in an SOA also leads to a variation of the refractive index of the material. This refractive index modulation imposes a phase variation on the optical waves propagating through the SOA. This process called cross-phase modulation (XPM) can be converted into amplitude modulation using interferometric configurations [25, 43]. The simplest configuration utilizes XPM induced in one arm of a Mach Zehnder Interferometer (MZI) with SOAs as shown in Fig. 2-3. The light from a CW laser (probe) is split equally between the two SOAs of the MZI while the high power input signal (pump) is coupled into only one of the SOAs (referred to as the common SOA). By adjusting the phase shifter in the lower arm to introduce a phase shift of p radians, the CW probe components in the two arms can be made to interfere destructively in the absence of a pump pulse. 16 SOA 2 SOA 1 Filter Signal (pump) CW (probe) Output Phase - Phase-shifter - Fig. 2-3. Cross phase modulation. Pump pulses cause refractive index variations in SOA1 which are converted into amplitude modulation by the MZI structure. However whenever a pump pulse enters the common SOA, it cause depletion of the carrier density, which leads to a modulation of the refractive index. The refractive index variation leads to a modulation of the phase of the CW probe propagating through the common SOA. Thus the destructive interference condition is no longer satisfied at the MZI output and a pulse appears on the probe wavelength, which can be separated via optical filtering. The rise time of the output pulse is determined by the rise time of the input pulse but slow carrier recovery still leads to slow fall times. The SOA-MZI can be driven in a differential push-pull configuration to eliminate the effects of the slow carrier recovery [88]. These switches, called differential mode switches, are discussed further in chapter 4. The MZI configuration also enables inverted wavelength conversion if the phase- shifter is set to introduce no additional phase shift. In such a situation, the CW probe components interfere constructively in the absence of a pump pulse and a phase variation causes a drop in the probe power at the MZI output. XPM-based 17 wavelength converters have been demonstrated at very high bit-rates (up to 160 Gb/s). Since the process relies on interferometric properties it is possible to obtain high output extinction ratios by minimizing the power in the output 0s through destructive interference. Equally efficient up and down conversion can be realized since the refractive index variation affects all wavelengths equally, as long as the probe power doesn’t contribute significantly to the SOA’s saturation. The XPM wavelength converter, however, has limited input signal dynamic range due to its sensitivity to its operating conditions. The XPM configuration has been exploited for the development of several signal processing modules including optical regenerators that have enabled transmission over thousands of km of fiber without OEO conversion. 2.3 Cross-polarization modulation SOAs typically exhibit asymmetry in their structure that leads to different confinement factors, effective guide refractive indices and carrier distributions along the TE and TM orientations. Thus, there exists a small amount of birefringence in the SOA. Additional birefringence can be introduced in the SOA by injecting a high power pump pulse. Thus the components of the probe along the TE and TM orientations experience different phase shifts. This difference in the phases of the TE and TM mode leads to a polarization rotation of the probe light passing through the SOA [81]. This process is called cross-polarization modulation (XpolM). A polarizer placed after the filter at the output can be used to convert this polarization 18 rotation into amplitude modulation. Inverted as well as non-inverted wavelength conversion can be achieved. Since the inverted mode works in conjunction with XGM it leads to higher extinction ratio, unlike the non-inverted mode that operates against XGM. XpolM has become popular recently because it enables processing based on refractive index changes without the need for an interferometric configuration. Differential XpolM has also been demonstrated [105] as a method to enhance the operational bandwidth of the technique. Moreover, since refractive index changes occur even for wavelengths which lie in the transparency window of the SOA, wavelength conversion between the 1550 and 1310 nm bands can be achieved [95]. 2.4 Four-wave mixing When two high power signals are injected into an SOA, the carrier population oscillates at the beat frequency of the two signals if it happens to be small enough to be within the SOA modulation bandwidth. l l l l CW (probe) l l l l 1 l l l l 2 l l l l b w w w w b = 2 w w w w 2 - w w w w 1 w w w w a = 2 w w w w 1 - w w w w 2 l l l l a Signal (pump) Fig. 2-4. Four wave mixing. Pump and probe waves set up dynamic gain and refractive index gratings leading to new optical products. 19 This sets up a dynamic gain and refractive index grating in the medium from which the input waves can diffract to produce completely new optical products. This process of wavelength conversion is called four-wave mixing (FWM) [111] and is depicted in Fig. 2-4. Carrier population oscillation is the primary phenomenon implicated in the generation of the new wavelength products when the detuning between the mixing waves is small (~10s of GHz). However, other processes e.g. spectral hole burning and carrier heating [87] have also been cited as contributing factors. Spectral hole burning relates to the modulation of the occupation probability of the carriers within a band, leading to fast gain modulation. Carrier heating induces gain modulation due to the variation in temperature that results from free-carrier absorption adding carriers to higher energy levels, while stimulated emission subtracts carriers from cooler low-energy levels. Spectral hole burning and carrier heating have characteristic times of the order of a few hundred femtoseconds. FWM is an ultra-high speed process since it relies on the beating of optical waves. Also, the efficiency of the conversion goes down as the wavelength spacing between the input signals increases. FWM has been used in several applications including wavelength conversion [46], demultiplexing [96], and multicasting [21]. Since it is a phase preserving process it is also applicable to phase-based formats like differential phase shift keying (DPSK) [24]. 20 2.5 Second harmonic generation and difference frequency generation Parametric wavelength conversion in periodically-poled lithium niobate waveguides has been used extensively for developing optical frequency mixers. Ultrafast, highly efficient all-optical gated mixing [69], nearly arbitrary wavelength conversion [11], and spectral inversion for dispersion compensation [37] using such mixers have been demonstrated by several research groups during the last decade. Applications of nonlinear mixing go beyond simple wavelength conversion and several bit-level digital signal processing modules have been investigated. Nonlinear mixing satisfies the major criteria that justify the development of optical modules that can assist/replace electronic subsystems. These properties include high-speed operation (scalable beyond 100 Gb/s), parallel operation on multiple wavelength channels and preservation of information (e.g., phase) carried in the optical domain, usually lost in optical–electronic conversion. Thus, nonlinear mixing is a suitable platform for development of all-optical digital signal processing techniques. Second harmonic generation (SHG) followed by difference frequency generation (DFG) in periodically poled lithium niobate (PPLN) waveguides has been used for wavelength conversion in several applications [47]. A photograph of the device is shown in Fig. 2-5 and the wavelength conversion process is explained in Fig. 2-6. The device employs cascaded (2) : (2) processes and creates a new wavelength at l out 2l pump - l in . 21 Fig. 2-5. A connectorized periodically poled lithium niobate waveguide. First, the pump signal undergoes second harmonic generation, resulting in a component at ~l pump /2. This signal then mixes with the signal on the other input wavelength (l in ) resulting in a converted signal at l out . l (nm) pump in c c c c (2) ~ pump /2 SHG out c c c c (2) mixing (DFG) Fig. 2-6. Second-harmonic generation followed by difference-frequency generation in a PPLN waveguide. The output wavelength is a “mirror-image” of the input wavelength relative to the pump wavelength. From a system designer’s perspective, a single-pump PPLN waveguide can operate as an optically controlled multi-pole single-throw switch. This means that there can be several inputs, which are individually transferred to their corresponding outputs, 22 when the optical control signal (the PPLN waveguide’s pump) turns on, as shown in Fig. 2-7. Inasmuch as the inputs and outputs are identified by their wavelengths, PPLN waveguides can operate on multiple WDM channels simultaneously. l l l l (nm) c c c c (2) SHG c c c c (2) mixing l l l l out4 l l l l out1 l l l l s1 l l l l s4 l l l l pump ~l ~l ~l ~l pump /2 l l l l out(n) ~ 2 X l l l l pump – l l l l s(n) l l l l s4 l l l l s2 l l l l s3 l l l l s1 Input 1 Input 2 Input 3 Input 4 l l l l out4 l l l l out2 l l l l out3 l l l l out1 Optical Control PPLN Waveguide Output 1 Output 2 Output 3 Output 4 l l l l pump l l l l outn ~ 2 X l l l l pump - l l l l sn Fig. 2-7. Single-pump operation of a PPLN waveguide. Each input is individually wavelength-converted through the process of SHG:DFG. This switching behavior corresponds to a multi-pole single-throw switch. A PPLN waveguide may be designed for operation with multiple pumps. In such a device, several inputs can be directed to a set of outputs (determined by the set of 23 pump wavelengths), each individually controlled by the different control signals (pumps). This switching action corresponds to a multi-pole multi-throw switch, as shown in Fig. 2-8. It is possible to have multiple outputs emerge at the same wavelength if the input wavelengths are chosen appropriately. l l l l (nm) c c c c (2) SHG c c c c (2) mixing l l l l out22 l l l l out21 l l l l s1 l l l l s2 l l l l pump1 ~l ~l ~l ~l pump2 /2 l l l l pump2 ~l ~l ~l ~l pump1 /2 l l l l out12 l l l l out11 l l l l out(mn) ~ 2 X l l l l pump(m) – l l l l s(n) l l l l s2 l l l l s2 l l l l s1 l l l l s1 Input 1 Input 2 l l l l out22 l l l l out12 l l l l out21 l l l l out11 Optical Control-1 PPLN Waveguide Output 1 Output 2 Output 3 Output 4 l l l l pump1 l l l l out(mn) ~ 2 X l l l l pump(m) – l l l l s(n) Optical Control-2 l l l l pump2 Fig. 2-8. Multi-pump operation of a PPLN waveguide. Each input is wavelength- converted to multiple outputs (governed by the pump wavelengths). This switching behavior corresponds to a multi-pole multi-throw switch. The specific example in the figure refers to a case of two inputs and two pumps. 24 Optical switching in a PPLN waveguide has several attractive properties, including 1) quantum-limited spontaneous emission noise; 2) no added chirp; 3) wide operational bandwidth (> 70 nm); 4) ultrahigh-speed operation (> 1 THz); 5) similar up- and down-conversion efficiencies; and 6) multi-channel operation with minimal crosstalk. The nonlinear processes in the PPLN waveguide lead to phase conjugation [17] of the input signal. This spectral inversion with respect to the PPLN waveguide’s pump wavelength can prove useful for several applications including chromatic dispersion compensation. Moreover, because the wavelength conversion process preserves the phase relationship between data bits, it can be used for phase- coded signals, e.g., differential phase-shift keying (DPSK) and quadrature phase shift keying (QPSK). 25 Chapter 3 Digital optical modules based on SOAs and PPLN waveguides for network applications 3.1 All-optical XNOR gate using simultaneous XGM and FWM in an SOA In order to enable optical logic subsystems that can assist/replace their electronic counterparts in data routers, and thereby avoid latency due to OEO conversions, basic optical logic gates may be required. All-optical versions of various logic gates have been demonstrated. All-optical exclusive-OR gates, commonly called the XOR gates are of particular interest. XOR gates can enable a diverse set of processing functions, including (i) comparison of data patterns for address recognition and subsequent packet switching [30], (ii) basic or complex computing as a component of digital-addition modules, (iii) optical generation of pseudorandom patterns, (iv) data encryption/decryption, and (v) parity checking [72]. A comprehensive review of various proposals for optical XOR gates is provided in [114]. However, the complementary function of the XOR, the XNOR, has not been investigated extensively. Since the XOR and XNOR provide logically inverted outputs, one may be able to replace the other in specific applications. For example, a pattern-matching module that uses an XOR gate will generate output pulses for all the bits that don’t match, while one operating on an XNOR gate will produce output pulses for all the 26 bits that do. Thus a threshold detector looking for an output pulse signals a pattern- mismatch using an XOR gate, but the same functionality can be obtained by using an XNOR gate with a threshold detector looking for a missing pulse at the output. It may be possible to design all-optical XNOR gates that are simpler and more stable than XOR implementations. Earlier proposals for all-optical XNOR gates include (i) using semiconductor micro- ring resonators [100], and using a semiconductor optical amplifier (SOA)-based Mach-Zehnder interferometer [49]. However, these implementations require two nonlinear optical elements and integration of the devices. In this section a novel design for an all-optical XNOR gate utilizing simultaneous four-wave mixing (FWM) and cross-gain modulation (XGM) in a single SOA is discussed. The FWM performs the AND operation and XGM implements a NOR gate. The AND and NOR outputs are then combined to produce the XNOR output. Error free operation is observed for 5 Gb/s RZ data with <2 dB power penalty. The module may also be used as an all-optical serial bit-wise half adder since it generates the AND and XNOR outputs simultaneously which correspond to the CARRY and inverted-SUM outputs of a half adder. 3.1.1 Operation of the XNOR gate As shown in Fig. 3-1, an XNOR gate operates on two serial data streams (A and B). The output is ‘on’ if both the input bits are ‘on’ or if both the input bits are ‘off’. 27 The truth table also shows that the XNOR logic corresponds to an OR operation between the AND and NOR outputs. 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 AND NOR B A XNOR A B A B Conventional representation Truth Table XNOR 1 0 0 1 Fig. 3-1. Truth table of an XNOR gate. The XNOR is equivalent to performing an OR operation on the results obtained from a NOR operation and an AND operation. Therefore, if we can perform the AND and NOR operations through optical nonlinear elements, the two outputs can be combined using a coupler acting as an OR gate to obtain the XNOR function. The required optical circuit is shown in Fig. 3-2. A B NOR AND XNOR A+B (A+B)+(A.B) A B • Parallel gates • Simultaneous nonlinear optical processes • FWM and XGM in an SOA OR A.B Fig. 3-2. Digital circuit for XNOR gate. Since the NOR and AND operations need to be performed in parallel, simultaneous nonlinear processes need to be employed. Four-wave mixing and cross-gain modulation in an SOA are two such simultaneous processes. Since the circuit requires two optical gates (NOR and AND) operating in parallel, we need to utilize nonlinearities that occur simultaneously, in the same device in order to keep the component count low. Two such nonlinearities are four-wave mixing 28 and cross-gain modulation in an SOA. The FWM process is equivalent to the logic AND operation between the two input signals while the XGM process can be used to implement the NOR logic. A coupler acting as the OR gate can be used to combine NOR and AND outputs to generate the XNOR output. This is shown schematically in Fig. 3-3. A B NOR AND XNOR A.B A+B XGM FWM Coupler OR Fig. 3-3. Optical equivalent circuit for XNOR gate. FWM in the SOA generates the AND output while the NOR is obtained using XGM. These two outputs are combined using a coupler to obtain the XNOR output. The two input signals (at l 1 and l 2 ) between which the XNOR operation is to be performed are synchronized, amplified and injected into the SOA. A lower power pulse train (probe signal) at l p , synchronized with the signal pulses is also injected. The two high power signals at l 1 and l 2 undergo FWM, which results in products at l a and l b . The product signals have a pulse only when pulses are present on both the input signals simultaneously. This corresponds to the AND operation. A sample bit- stream showing this behavior is shown in Fig. 3-4. On the other hand each of the amplified input signals acts as a pump for the XGM process. Whenever a pulse is present on either of the input signals, it saturates the SOA’s gain and as a result the corresponding pulse on l p sees a reduced gain while traveling through the SOA. 29 Only those pulses on l p that have no corresponding pulses on l 1 or l 2 emerge at the output. SOA Signal 1 on l l l l 1 Signal 2 on l l l l 2 OUTPUT (S1 . S2) on l l l l a filter l l l l a 1 0 1 1 0 1 0 1 1 0 t 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 t t 0 1 1 0 0 1 0 0 1 1 t 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 t 0 0 1 0 0 1 0 0 1 0 t 0 1 0 1 0 0 1 t 0 0 1 0 0 1 0 0 1 0 t Fig. 3-4. AND gate performance of FWM in an SOA. The output on the new wavelength is ‘on’ only if both the inputs are ‘on’ simultaneously. This is equivalent to a NOR operation between the input signals. Fig. 3-5 shows this process for a short bit stream. SOA Clock on l l l l p 0 0 0 0 1 0 1 0 0 0 t 0 0 0 0 1 0 1 0 0 0 t t 1 0 1 1 0 1 0 1 1 0 t 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 t t 0 1 1 0 0 1 0 0 1 1 t 0 1 1 0 0 1 0 0 1 1 t t t Signal 1 on l l l l 1 Signal 2 on l l l l 2 Output on l l l l p S1 + S2 Fig. 3-5. NOR operation based on XGM in an SOA. Only when both the signals are ‘off’, the corresponding pulse from the low power clock input emerges at the output. 30 The NOR output on l p and AND output on l a are individually filtered using optical band pass filters with 0.6 nm bandwidth. Both the outputs are then amplified to equal power levels and recombined using a coupler to produce the XNOR output. The overall process is depicted in Fig. 3-6. S 1 S 2 SOA } Inputs Output AND NOR XGM FWM } XNOR Clock Fig. 3-6. Signal flow through the XNOR gate. FWM in the SOA generates the AND output while the NOR output is obtained from the XGM process. The two outputs are combined to generate the final XNOR signal. Even though the XNOR output is composed of bits on two different wavelengths, this is not a significant problem since many applications of an all-optical XNOR gate may relate to a processing operation that results in a switching-decision being made after local detection of the XNOR output. If the XNOR output needs to be transmitted over fiber, another wavelength conversion stage can be added to convert all the output pulses to the same wavelength. 3.1.2 Experimental results and discussion The experimental setup is shown in Fig. 3-7. Two lasers at ~1550nm and ~1549nm respectively, are modulated with 5 Gb/s RZ data to generate the inputs to the XNOR 31 gate. The two signals are amplified and injected into the SOA as pump signals. A lower power probe signal at ~1546nm which is modulated by a 5 GHz clock to generate a pulse stream is also coupled into the SOA. The pulses on all three wavelengths are synchronized in time using tunable delay lines before entering the SOA. SOA MOD l l l l 1 1549.04 nm l l l l 2 1550.08 nm 5 Gb/s RZ MOD SOA bias = 165 mA, Gain = 24 dB, P sat = 7 dBm Coupler Coupler MOD l l l l p 1545.98 nm 5 Gb/s Clock Coupler Coupler Filter l a =1548.04 nm Filter l p =1545.98 nm XNOR Fig. 3-7. Experimental setup for the all-optical XNOR gate. A commercial SOA biased at 165mA is used. The P sat for the SOA is 7 dBm. The spectrum of the SOA inputs is shown in Fig 3-8(a). The two pumps undergo FWM in the SOA giving rise to two products at ~1548nm and ~1551nm. The spectrum for this interaction is shown in Fig. 3-8(b). The SOA output spectrum is shown in Fig. 3-8(c). The AND output at ~1548nm and NOR output at ~1546nm are filtered separately. As is clear from the spectrum, the AND output has lesser power compared to the NOR output due to low FWM efficiency. 32 S 1 S 2 SOA } Clock Power (5 dB/div) Wavelength (2.5 nm/div) Wavelength (2.5 nm/div) Wavelength (0.5 nm/div) (a) SOA inputs (b) SOA FWM (c) AND & NOR outputs l l l l p -2 dBm l l l la -24 dBm l l l l 1 & l l l l 2 2 dBm l l l l p (NOR) -4 dBm l l l lb -28 dBm l l l l 1 & l l l l 2 -2 dBm l l l l a (AND) -24 dBm l l l l 1 =1549.04nm, l l l l 2 =1550.08nm, l l l l p =1545.98nm, l l l l a =1548.04nm, l l l l b =1551.12nm Fig. 3-8. (a) Inputs to the SOA. l 1 and l 2 are the signals and l p is the pulse train, (b) FWM spectrum for the SOA, (c) Output of the SOA: NOR output on l p and AND output on l a Therefore, the AND output needs to be amplified before being re-combined with the NOR output to provide the final XNOR output. Power levels of all the inputs are adjusted using EDFAs and attenuators to optimize the performance of the module. AND (l l l la) Signal 2 (l l l l2) XNOR (l l l la & l l l lp) NOR (l l l lp) Signal 1 (l l l l1) 500 ps/div 5 0 0 m m m m W /d iv 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 Fig. 3-9. Bit patterns showing the XNOR gate’s performance. 33 A sequence of bits demonstrating the XNOR function is shown in Fig. 3-9. The AND output is ‘on’ only when both the inputs are ‘on’, while the NOR output is ‘on’ only when both the inputs are ‘off’. These two outputs are combined to provide the XNOR output. Error free operation was achieved for 2 7 bits at 5 Gb/s. BER curves obtained for the various outputs (Fig. 3-10) show less than 2 dB power-penalty at 1e- 9 bit error rate. Eye diagrams for the individual outputs and the combined XNOR output are also shown in Fig. 3-10. 2 3 4 5 6 7 8 9 10 -17.5 -17 -16.5 -16 -15.5 -15 -14.5 -14 Received Optical Power (dBm) DATA XNOR NOR AND DATA XNOR NOR AND Fig. 3-10. Bit-error-rate curves for the XNOR gate. The NOR output suffers a power penalty of 0.5 dB for BER=1e-9, and an additional 1 dB penalty is incurred by the AND output. The final XNOR signal exhibits a power penalty of 2 dB. Since FWM is a near-instantaneous process, the speed of this module is limited by the slow XGM process. The speed of the XGM process is determined by the gain recovery time in the SOA. Carriers in the SOA recover on a finite time-scale, which typically ranges between a few 10s to low 100s of ps. Several operational parameters can be adjusted to reduce the carrier recovery time and increase the 34 modulation bandwidth of the SOA. These include increasing the bias-current, increasing the optical powers used in the SOA and using assist light in the form of a CW reservoir channel coupled into the SOA. The net result of all these techniques is to keep the SOA in deep saturation. However, the higher the saturation levels of the SOA, the less efficient is the XGM process. As a result a balance has to be struck between XGM efficiency and modulation bandwidth by fine-tuning the operational parameters. It is worth mentioning that since the module provides an XNOR output and an AND output (at the FWM products) it behaves like an all-optical half adder where the AND output represents the CARRY signal and the XNOR output represents an inverted SUM signal. 3.2 All-optical serial half adder using an SOA and a PPLN waveguide in an XOR-less configuration There are many routing functions, whose realization in the optical domain may benefit from the development of optical half/full adders. One such function is “checksum verification/calculation”, performed by a router on incoming packets to ensure data integrity. For typical IP packets, the checksum is a 16-bit field that contains the one’s complement of the one’s complement sum of all the 16-bit words that make up the packet [83]. As a result, addition of all the 16-bit words including the checksum results in a 0. A router performs this addition on each incoming 35 packet (checksum verification). If the result of the addition is a non-zero number, the packet is dropped since the data has been corrupted. If an incoming packet passes the checksum test, other processing operations can proceed which may involve modification of the fields in the packet’s header. For example, the time-to-live field is decremented by 1 if the packet is being forwarded to another router node. Since the bits in the packet are changed, a new checksum is computed (checksum calculation) that maintains the zero-sum relationship between all the 16-bit words. The next router can perform the same test again to verify error-free transmission from the previous node. To address the need for all-optical adders, various techniques suitable for conventional fiber optic communication wavelengths have been proposed. These include: (i) using two semiconductor laser amplifiers in a loop mirror (SLALOMs), one configured as an AND gate and the other as an XOR gate [44], (ii) using three terahertz optical asymmetric demultiplexers (TOADs), one acting as an AND gate and the other two configured to provide the XOR output [71], (iii) using four semiconductor optical amplifiers (SOAs), two of them integrated into a Mach- Zehnder interferometer AND gate and the other two generating the XOR output [42]. The first two techniques employ fiber loop based interferometers and may suffer from instability while the third technique uses four active elements and requires integration. 36 In this section, an all-optical half adder that requires only two non-linear optical elements and does not rely on interferometric techniques is described. Difference frequency generation in a PPLN waveguide is used to perform the AND operation which corresponds to the Carry output and cross-gain modulation in an SOA is utilized to imitate an XOR gate that generates the Sum output. Power penalties of <1 dB for the Carry output and <2 dB for the optimally filtered Sum output are observed. 3.2.1 Design and operation of the half adder A half adder is a digital logic module that has two inputs and two outputs. The inputs, A and B are serial data streams that are to be added. Any two corresponding bits result in two output bits – the Carry bit that is ‘on’ only when both the inputs are ‘on’, and the Sum bit that is ‘on’ if and only if one of the two inputs is ‘on’. The Carry bit corresponds to the logic AND function, while the SUM bit corresponds to the XOR function, as shown in Fig. 3-11. 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 CARRY SUM B A XOR AND A.B A B CARRY SUM A B Conventional representation Truth Table Fig. 3-11. Logic diagram and truth table for a half adder. The Carry output is ‘on’ only when both the inputs are ‘on’ and the Sum output is ‘on’ if and only if one of the two inputs is ‘on’. 37 Typically, implementing an XOR gate in the optical domain requires more than one nonlinear element. Instead, a well-known equivalent schematic (shown in Fig. 3-12) that uses elementary gates to achieve the XOR functionality may be employed. NOT (A.B).(A+B) A B A B OR AND AND CARRY (AND) SUM (XOR) A.B A+B A.B Fig. 3-12. XOR-less equivalent circuit for the half adder. A first glance at this schematic may give the impression that it is a complicated design. However, as shown in Fig. 3-13, the optical equivalent circuit uses only two nonlinear optical elements and is easy to construct. This design does not require interferometric devices and therefore, sensitivity to input signal amplitude fluctuations may be reduced. The PPLN waveguide acts as the AND gate, the coupler mimics the OR gate, while XGM in the SOA is used to generate the XOR output by suppressing the coupler’s output passing through the SOA whenever the PPLN waveguide’s output is high. 38 A B CARRY (AND) SUM (XOR) A.B A+B Coupler PPLN waveguide SOA Fig. 3-13. Optical schematic for the half adder. DFG in a PPLN waveguide is used for the AND operation while cross-gain modulation in the SOA simulates the NOT and AND gates operating together to generate the XOR output. Signal propagation through the module is depicted in Fig. 3-14. The two incoming data streams which are bit-synchronized enter the AND gate (PPLN waveguide) which generates the Carry signal through the wave mixing process of SHG:DFG. PPLN A B CARRY SUM SOA } High power signal Low power signal Inputs Outputs Synchronized 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 SUM 1 SUM 2 Fig. 3-14. Signal propagation through the half adder module. The PPLN waveguide acts as a wavelength conversion device that maps incoming wavelengths onto their mirror images with respect to a pump wavelength. One of the signal wavelengths (l 1 ) coincides with the PPLN waveguide’s pump wavelength. 39 The device employs a (2) : (2) nonlinear process to shift the data on the other signal wavelength (l 2 ) to a new wavelength, l c 2*l 1 - l 2 . Since the conversion occurs only when the pump power is high (i.e. when the data on the pump wavelength is ‘1’), the data on the converted wavelength, l c is the logic AND of the incoming data on l 1 and l 2 . SHG:DFG is an ultra-high speed process with a wide operational bandwidth of ~ 70 nm. Moreover, the PPLN waveguide has negligible spontaneous emission noise and no intrinsic chirp. The incoming data streams are also coupled into the SOA as low power probe signals. The Carry output from the previous stage is amplified and injected into the SOA as a higher power pump signal. In XGM [25], a high power signal depletes the carriers in the SOA causing an inverse modulation of the gain. Therefore, whenever the Carry signal is ‘on’ it reduces the SOA’s gain causing the other signals propagating through the SOA at that time to be suppressed. As a result, the SOA output is ‘off’ whenever the Carry is ‘on’. However, if the Carry signal is ‘off’, the output of the coupler (OR gate) propagates through the SOA, gets amplified and emerges at its output port. This is equivalent to inverting the Carry output and performing an AND operation between the OR gate output and the inverted Carry output. Therefore, input bit combinations of 00, 01 and 10 will result in 0, 1 and 1 outputs respectively, while a 11 input will be converted to a 0 at the SOA output. This input-output relationship corresponds to an XOR operation and generates the Sum output for the half adder. The speed of the XGM process is limited by the SOA 40 gain recovery time. The gain recovery time depends on several operational parameters, which govern the level of saturation in the SOA. It can be reduced (to enable higher bit rate operation) by increasing the SOA bias current and the optical power of the signals. The wavelengths of the signals also affect the gain recovery time since wavelengths closer to the gain peak of the SOA will saturate it more. Careful optimization of the bias current, pump and probe powers is required in order to maintain a satisfactory extinction ratio while reducing the gain recovery time. 3.2.2 Experimental results and discussion The optical data streams are obtained by externally modulating two DFB lasers (1550.15 nm & 1548.53 nm) with a 5 Gb/s RZ pattern. The two streams are randomly delayed with respect to each other and bit-synchronized before entering the half adder module in order to allow for all possible input bit pairs (00, 01, 10 & 11). Bit-synchronization is achieved by using a tunable optical delay line for demonstration purposes. CARRY PPLN waveguide SUM SOA Isolator Circulator 2 1 3 MOD MOD Filter Filter Filter Filter Filter 50:50 Coupler Attenuator Optical delay l 1 1550.15 nm l 2 1548.53 nm 5 Gb/s RZ RF delay l c =1551.76 nm SOA bias = 165 mA, Gain = 24 dB, P sat = 7 dBm l reservoir 1539 nm Fig. 3-15. Experimental setup for the all-optical half adder. 41 The complete optical setup is shown in Fig. 3-15. As mentioned before, the module is divided into two stages. The first stage is the PPLN waveguide-based AND gate. The incoming data streams at l 1 =1550.15 nm and l 2 =1548.53 nm are amplified to 11 dBm, filtered (to suppress ASE noise) using 0.6 nm bandwidth filters and coupled into the PPLN waveguide using a 50:50 coupler. Through SHG:DFG, the data on l 2 is shifted to a new wavelength, l c 2*l 1 - l 2 = 1551.76 nm, whenever the signal on the pump wavelength (l 1 ) is ‘on’, thereby providing the AND functionality. The PPLN wavelength conversion spectrum is shown in Fig. 3-16(a). The conversion efficiency of the device is ~ -24 dB at 11 dBm input pump power. Higher pump powers improved the conversion efficiency to –15 dB but this would require a separate attenuator for the pump wavelength to equalize its power to the other input wavelength before the SOA. An optical band-pass filter with a bandwidth of ~0.7 nm is used to filter out l c . This signal is then amplified and re-filtered to reduce ASE noise. This forms the Carry output of the half adder as shown in Fig. 3-16(b). It is important that the output of the first stage be of high quality since it influences the nonlinear process in the second stage. For such a design, the almost-noise-free PPLN waveguide is an ideal candidate. The second output of the 50:50 coupler serves as the output of the OR gate in the logic diagram. Since the two input wavelengths are different, there is no interference between them and the optical power in the corresponding bits is added up. It should be noted that the output of the coupler has 3 levels corresponding to the 00, 10(or 42 01), and 11 cases of the logic levels of the two input bits. However, the 11 case is unimportant since it results in the Carry being ‘1’, which saturates the SOA in the second stage, preventing the coupler output from emerging at the Sum port. l l l l c 7.9 dBm l l l l 2 2 2 2 8.52 dBm l l l l 1 1 1 1 8.48 dBm l l l l c -13.0 dBm 5 dB/div 0.8 nm/div 5 dB/div 0.8 nm/div 1550.15 nm 1550.15 nm (a) (b) Fig. 3-16. (a) Output spectrum of PPLN waveguide. Signal on l 2 =1548.53 nm is converted to l c =1551.76 nm only when the signal on l 1 =1550.15 nm is high (logic 1). (b) The converted signal is filtered and amplified to form the Carry output. The second stage makes use of XGM in the SOA to generate the Sum output. A commercially available packaged SOA is used as the active element in this stage and is driven at 165 mA. The output of the coupler is fed into the SOA via an optical attenuator and an isolator. The total power injected is approximately -9 dBm. The Carry output from the first stage is amplified to ~7 dBm and input to a circulator’s port 1 through a tunable optical delay, with port 2 connected to the other end of the SOA. The Carry signal serves as the ‘large signal’ to saturate the SOA whenever it is ‘on’. The optical delay is adjusted to ensure that the OR gate output interacts with the corresponding AND gate output in the SOA. When the Carry signal is ‘1’ (11 input) it saturates the SOA and there is no output at the circulator’s port 3, resulting in a ‘0’ at the Sum output port. When the Carry signal is ‘0’ the logical output of the 43 Sum port is the same as that of the OR gate. This can either be a ‘1’ on l 1 (10 input), a ‘1’ on l 2 (01 input) or a ‘0’ (00 input). The output at port 3 of the circulator is filtered using a ~1.4 nm band-pass filter centered between l 1 and l 2 . Ideally, a WDM filter should be used to further suppress the ASE noise that exists in the spectral region between l 1 and l 2 . This should improve the performance of the module and reduce the penalty introduced by the second stage. As is clear from Fig. 3-14, the Sum output is comprised of pulses on both l 1 and l 2 . If the Sum output of the half adder is to be transmitted over fiber, dispersion-related distortions can be avoided by using a wavelength converter to transfer the pulses from both the Sum wavelengths onto a single wavelength. Certain applications of half adders may not involve fiber transmission at all. Instead, the resultant output may be detected locally e.g. to make a switching decision, as would be the case for a checksum verification module. The powers of all the optical signals entering the SOA are optimized to obtain reliable output bit patterns. The speed of the XGM process in the SOA depends on the bias current and the optical power injected into it. To enhance the performance of the second stage, a reservoir CW signal (1539 nm) at a power of –2.8 dBm is also coupled into the SOA to optically bias the gain, close to saturation. This helps in reducing the gain recovery time, enabling high speed processing and limits the nonlinear distortion suffered by the signals. The need for a reservoir channel may be eliminated if the Carry signal injected into the SOA is suitably amplified. The spectra showing the inputs and output of the SOA are presented in Fig. 3-17(a) and Fig. 3-17(b), respectively. 44 l l l l cw (reservoir) -2.8 dBm 5 dB/div (inputs) l l l l 2 & l & l & l & l 1 ~-14 dBm l l l l 2 -0.61 dBm l l l l 1 -0.58 dBm ASE noise -23 dBm 5 dB/div Wavelength (0.8 nm/div) 1550.15 nm 1544.15 nm (a) (b) Wavelength (3 nm/div) Fig. 3-17. (a) Spectrum of the input to the SOA comprising of pulses on l 1 =1550.15 nm and l 2 =1548.53 nm. A reservoir CW channel, l cw =1539 nm is also coupled in to the SOA. (b) SOA output (Sum) spectrum after filtering. The Sum is comprised of pulses on both l 1 and l 2 , which are filtered together. The experiment was conducted with various data patterns to verify that the module did not suffer from pattern dependence. Fig. 3-18 shows the bit patterns obtained for a 25-bit segment. The Sum output on individual wavelengths is also presented. SIGNAL B (l 2 ) SIGNAL A (l 1 ) CARRY (l c ) SUM (on l 2 ) SUM (on l 1 ) SUM (on l 1 & l 2 ) 1011010110001110101101011 1010010100000010101001010 0001000010001100000100001 0000100001100001000010000 0001100011101101000110001 1010110101100011101011010 1 mV/div 500 ps/div Fig. 3-18. 5 Gb/s RZ bit patterns for the half adder. The Carry output is ‘on’ only when both the inputs are ‘on’. The SOA outputs on l 1 and l 2 are filtered together to obtain the Sum output. 45 The Carry output is ‘on’ only if the two input signals are ‘on’ simultaneously. Whenever the Carry signal is ‘off’ the corresponding pulses, if any, on the input wavelengths emerge at the SOA output as is visible through the Sum (on l 1 ) and Sum (on l 2 ) patterns. These two outputs are filtered together to generate the combined Sum output. It should be emphasized that good quality of the Sum output can only be obtained by ensuring that the pulses that emerge at the Sum output port are all of equal power even though they appear on different wavelengths. Since the SOA’s gain and gain saturation efficiency depend on the wavelength of the signal, separate attenuators may be needed to control the injected powers of the individual signal wavelengths. This is not the case as long as the wavelengths are not vastly different, as demonstrated in this work. The Carry output shows an extinction ratio in excess of 20 dB while the extinction ratio for the Sum outputs on individual wavelengths is around 18 dB. The combined Sum output obtained by centering the output filter between l 1 and l 2 is noisier than the Sum outputs on individual wavelengths due to the unfiltered ASE noise between the wavelengths and slight chirp on each wavelength due to off-centered filtering. Both these problems can easily be rectified using a WDM filter. The extinction ratio for the Sum output, nevertheless, is found to be greater than 14 dB. 46 2 3 4 5 6 7 8 9 10 -33 -32 -31 -30 -29 -28 -27 -Log (BER) Received Optical Power (dBm) DATA SUM ON l l l l1 CARRY SUM Fig. 3-19. BER measurements for the half adder, taken using a pre-programmed pattern of 2 7 bits. The Carry output exhibits <1 dB power penalty while the Sum output on a single wavelength shows <2 dB penalty. An excess 1.8 dB penalty is observed for the combined Sum output. BER measurements are conducted to determine the power penalty introduced by the module. Since, the half adder transforms the inputs into new data streams, BER measurements require bit patterns to be manually coded into the measurement equipment. Input bit patterns are coded into the pulse pattern generator, the Carry and Sum outputs are calculated and these new bits are coded into the error analyzer. Fig. 3-19 shows the BER curves and eye diagrams for the input data, Carry output and the Sum output. The curve for the Sum output on l 1 is also included since this represents the power penalty if a WDM filter was used at the SOA output. The Carry output and the Sum output on l 1 show approximately 1 dB and 2 dB power penalties, respectively. An extra 1.8 dB penalty for the combined Sum output is due to unfiltered ASE noise and off-centered filtering. 47 Further improvement in the performance of the module is possible by optimizing wavelengths for XGM in the SOA and by using higher pump power for the PPLN waveguide in order to improve the conversion efficiency. Other techniques to generate a wavelength converted AND signal can also be used instead of the PPLN waveguide, e.g. using cross-absorption modulation in an electro-absorption modulator [1]. It should be noted that the module is compatible with NRZ data format, probably requiring some adjustment of the second stage operational parameters. Also, the module can scale to higher speeds, limited only by the gain recovery time for the XGM process. SOAs with gain recovery times in the low 10s of ps are commercially available and under specific operating conditions, XGM has been demonstrated up to 100 Gb/s [27]. 3.3 All-optical hard-limiting using XGM in an SOA for alleviating the ‘near-far’ effect in O-CDMA networks There has been recent renewed interest in optical code-division-multiple-access (O- CDMA) due to its potential for enhanced data security, especially when considering the fine granularity of traffic and need for asynchronous data transfer in local area networks (LANs) [82]. A one-dimensional O-CDMA system divides a transmitted bit into a number of distinct pulses (chips) with a pattern that is unique to each user [78, 79]. One method to increase the number of users in an O-CDMA system has been the use of a two-dimensional (2-D) O-CDMA scheme (Fig. 3-20), which 48 divides a transmitted bit into a number of distinct pulses (chips) on different wavelengths [29, 89]. 1D OCDMA 2D OCDMA “1” t “1=1001” t OCDMA encoded bit with chips “1001” 1 2 3 4 t 1 t 2 t 3 t 4 wavelength l l l l 1 0 0 l l l l 4 time chips: input bit Fig. 3-20. 2-D (time, wavelength) O-CDMA. 2D OCDMA allows more orthogonal codes for a given number of chip times In both cases the pattern of the sequence is unique to each user with proper auto and cross correlation properties to ensure the detection of each user’s data in the presence of other users. Because there is a probability of multiple users transmitting at the same time, and users are transmitting asynchronously with respect to each other, other user chips act as “interference” to a receiver tuned to a particular code. Asynchronous O-CDMA networks may suffer from two key limitations: (1) the amount of multiple-access interference (MAI) that can be tolerated by the receiver. MAI will occur when another user’s code has energy in some subset of the desired code’s chip times and wavelengths, and (2) near-far effect, i.e. when the decoded autocorrelation and observed MAI for the user of interest depend on the relative distances of the interfering users. One potential method for reducing MAI would be to implement hard-limiting in the O-CDMA receiver [4, 76]. A hard-limiting 49 receiver will only detect a maximum optical power of a predetermined “unitary” level within each chip time-wavelength bin, thereby limiting the accumulated MAI. In this section, we describe a novel missing chip detection (MCD) technique which implements an all-optical hard limiter. The receiver should output a ‘1’ bit only if all the chips that make up the user’s code are present in the autocorrelation peak. Moreover, we show that the proposed technique mitigates the near-far effect in an O- CDMA system. Penalty due to near-far effect is reduced by >8dB compared to the conventional receiver and the tolerable interference range extended by >6dB. 3.3.1 Near-far problem and its mitigation through missing chip detection Figure 3-21 describes the operation of a 2-D O-CDMA system. A user’s encoder accepts the bit-pattern ‘010’ and splits every ‘1’ bit into a set of pulses (called chips), the temporal positions and wavelengths of which are determined by the user’s code. The total number of pulses that encode a bit is called the ‘code weight’. The encoded bits then pass through a star coupler, where interference from other users is added to the user’s data. At the receiver, a matched decoder stacks all the chips of the user of interest on top of each other, resulting in an autocorrelation peak. In the example shown in Fig. 3-21, since the user’s code has weight=4, the autocorrelation peak is 4 chips high. 50 1 0 0 Encoder Decoder Gate Interference from Other User Rx 1 0 0 1 0 0 Conventional receiver Threshold Fig. 3-21. Operation of a 2-D O-CDMA system. ‘1’ bits are encoded into a sequence of chips with predetermined temporal and spectral location. The gating system rejects any interference falling outside the autocorrelation peak and then a threshold detector samples the autocorrelation peak to recover the original bits. It should be noted that the amount of MAI that can overlap with the autocorrelation peak is limited based on the design of the orthogonal codes. However, O-CDMA networks may suffer from the near-far problem [75] that is explained in Fig. 3-22. If the interfering user’s chips have the same or less power than those of the user of interest, the threshold will not be exceeded as long as the number of active users in the network is within the bounds placed by the code parameters. But if the interfering user has higher power in its chips compared to the user of interest, the total power in the gated window can become higher than the threshold. In this case, the bit is erroneously decoded as a ‘1’. The middle bit in Fig. 3-22 depicts this case. This condition can occur if the interfering user is ‘nearer’ to the receiver than the user of interest. Thus, the relative distances of the user of interest and the interfering user (and consequently the power arriving from each), impact the performance of the system. This is called the ‘near-far’ problem. 51 t t 1 l l l l 1 l l l l 2 l l l l 3 l l l l 4 User of Interest t 1 0 1 Threshold Autocorrelation Peaks MAI from ‘Far’ Interferer Threshold t 1 1 False positive + 1 t 1 0 MAI from ‘Near’ Interferer t t 1 l l l l 1 l l l l 2 l l l l 3 l l l l 4 User of Interest t 1 0 1 Threshold Autocorrelation Peaks MAI from ‘Far’ Interferer Threshold t 1 1 False positive + 1 t 1 0 MAI from ‘Near’ Interferer Fig. 3-22. Near-far problem: Interfering users located closer to the receiver than the user of interest can produce enough power in the autocorrelation position to cause ‘0’ bits to be detected as ‘1’s. In this section a novel O-CDMA receiver structure that significantly mitigates the ‘near-far’ problem is investigated. It should be noted that the technique aims to prevent ‘false-positives’ caused by MAI and beat noise is not taken into account. The receiver’s design is motivated by the fact that a ‘1’ bit is characterized by the presence of all the chips that make up the user’s code in the autocorrelation peak. Thus, instead of comparing the autocorrelation magnitude to a preset threshold (conventional technique) one can check for the presence of all the chips that make up the code. The receiver implements a novel technique for all-optical hard limiting. Optical filters (tuned to the wavelengths employed by the user of interest) and optical delay lines are used to re-spread the gated autocorrelation peak into individual chips positioned at predetermined locations. All-optical sampling of these positions provides an indication of missing chips. If the sampling process reveals the absence of a chip at any of the possible positions, it can be concluded that the particular bit being tested was a ‘0’. As shown in Fig. 3-23, if the user of interest transmitted a 52 ‘0’, MAI from interfering users may populate some of the re-spread chip positions but there will be at least one chip position that remains vacant. Re-spreading using l l l l- dependent delays t 1 0 1 1 0 1 t t t Electronic Processing l l l l 2 2 2 2 l l l l 3 3 3 3 l l l l 4 4 4 4 l l l l 1 1 1 1 Bit Time Missing chip generation Missing chips Missing chip indicator Detected bits } MAI MAI All-optical hard-limiting Fig. 3-23. Missing Chip Detection: The auto correlation peak is re-spread and then the missing chips are detected using all-optical sampling. The presence of any missing chips indicates a ‘0’ bit. Even if the power in the MAI chips is significantly higher than that of the user of interest, it only leads to more power appearing in some of the re-spread chip positions. The vacant chip positions are left untouched and can be detected as missing chips through the sampling process. In this way, the proposed technique can mitigate the penalty incurred due to the ‘near-far’ problem. Some form of electronic processing is required to convert the missing-chip indicators into the original bits. 3.3.2 Experimental results and discussion The experimental implementation (Fig. 3-24) of all-optical hard limiting through the process of MCD relies on using cross-gain modulation (XGM) in a semiconductor optical amplifier (SOA) to perform the sampling. 53 Demux 1T 2T 3T 4T Coupler SOA Rx MOD User of interest MAI Missing Chip Detector Hardware t t Autocorrelation peak after decoder Sampling pulses Re-spread OCDMA data Filter 2X1 Mode-locked laser Fig. 3-24. Experimental setup. The chips in the autocorrelation peak are spectrally separated and re-spread to specific temporal positions. These positions are sampled by pulses from the mode-locked laser. The user of interest transmits data at a bit-rate of 1 Gb/s with 4 pulses per bit, (l 1 =1549.7, l 2 =1550.7, l 3 =1551.4 and l 4 =1552.1 nm). It is assumed that the gated autocorrelation peak is available after the decoder. Thus, all 4 pulses are located at the same temporal position. An arrayed-waveguide grating (AWG) is used to wavelength demultiplex the autocorrelation peak and time delays of 200 ps, 400 ps, and 600 ps are used to delay l 2 , l 3 and l 4 respectively (relative to l 1 ). The result is the re-spread O-CDMA signal consisting of a series of 4 pulses spaced 200 ps apart for a ‘1’ bit and no pulses for a ‘0’ bit. The experimental patterns obtained for a bit sequence of ‘1001’ are shown in Fig. 3-25. 54 User of interest without MAI User of interest with MAI 1 1 0 0 1 1 0 0 2 sampling pulses suppressed by MAI, but 2 missing chips detected Missing-chips 1 Gb/s, 10 chip-times per bit, 4 pulses per bit, each on a different wavelength (l 1 =1549.7, l 2 =1550.7, l 3 =1551.4 and l 4 =1552.1 nm) Missing chip indicator Missing chip indicator 4 missing chips detected for ‘0’ bits { { l l l l 1 - 4 l l l l 3 l l l l 4 1 mW/div. 1 mW/div. 500 ps/div. 500 ps/div. Fig. 3-25. Experimental patterns for missing chip detection technique. Top patterns show the re-spread O-CDMA signal, with and without interference. Bottom patterns show the SOA output (missing chip indicators). Pulses from a mode-locked laser (l s =1540 nm) are broadened to 20 ps FWHM using an optical filter and modulated with a repetitive pattern to obtain 4 sampling pulses per bit, spaced 200 ps apart. This pulse stream is synchronized with the pulses from the re-spread O-CDMA data and coupled into the SOA. The power for the sampling pulses is maintained low while that of the O-CDMA data is kept high. As a result, whenever a chip is present in the O-CDMA data it saturates the SOA’s gain, thereby suppressing the corresponding sampling pulse propagating through the SOA. At the SOA’s output, a bandpass filter is used to recover the sampling pulses. In such a configuration, only those sampling pulses emerge at the output that do not have a corresponding pulse in the re-spread O-CDMA signal. Thus each pulse emerging at the SOA’s output indicates a missing chip for that particular bit. 55 For a ‘1’ bit, all pulses are suppressed while for a ‘0’ bit, in the absence of MAI, all 4 pulses will emerge at the SOA output, as shown in Fig. 3-25. In the presence of MAI, some re-spread positions might be occupied even for a ‘0’ bit and the corresponding pulses will be suppressed at the SOA output. However, there will be at least one missing chip per ‘0’ bit which will manifest itself at the output in the form of a pulse. In the sample pattern of Fig. 3-25, MAI causes suppression of the third and fourth sampling pulses for the second bit, but the first two pulses emerge at the output indicating that the bit under consideration was a ‘0’. This is a demonstration of all-optical hard limiting since only the presence of all the chips in the user’s code can suppress all sampling pulses. Also, from Fig. 3-25 it is clear that since the MAI chips are much larger in amplitude than those of the user of interest, a conventional thresholding receiver will not be able to recover this data without errors. However, the proposed technique generates missing-chip indicators with an open eye-diagram, even under such a condition. This goes on to prove that the process of MCD mitigates the ‘near-far’ problem since it can tolerate higher MAI levels. To determine the limits on tolerable levels of MAI, BER measurements are conducted on the missing chip indicator signal for a PRBS input to the MCD module. Fig. 3-26 shows the BER curve obtained for the worst case MAI that could be tolerated for a BER of 1e-10. 56 4 5 6 7 8 9 10 -8.5 -8 -7.5 -7 -6.5 Received Optical Power (dBm) -10 log(BER) 4 5 6 7 8 9 10 -8.5 -8 -7.5 -7 -6.5 Received Optical Power (dBm) -10 log(BER) 6.9 dB Missing chip indicator Eye diagram User chips MAI chips Fig. 3-26. BER measurement for the worst case, tolerable MAI (6.9 dB interference to signal ratio) As shown in the inset, the MAI chip’s power was 6.9 dB higher than the power of the user’s chip. It should be noted that some form of electronic or optical processing will be required to convert the missing-chip indicator signal into the original data bits. Further, the performance of the proposed technique is compared to the conventional receiver for different levels of MAI. The ratio of the power of the interference chips to that of the user of interest is varied over a large range and power penalties with respect to the case of no MAI are determined individually for the two receiver designs. main user power per chip 0 2 4 6 8 10 -2 0 2 4 6 8 Power Penalty (dB) 10 log interference power per chip Conventional Receiver Missing Chip Detection main user power per chip 0 2 4 6 8 10 -2 0 2 4 6 8 Power Penalty (dB) 10 log interference power per chip Conventional Receiver Missing Chip Detection 0 2 4 6 8 10 0 2 4 6 8 10 -2 0 2 4 6 8 -2 0 2 4 6 8 Power Penalty (dB) 10 log interference power per chip Conventional Receiver Missing Chip Detection Fig. 3-27. Comparison of Missing Chip Detection and conventional receiver. MAI tolerance is increased by ~6 dB 57 As shown in Fig. 3-27, the conventional thresholding receiver cannot maintain a bit- error-rate <1e-9 for MAI chip power 1 dB greater than the user of interest, while the MCD technique can extend the error-free window beyond 7 dB. For 1 dB greater MAI chip power, the conventional receiver suffers a power penalty > 8 dB, while the MCD technique exhibits only 0.5 dB power penalty for maintaining BER=1e-9. The sampling process in the proposed technique can also be performed through other means. For example, cross-absorption modulation in an electro-absorption modulator can be employed. In this case, the sampling pulses would emerge at the output only in time-slots occupied by the re-spread OCDMA data. Therefore, a missing chip would be indicated by a missing sampling pulse. Since the proposed all-optical hard limiter converts OCDMA data into missing chip indicators, a modified version of the scheme can be used to develop an OCDMA-to-TDM or OCDMA-to-WDM converter. The modified design would all-optically convert the multiple missing chip indicators occurring for each ‘0’ bit into a single pulse. By individually re-spreading decoded OCDMA signals from different users and sampling them with pulses of different wavelengths, the OCDMA information can be converted into a WDM OOK data stream, mapping each user’s data to a specific wavelength. If the same sampling wavelength is used for all the users, time interleaving of the missing chip indicators can be performed to convert the OCDMA signals into a TDM data stream. 58 Chapter 4 Deleterious effects in differential mode wavelength converters and their compensation through optical signal processing techniques Switches/wavelength converters based on XPM or XGM in SOAs exhibit unwanted signal degradations due to slow carrier recovery, including pattern dependence and pulse asymmetry/broadening. In order to mitigate some of these effects, differential mode (DM) switches have been proposed. These switches that rely on interference of time-offset copies of phase-modulated signals effectively mask the slow recovery processes in the SOAs and can potentially enable very high speed all-optical wavelength conversion [65]. In this chapter two types of DM switches are described and their behavior is simulated using a wideband dynamic SOA model in conjunction with commercial optical system simulation software. Non-idealities introduced by the DM switches are studied and methods to alleviate their detrimental effects are experimentally investigated. 4.1 Delayed-interference signal converter The delayed-interference signal converter (DISC) provides a simple, yet elegant solution for wavelength conversion, requiring only one SOA and an Asymmetric Mach-Zehnder Interferometer (AMZI) [88]. It has been used in several signal 59 processing applications [50, 106]. The structure of the DISC is shown in Fig. 4-1 and its operation can be understood from Fig. 4-2. Filter Output D D D Dt (delay) F F F F (phase-bias) CW (probe) Signal (Pump) SOA Fig. 4-1. Structure of the delayed-interference signal converter. A CW probe signal and an RZ modulated pump signal are injected into an SOA. The pump imposes phase modulation on the CW probe with a fast rise time (determined by the input pulse rise time) and slow fall time (determined by the carrier recovery time in the SOA). This phase modulated signal enters an AMZI, which is an MZI with a time delay in one arm. 0 5 0 0.5p Output Phase mW rad Dt 0 25 Input mW 0.15 0 Time (ns) 0 5 0 0.5p Output Phase mW rad Dt 0 25 Input mW 0.15 0 Time (ns) Fig. 4-2. Operating principle of the DISC. The input signal causes phase variation of the probe. This phase modulated signal is made to interfere with its own delayed copy using the AMZI, generating narrow output pulses and trailing sub-pulses. 60 The phase modulated probe and its time-delayed copy interfere at the output of the AMZI. Since the output is governed by the phase difference between the two interfering components, narrow switching windows are opened due to each pump pulse. If the phase-bias between the arms is set to p radians, output pulses emerge only during these switching windows. As a result, the slow carrier recovery is nullified and narrow output pulses can be obtained. In effect, the phase modulated probe component that arrives at the output first, opens the switching window that is shut by the arrival of the delayed copy. Thus the output pulse-width is determined by the time differential between the two arms, instead of the slow carrier recovery. As is visible from the phase diagrams, in an ideal case (delayed copy is a true replica of the original phase modulated probe) the delayed copy will always overshoot the original phase variation leading to negative phase differences. For a phase-bias of p this corresponds to constructive interference too and leads to the appearance of sub- pulses as shown in Fig. 4-2. These sub-pulses have recently been predicted [99] and their existence verified experimentally [77]. The sub-pulses can lead to degrading effects when the converted signal is launched over a transmission link. 4.2 Differential cross-phase modulation The differential cross-phase modulation (DXPM) configuration is similar to the DISC in its operation with one major distinction. As shown in Fig. 4-3, the structure actually includes the SOAs within an MZI, while the pump signal is injected into the two SOAs with a time differential. Since the pump is split between the two SOAs it 61 is possible to independently control the amount of phase modulation induced in each SOA by controlling the splitting ratio. If the pump power injected into each SOA is kept equal the interference at the output resembles that of the DISC. Filter Output F F F F (phase-bias) CW (probe) Signal (Pump) SOA SOA D D D Dt (delay) S split Fig. 4-3. Structure of the differential cross-phase modulation wavelength converter. However the power in the delayed pump signal injected into the lower arm SOA can be reduced such that its slow phase recovery coincides with the one from the top arm, as shown in Fig. 4-4. Thus, delayed phase overshoot can be prevented and the sub-pulses may be minimized. Input 0 0.15 0 5 Time (ns) 0 0.5p 0 25 S split :0.75 Input Output Phase mW mW rad Fig. 4-4. Operating principle of the DXPM wavelength converter. By adjusting the signal splitting ratio S split, the recovery of the phase in the two arms can be made to coincide, minimizing the deleterious sub-pulses. 62 The DXPM structure, though more complex due to the presence of an MZI with embedded SOAs, provides an extra degree of freedom to mitigate one of the non- idealities introduced by the DISC structure. The DXPM configuration has been utilized for several high-speed signal processing demonstrations. 4.3 Sub-pulses in a DISC In order to study the impact of sub-pulses on signal quality a model for the DISC has been developed and simulations are performed at 40 Gb/s for 5 ps FWHM Gaussian pulses. A wideband numerical model of an SOA [20] that includes ASE noise is used. Finite difference techniques are used to obtain dynamic carrier density distribution along the SOA. Accurate predictions of the gain and phase dynamics can thus be made. The MATLAB code for the model is presented in appendix A. The phase-shifter and the asymmetric MZI are modeled analytically. These models have been interfaced to a commercial optical communication system simulation package that provides the models for other elements of the simulation. The SOA is biased at 210 mA and the pump and probe powers are fixed at 5 dBm and 10 dBm, respectively. Dt is set equal to 5 ps to enable pulsewidth maintaining wavelength conversion and the phase-offset is adjusted to ‘p’ to keep the power in the output zeros at a minimum. It has been shown experimentally that due to non- ideal behavior of the DISC, the phase variations in the interfering components are not identical, leading to the observation of smaller sub-pulses. To mimic this fact, 63 independent phase variations are simulated in the two arms of the MZI. By adjusting the ratio of the peak phase variation in the upper arm to that of the lower arm the peak power in the sub-pulses can be reduced to more realistic levels. 4.3.1 Analysis of the temporal-chirp on the DISC’s output In order to analyze the deleterious effects of the sub-pulses and determine methods to alleviate them, an understanding of the differences between the main-pulse and sub- pulse is required. The temporal chirp profile of the wavelength-converted signal is shown in Fig. 4-5. Time (ns) 0.2 0 0.1 0 1.8 0.9 -25 15 0 Power (mW) Chirp (GHz) Main-pulse Red-shifted Sub-pulse Blue-shifted MZI arm1 (a) (b) Fig. 4-5. (a) Output of the DISC showing small sub-pulses trailing the main pulses. (b) Temporal chirp profile of the wavelength converted output. The main pulses are red-shifted while the sub-pulses are blue-shifted. 64 Since the leading as well as the trailing edges of the converted signal pulses are produced by signal pulse-induced increase in the refractive index of the SOA material, almost the entire pulse is chirped towards lower frequencies (red-shift). On the other hand, the sub-pulses are produced during the slow gain recovery of the SOA and are consequently blue-shifted. Since the main pulse and sub-pulse are oppositely chirped they are expected to move towards each other due to dispersion in a fiber. Apart from back-to-back power penalty due to the presence of the sub- pulses, this temporal chirp relationship between the main-pulses and sub-pulses may lead to additional penalties when fiber transmission is involved. 4.3.2 Suppression of sub-pulses through detuned-filtering The blue-shift of the sub-pulses can be exploited to suppress them by filtering the output signal with the filter detuned towards longer wavelengths. Fig. 4-6 shows the variation of the converted signal’s Q-factor with filter detuning towards longer wavelengths. 1 Filter detuning (nm) 0 0.4 Q (dB) 10 30 5 20 15 25 160 GHz 120 GHz 80 GHz Filter BW 0.2 0.8 0.6 0 nm detuning 0.6 nm detuning Filter BW=160 GHz Q=20 dB Q=26 dB Fig. 4-6. Red-shifted filter detuning to suppress sub-pulses. Red-detuning the output filter leads to Q-factor improvement until the OSNR starts degrading. 65 As the filter detuning is increased, the eye opening improves due to suppression of sub-pulses until the optical OSNR starts degrading due to loss of converted signal power. The improvement in Q is more significant for smaller bandwidth filters, a result of interest for dense wavelength division multiplexed systems. The eye diagrams obtained for a 160 GHz bandwidth optical filter and a 40 GHz bandwidth receiver clearly show a reduction in inter-symbol interference from the sub-pulses when the filter is detuned by an optimum value of 0.6 nm. 4.4 Data-pattern dependence in differential mode wavelength converters As described in the previous section, in order to nullify the slow carrier recovery in SOAs, differential mode (DM) XPM switches that utilize a push-pull configuration have been used. Even though DM wavelength converters at bit-rates >160 Gb/s have been demonstrated [97], they suffer from nonlinear pattern dependence [67]. Large variation in the amplitude of the output pulses (Fig. 4-7) is observed that can lead to eye-closure. SOA-based Wavelength Converters Input Output Carrier density Pattern dependence time time time Fig. 4-7. Data-pattern dependence due to slow carrier recovery in SOA based wavelength converters. 66 As shown in Fig. 4-8 (simulated using an SOA model described in [20]), the eye- closure penalty increases rapidly with increasing bit-rate for long carrier recovery times (t r ). 0 0 16 40 10 20 30 12 4 8 Eye-closure penalty (dB) Bit-rate (Gb/s) ) g eye openin e opening average ey ( log 10´ Eye-closure penalty t t t t r =45 ps t t t t r =28 ps t t t t r =20 ps 0 0 16 40 10 20 30 12 4 8 Eye-closure penalty (dB) Bit-rate (Gb/s) ) g eye openin e opening average ey ( log 10´ Eye-closure penalty t t t t r =45 ps t t t t r =28 ps t t t t r =20 ps t t t t r =20 ps t t t t r =28 ps Avg. eye opening Eye opening avg. 1-level t t t t r =20 ps t t t t r =28 ps Avg. eye opening Eye opening avg. 1-level t t t t r =20 ps t t t t r =28 ps Avg. eye opening Eye opening avg. 1-level Gain recovery time Fig. 4-8. Eye-closure penalty due to increasing bit-rate for differential mode wavelength converters. The problem becomes even more pronounced when many such wavelength converters are cascaded. As shown in Fig. 4-9, the pattern dependence is cumulative and increases rapidly in a chain of wavelength converters. Since the output of the first wavelength converter is the driving signal for the second, pattern dependence in the signal’s amplitude translates into pattern dependence in the cross-phase modulation induced by it. This pattern dependence adds on to the pattern dependence that exists due to slow carrier recovery in the second wavelength converter itself, leading to greater penalty. 67 0 0 10 4 6 8 6 2 4 Eye-closure penalty (dB) Number of l-converters ) g eye openin e opening average ey ( log 10´ Eye-closure penalty 20 Gb/s 10 Gb/s 2 0 0 10 4 6 8 6 2 4 Eye-closure penalty (dB) Number of l-converters ) g eye openin e opening average ey ( log 10´ Eye-closure penalty 20 Gb/s 10 Gb/s 2 Gain recovery time = 28 ps Bit-rate After 6 converters Avg. eye opening Eye opening avg. 1-level After 2 converters After 6 converters Avg. eye opening Eye opening avg. 1-level After 2 converters Fig. 4-9. Eye-closure penalty in cascades of differential mode wavelength converters. Pattern dependence-induced eye-closure grows rapidly. 4.4.1 Origin of nonlinear data-pattern dependence in a DISC Recently, a technique based on detuned optical filtering [68] was proposed to reduce the nonlinear pattern-dependence in the DISC. The technique uses the pattern dependence in the chirp induced on the pulses to compensate for the pattern dependence in the amplitudes of the pulses. However, the loss of signal-to-noise ratio incurred due to off-center optical filtering limits the improvement in signal quality that can be achieved. Moreover, since the chirp changes over the width of the pulse, it is possible that the pulses will suffer from distortion if excessive filter detuning is used to nullify the pattern dependence. Other properties of the output signal can be exploited to reduce the pattern dependence in the pulse amplitudes. Previous work has shown that pattern dependent signal distortion induced by gain saturation in SOAs leads to overshoots 68 at the rising edges of signals that are being amplified. Several techniques to mitigate this effect have been explored, including ‘polarimetric filtering’ [6]. This technique leverages the large birefringence induced in the SOA by the rising edges of the input pulses and uses a polarizer placed after the SOA to improve the signal quality. In order to explore the use of polarimetric filtering for the DISC, a deeper understanding of the mechanics of XPM and the simultaneously occurring cross- polarization modulation (XpolM) is required. The structure of the DISC is shown again in Fig. 4-10 and its ‘ideal’ operation is explained in Fig. 4-11. Filter Output D D D Dt (delay) F F F F (phase-bias) CW (probe) Signal (Pump) SOA Fig. 4-10. Structure of the delayed-interference signal converter In Fig. 4-11 the SOA dynamics have been assumed to include only linear pattern dependence. This means that the carriers recover slowly when an input pulses is switched off, but the amount of carrier suppression (or phase-swing) induced by consecutive pulses is always the same. As explained earlier, in the absence of a signal pulse, the probe components in the MZI arms interfere destructively due to a ‘p’ phase offset between them. Input signal pulses suppress the carrier density in the SOA leading to a change in the refractive index and a corresponding modulation of 69 the phase of the co-propagating probe beam. The phase variations of the signals in the two arms are shown in Fig. 4-11 where a time offset is created by the delay Dt in one of the arms. From Fig. 4-11 it is clear that if only linear pattern dependence is included in the analysis, DF a =DF b i.e. consecutive pulses, A and B induce equal amounts of cross phase modulation on the probe even if the time between the input pulses (determined by the input signal bit-rate) is shorter than the SOA’s carrier recovery time. Only linear pattern dependence in SOA 0 0 1 Input (a.u.) 1 0 Phase in MZI (rad) 0.8p 200 0 Time (ps) Output (a.u.) 100 (Df Df Df Df A =Df Df Df Df B ) A Df Df Df Df A B Df Df Df Df B Slow phase recovery l l l l in l l l l c l l l l c Fig. 4-11. Operation of the DISC assuming only linear pattern dependence exists in the SOA. All pulses induce the same amount of phase-swing and the differential mode completely compensates for linear pattern dependence. 70 The modulated probe component that reaches the output of the MZI first opens a switching window that is closed by the arrival of the delayed component. Since the opening and closing of the window is induced by the fast carrier suppression, the window width is controlled by the time-delay between the interferometer arms, rather than the slow carrier recovery. Thus the DISC completely eliminates the linear pattern dependence due to slow carrier recovery. However, the assumption of linear pattern dependence in the SOA is not true. In reality, the pulses that enter the SOA after a 0-bit cause a bigger phase swing than ones that follow another pulse (DF a >DF b ) as shown in Fig. 4-12. 0 0 1 Input (a.u.) 1 0 Phase in MZI (rad) 0.8p 200 0 Time (ps) Output (a.u.) 100 A B Df Df Df Df A Df Df Df Df B Pattern dependence l l l l in l l l l c Nonlinear pattern dependence in SOA (Df Df Df Df A >Df Df Df Df B ) Fig. 4-12. Operation of the DISC including nonlinear pattern dependence in the SOA. The amount of phase-swing induced by input pulses reduces in a long string of 1’s leading to a reduction in output pulse amplitudes 71 Thus, in the converted output the peak power of the first pulse in a string of pulses is much higher than the ones that follow it. This effect is called ‘nonlinear pattern- dependence’ [67] since it arises from the dependence of the optically-induced carrier density variation on the instantaneous value of the carrier density itself. As shown in Fig. 4-12, a long sequence of ‘1s’ leads to progressively less phase modulation of the CW probe. However, the absolute deviation of the phase from the original steady state continues to increase. Successive pulses keep depleting the carrier population in the SOA, leading to increased gain suppression. This can be verified experimentally by observing the power variation of the CW probe after the SOA, as shown in Fig. 4-13 since gain and phase dynamics are both primarily driven by the same source, i.e. carrier density variation. Since the gain saturation for input pulse ‘B’ is deeper than that for ‘A’, we can conclude that the smaller pulses (e.g. ‘B C ’) at the output of the DISC correspond to deeper gain saturation of the SOA. B A DISC Input A C B C DISC Output Probe power at SOA output 200 ps G B G A l l l l in l l l l c l l l l c (G B >G A ) Larger gain suppression Optical power (a.u.) Time (200 ps/div.) Fig. 4-13. Correspondence between gain suppression and pattern dependence. Output pulses that exhibit lower power correspond to larger gain saturation in the SOA. 72 4.4.2 Experimental investigation of the polarization properties of the DISC’s output It is well known that if the CW probe is split between the TE and TM modes of the SOA, the pump signal induces different phase change on the two components due to the SOA’s structural asymmetry and difference in the confinement factors of the two modes. This optically-induced birefringence translates into a polarization rotation of the probe. Since the polarization rotation increases with gain saturation, one can expect the polarization states of the output pulses in a long string of ‘1s’ to be different. A polarization controller placed at the output of the DISC, followed by a polarizer, can be adjusted to equalize these pulses by ensuring that the projections of the polarization states of all the pulses on the polarizer’s axis are of equal magnitude. To explore the relationship between gain saturation and polarization rotation a 10 GHz, 2 ps FWHM pulse train from a semiconductor mode-locked laser is injected as the pump into the SOA. The output of the SOA is passed through a 25 ps delay interferometer before being filtered to recover the probe wavelength. If only the cross-gain modulated probe is required the delay interferometer is bypassed. While increasing the average power of the pump signal, the polarization states of the output pulses obtained from the DISC are observed using a polarization analyzer. The experimental setup, cross-gain modulated probe and the observed polarization states of the DISC output for three different pump powers are shown in Fig. 4-14. 73 l-converted output Mode-locked Laser 25 ps SOA Probe Laser DISC 10 GHz, 2 ps pulses Phase-shifter F~p Probe output DISC output Polarization -26 dBm -11 dBm -2 dBm Pump Pump Polarization controller Filter Attenuator Fig. 4-14. Experimental setup to observe polarization state of DISC’s output for an input (pump) pulse train. As the pump power increases, the amount of gain saturation and polarization rotation increases. As a representation of the amount of polarization rotation, the polarization ellipse’s azimuth is recorded. This polarization rotation observed is plotted in Fig. 4-15 along with the gain saturation curve. As expected a greater polarization rotation is observed with decreasing gain. From these measurements it can be concluded that pulses with smaller amplitude at the output of the DISC are more polarization rotated (due to deeper carrier suppression) than the ones that have higher amplitudes. 74 -30 5 -25 -20 0 Input signal power (dBm) -15 -10 -5 0 40 30 10 20 Polarization rotation (deg.) 50 4 12 10 6 8 Gain (dB) 14 16 18 Fig. 4-15. Gain suppression and polarization rotation as a function of input optical signal power. Pulses that correspond to larger gain suppression undergo greater polarization rotation. 4.4.3 Reduction of data-pattern dependence in a DISC through polarimetric filtering The experimental setup used to investigate the polarimetric pattern dependence reduction technique is shown in Fig. 4-16. The SOA used is a commercial device, biased at 180 mA with a 10-90 % gain recovery time in excess of 300 ps. Pulses with 2 ps FWHM at a wavelength of 1547 nm from a semiconductor mode-locked laser are modulated with 2 31 -1 PRBS data at 10 Gb/s and injected into the SOA with an average power of –0.5 dBm. The CW power (wavelength = 1535 nm) coupled into the SOA is 1 dBm. The method to suppress the pattern dependence involves placing a polarization controller and a polarizer at the DISC output. The polarization controller is adjusted such that the pulses with larger amplitude are preferentially attenuated relative to the smaller pulses on passing through the polarizer. A conceptual diagram of the technique is shown in Fig. 4-17. 75 Wavelength converted output Mode-locked laser SOA Modulator Probe laser } Polarizer Polarization controller DISC 10 GHz, 2 ps FWHM 10 Gb/s, 2 31 -1 PRBS EDFA EDFA Polarimetric filtering 25 ps Phase-shifter F~p Fig. 4-16. Experimental setup. The SOA and the 25 ps delay-interferometer form the DISC. The polarization controller and polarizer are added to control the pattern dependence of the output signal. Input pulses Output pulses Output polarization t t t Polarimetric filtering Equalized output Fig. 4-17. Principle of polarimetric pattern dependence reduction. The polarization controller and polarizer placed after the DISC are adjusted such that the pulses with larger amplitude are preferentially attenuated relative to the smaller pulses. 76 An EDFA is used to compensate for the overall loss introduced by the polarizer. The final output shows no pattern dependence and a clear eye opening (Fig. 4-18). l-converted output Tx (Pump) Probe Laser DISC 10 Gb/s, 2 ps pulses Input signal Signal after DISC Signal after equalization Time (200 ps/div) 500 m m m mW /div 500 m m m mW /div Time (200 ps/div) Time (200 ps/div) 1 m W /div l l l l in =1547 nm l l l l in =1535 nm l l l l in =1535 nm Fig. 4-18. Reduction of pattern dependence in DISC Due to slow carrier recovery, at the output of the DISC, the ratio of the largest pulse power to the smallest pulse power is 3.3 dB, which is completely nullified using the polarizer (Fig. 4-19). If the axis of the polarizer is so aligned that it preferentially attenuates the smaller pulses, the pattern dependence is enhanced leading to a completely closed eye as shown in Fig. 4-19, giving further proof of the principle involved. In fact, the variation in the polarization states of the output pulses is significant enough to actually reverse the pattern dependence, i.e. the pulse power increases for successive pulses in a long string of ‘1s’. By equalizing the power in the output pulses, the eye opening can be improved by more than 33%. 77 Patterns Eyes Input Output with pattern dependence Output with pattern dependence removed Output with pattern dependence increased (‘1’ level–D 1 )-(‘0’ level+D 0 ) ------------------------------ (‘1’ level–’0’ level) OF = Metrics OF = 0.678 PD = 3.3 dB OF = 0.888 PD = 0 dB OF 0 PD ~ 7 dB 200 ps Fig. 4-19. Bit-patterns and eye diagrams showing control over the pattern dependence. Through appropriate adjustment of the output polarization controller, the pattern dependence can be reduced from 3.3 dB to 0 dB or increased to >7 dB. To quantify the improvement in signal quality, bit-error-rate measurements are performed for 2 31 -1 PRBS data. The BER curves shown in Fig. 4-20 indicate a power penalty improvement of 2.6 dB at a bit-error-rate of 1e-9. -13 -12 -11 -10 -9 -8 -7 4 5 6 7 8 9 10 11 -13 -12 -11 -10 -9 -8 -7 4 5 6 7 8 9 10 11 Received power (dBm) - Log (BER) Without proposed technique With proposed technique 2.6 dB Fig. 4-20. Bit-error-rate measurements showing 2.6 dB power penalty improvement at BER=1e-9. Eye opening is improved by more than 33%. 78 In this experiment the SOA used has a recovery time more than three times longer than the bit-time. Similar results should be expected for higher bit-rates if faster SOAs are used, e.g. using an SOA with 75 ps recovery time for a 40 Gb/s system. The same concept applies to other differential mode switches also, e.g. differential cross-phase modulation [61]. Configurations comprising an SOA followed by a detuned filter [66] to exploit the SOA’s chirp for wavelength conversion may benefit from this polarimetric technique, enabling higher speed operation. 4.5 Operational parameters and their interplay in DXPM wavelength converters For high speed (40 Gb/s) systems, wavelength converters based on differential cross-phase modulation (DXPM) in SOAs have emerged as a promising technology [88]. As described earlier, this technique uses two SOAs placed within an MZI to enable wavelength conversion not restricted by the slow gain recovery time of the SOAs. This is achieved by using the pump (input) signal to open a switching window for a co-propagating CW probe via cross-phase modulation [25] in one of the SOAs which is closed a short time later by the injection of a delayed copy of the pump signal into the other SOA. Deleterious overshoots of the delayed phase variation are suppressed by reducing the power in the delayed copy of the pump such that the trailing edges of the phase variation in the two arms coincide. Thus, a high- extinction ratio switching window is generated whose width is determined solely by the differential delay between the two copies of the pump. 79 The flexibility provided by the design of the DXPM wavelength converter comes along with a host of operational parameters that must be carefully optimized in order to enhance the device’s performance. Thus, an understanding of these parameters, their effects and their interplay is of critical importance. Moreover, the optimum values of the different control variables may depend not only on the desired output characteristics but also on the properties of the input signal. In order to explore some of these interdependencies and arrive at design rules for enhanced performance of DXPM wavelength converters, simulations are performed using the wideband numerical SOA model described earlier [20]. Pulse width Signal polarity, ER Pulse shape Power balance in MZI, ER Power balance in MZI, ER D D D Dt F F F F S split P split P coup Filter Signal (Pump) CW (probe) Output F F F F (phase-bias) D D D Dt (delay) SOA SOA S split P split P coup Filter Signal (Pump) CW (probe) Output F F F F (phase-bias) D D D Dt (delay) SOA SOA S split P split P coup Parameter Output Signal Property Fig. 4-21. Structure of the DXPM wavelength converter and the various operational parameters that impact the device’s performance. Fig. 4-21 shows the structure of a DXPM wavelength converter and the various operational parameters that impact its performance. The signal splitting ratio, A:(A+B) is referred to as S split and need to be optimized to ensure good quality of the switching window. The probe splitting ratio, P split and coupling ratio, P coup are set 80 equal to 0.5 to guarantee low output zero-level power (and thus high output extinction ratio) through destructive interference of probe components in the two arms when no signal pulse is present. The phase-shifter (F) in one of the arms is a critical element in ensuring that the interference conditions are optimized. The output pulse-width and pulse-shape is dependent on the differential time delay (Dt) between the two copies of the pump signal injected into the SOA-MZI arms. Achieving the desired response from the device requires careful optimization of these parameters and makes it important to understand their individual effects and their interaction with each other. The simulations are based on a 40 Gb/s, 2 7 -1 PRBS, 5 ps FWHM RZ input signal with pump and probe powers of 5 and 13 dBm, respectively. Even though the DXPM technique eliminates linear pattern dependence by generating narrow switching windows not limited by the SOA’s recovery time, slow carrier recovery can limit the amount of phase-swing induced by successive pump pulses. As a result, output 1-bits that follow a string of 0-bits may exhibit higher peak power than those that follow another 1-bit. The eye-closure penalty resulting from this nonlinear patterning effect [67] can be reduced by biasing the SOA in deep saturation. In our simulations the SOAs are biased at 250 mA to obtain ~20 ps 10-90% recovery time. These conditions force the nonlinear pattern dependence to be negligible allowing the simulations to be targeted towards analyzing the device’s performance with respect to the various operational parameters. 81 Fig. 4-22 shows the ideal probe phase variations in the two arms of the SOA-MZI structure when the operational parameters have been optimized to generate a high quality output signal with 5 ps FWHM pulses (pulse-width preserving wavelength conversion). Phase (a.u.) Top Bottom Phase diff. (a.u.) t t Switching window Fig. 4-22. Ideal probe phase variations induced by a single pump pulse for the DXPM wavelength converter. The slow recovery in the bottom arm (blue) coincides with the recovery in the upper arm (red) leading to a high-quality switching window. The phase difference between the two arms which represents the switching window is also shown. These phase plots can be thought of as a representation of the ideal device response. Any deviations from this response may potentially lead to deleterious effects that degrade the output signal’s quality. Fig. 4-23 lists the possible deviations that can occur and their corresponding phase plots. These include · Relative amplitude change between the phase variations in the two arms · Horizontal offset between the phase variations in the two arms · Vertical offset between the phase variations in the two arms 82 Phase (a.u.) Top Bottom Phase diff. (a.u.) t t Sub-pulse Relative amplitude change Horizontal offset Phase (a.u.) Top Bottom Phase diff. (a.u.) t t Broadening Phase (a.u.) Top Bottom Phase diff. (a.u.) t t Loss of ER and undershoots Vertical offset Sub-pulse Fig. 4-23. Deviations from the ideal condition for the DXPM wavelength converter. Relative amplitude changes, horizontal or vertical offsets between the phase variations in the two arms lead to degradation of the output signal. 4.5.1 Relative amplitude change due to non-optimum S split Fig. 4-24. shows the normalized receiver power penalty for the wavelength converted output vs. S split for a fixed value of Dt=5 ps. The optimal (minimum penalty) S split for the particular operating conditions is ~0.75 and the corresponding eye diagram shows minimal distortion. S split =0.75 -0.5 0.5 1.5 2.5 0.55 0.725 0.90 Norm. Rx. penalty (dB) Signal Splitting Ratio (S split ) D D D Dt = 5ps Fig. 4-24. Optimizing signal splitting ratio for the DXPM wavelength converter. 83 The temporal phases in the MZI arms and the difference between them for S split =0.75 are shown in Fig. 4-25 and are very similar to the ideal response described earlier. However if S split deviates from optimum, it results in a relative amplitude change between the two phase profiles. S split =0.90 S split =0.55 Phase variation in MZI Phase variation in MZI Phase diff. Phase diff. 0 0 Phase (a.u.) Phase (a.u.) Delayed-phase overshoot causes trailing sub-pulse Delayed-phase undershoot leads to broadened pulse t t S split =0.75 Phase variation in MZI Phase diff. 0 Phase (a.u.) t Device response is close to ideal with high quality Fig. 4-25. Deleterious effects of non-optimum signal splitting ratio. Less than optimum signal splitting ratio causes delayed-phase overshoots leading to sub-pulses while exceeding the optimum value causes pulse broadening. If S split reduces, it leads to an overshoot of the delayed phase variation generating a deleterious sub-pulse following each output pulse. The case for S split =0.55 is shown in Fig. 4-25 and the corresponding eye diagram reveals the distortion due to trailing sub-pulses. On the other hand an increase in S split prevents the delayed phase variation from entirely closing the switching window leading to broad output pulses with tails determined by the gain recovery time of the SOAs. This broadening is easily observable in the eye diagram shown in Fig. 4-25 for S split =0.90. The phase 84 profiles for S split =0.90 shown in Fig. 4-25 clearly identify the undershoot of the delayed phase variation as the cause for the observed penalty. 4.5.2 Horizontal offset due to non-optimum D D D Dt It should be noted that delayed phase overshoots or undershoots can also occur if the differential delay between the copies of the pump perturbing the SOAs drifts from the value associated with the particular S split value. This condition can be envisioned as a horizontal shift between the two phase profiles for a fixed value of S split . Thus the optimal S split value depends on the differential delay Dt being used. If the phase variation in the delayed arm is initiated after a longer time (larger Dt) it requires lesser phase change to catch up with the original phase profile which has had a longer time to decay. This means that the S split required is larger. S split = 0.6 S split = 0.6 -0.5 0.5 1.5 2.5 0.55 0.65 0.75 0.85 Norm. Rx. penalty (dB) Signal Splitting Ratio (S split ) 2 ps 5 ps 8 ps D D D Dt S split = 0.85 D D D Dt=8ps D D D Dt=2ps Fig. 4-26. Variation of optimum signal splitting ratio with differential delay. 85 On the other hand, if Dt is smaller, a larger phase variation is required in the delayed arm to ensure that the delayed phase profile catches up with the original phase variation and the slow decays coincide. This corresponds to a case of smaller S split . As shown in Fig. 4-26 the optimal S split increases as Dt is increased. Since drifts in either of these parameters leads to delayed phase overshoots or undershoots, they have to be jointly optimized while keeping in mind the required output pulse width and shape. For all further simulations, Dt and S split are fixed at 5 ps and 0.75 respectively, to study an optimized DXPM wavelength converter that performs pulse-width preserving conversion. 4.5.3 Vertical offset due to non-optimum F F F F The sensitivity of the device to the phase-bias between the MZI arms [98] is shown in Fig. 4-27 where the penalty is calculated with respect to the optimum point. 0 2 4 0.94p p p p p p p p 1.06p p p p MZI Phase Bias (rad) Norm. Rx. Penalty (dB) Fig. 4-27. Sensitivity to MZI phase-bias in DXPM wavelength converters. 86 Under ideal conditions, the output signal’s extinction ratio can be maximized by ensuring that the power level in the 0’s is minimal. This can be achieved by setting the phase-bias between the MZI arms to ‘p’ which leads to perfect destructive interference between the probe components traveling in the two arms when there is no pump pulse present to perturb the SOAs. This condition is shown in Fig. 4-28 and closely resembles the ideal device response. Deviation in phase-bias from the optimum, increases the power in the output zeros due to imperfect destructive interference, leading to reduced eye opening. Such a deviation can be pictured as a vertical offset between the phase profiles of the two arms. 0 2 4 0.94p p p p p p p p 1.06p p p p MZI Phase Bias (rad) 0-level 0-level • ER reduces • Sub-pulses & power undershoots • ER is high • Phase recoveries coincide • ER reduces • Power undershoots & pulse broadening Destructive point Destructive point 0 Phase (a.u.) Phase variation in MZI Phase diff. t Norm. Rx. Penalty (dB) F F F F-bias=0.94p p p p F F F F-bias=p p p p F F F F-bias=1.06p p p p Fig. 4-28. Deleterious effects of non-optimum phase-bias in MZI. Deviation from optimum leads to a loss of extinction ratio. 87 F< causes an overshoot of the delayed phase variation (Fig. 4-28) that results in higher penalty than an undershoot seen at equal phase deviation above . The eye diagrams in Fig. 4-28 clearly depict the degradation caused by non-optimal phase bias conditions. It is worth noting that small deviations in the phase-bias can lead to fairly large power penalties pointing to the requirement of very accurate control of the phase-bias. 4.5.4 Vertical offset due to variation in input signal extinction ratio Even if the average input pump and probe powers for a DXPM wavelength converter are kept fixed, changes in the input signal’s extinction ratio can significantly impact the device’s performance. A deeper analysis reveals that ‘p’ is the optimum phase- bias only for cases when the input signal extinction ratio is high (>25 dB). If the input signal extinction ratio reduces, it effectively causes a vertical offset between the phase variations in the two arms, driving the device response away from optimum. To understand this behavior, one needs to recall the fact that the pump power is split unequally between the two arms to ensure that the phase recoveries coincide at the output of the MZI. For an input signal with high extinction ratio the power in the 0’s is negligible. When this 0-level power splits unequally between the two arms, neither component is large enough to perturb the SOAs. As a result the probe carrier waves emerging from the SOAs in the two arms have the same phase. Under this 88 condition a phase-bias of ‘p’ in one of the arms leads to perfect destructive interference and high output extinction ratio. However, if the input signal’s extinction ratio is low, the 0’s have some finite power. When this non-negligible power splits unequally between the two SOAs, it affects them differently. As a result, the probe carrier waves emerging from the two SOAs are not in phase anymore. This trend is shown in Fig. 4-29 where the phase of the probe carrier wave after the two SOAs is plotted against the input signal’s extinction ratio. 0 0.3 25 30 10 20 15 0.1 0.2 0.4 5 Input Extinction Ratio (dB) Normalized Probe Phase (rad) SOA1 (upper) SOA2 (lower) S split =0.75 Fig. 4-29. Dependence of the phase of the probe carrier emerging from the two SOAs on the input signal extinction ratio. For reducing extinction ratios, the probe carrier phases in the two arms deviate from each other. In such a situation, to ensure that the output 0-level is the minimum possible, the phase-shifter needs to introduce a phase-bias F<p while taking into account the phase-shift that already exists due to unequal splitting of the pump power. Even for this optimum phase-bias, the destructive interference is not perfect owing to the probe power imbalance between the two arms. As shown in Fig. 4-30 89 the optimum phase-bias asymptotically approaches ‘p’ as the input signal’s extinction ratio increases. Optimum f (p rad) 0.94 5 20 35 1.02 1 Input ER (dB) Fig. 4-30. Variation of optimum phase-bias with input signal extinction ratio. As the input signal extinction ratio increases, the optimum phase-bias asymptotically approaches a value close to ‘p’ radians. In fact, it is highly unlikely that the phase recoveries in the two SOAs will coincide perfectly due to their different saturation conditions and as a result the optimum phase bias may be slightly greater than ‘p’ to compensate for the slight overshoot of the delayed phase variation. From a system viewpoint, the dependence of the optimum phase-bias on the input signal’s extinction ratio is very important. To determine the trend of the penalties expected, simulations are performed and the output signal extinction ratio is plotted against phase-bias for different input signal extinction ratios. The results shown in Fig. 4-31 confirm two important effects – the optimal phase-bias point moves away from ‘p’ and the maximum achievable output extinction ratio drops as the input signal extinction ratio reduces. 90 O u t p u t E R ( d B ) 0 10 5 20 15 Phase-bias (p p p p rad) 0.9 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 O u t p u t E R ( d B ) 0 10 5 20 15 Phase-bias (p p p p rad) 0.9 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 ERin=21 ERin=15 ERin=9 ER=9 Fig. 4-31. Sensitivity of output signal extinction ratio to MZI phase-bias for different values of input signal extinction ratio. It is worth noting that the regenerative nature (extinction ratio enhancement from input to output) of the device is highly dependent on ensuring that the device operates at the optimal phase-bias condition. If the device is setup with a phase bias of ‘p’ assuming a high input extinction ratio, several dB of potential extinction ratio improvement may be lost if the input signal extinction ratio is low (~9 dB). Similarly, the phase-bias should not be kept fixed assuming a low input extinction ratio. This dependence implies that operating conditions for the DXPM wavelength converter should be determined based on a broad set of input signal parameters to enable robust device performance. The best regenerative behavior can be maintained by monitoring the input extinction ratio and dynamically adjusting the phase-bias to the optimum point. The impact of dynamic reconfiguration is shown in Fig. 4-32 where the output signal extinction ratio has been plotted against the input signal extinction ratio. 91 O u t p u t E R ( d B ) 0 10 5 20 15 Input ER (dB) F=1.02p F=optimum 5 20 15 25 10 O u t p u t E R ( d B ) 0 10 5 20 15 Input ER (dB) F=1.02p F=optimum 5 20 15 25 10 ER out =ER in Fig. 4-32. Enhancement of the regenerative window for DXPM wavelength converters. Maintaining the optimum phase-bias as the input signal’s extinction ratio changes improves the output extinction ratio by ~5 dB. The dotted line refers to an extinction ratio preserving wavelength converter. The plot shows that if the phase bias is kept fixed at F~p (optimal for high input extinction ratio) regeneration can be achieved only in a small window of input extinction ratios. This is because the fixed phase-bias is not optimal for lower extinction ratios where regeneration is even more important. However, if the phase- bias is dynamically optimized for each value of input extinction ratio, significant enhancement can be achieved leading to a much wider range of input extinction ratios that can be regenerated. Based on this analysis, one can envision deviations in the various operational parameters of the DXPM wavelength converter as perturbations to the device’s ideal temporal phase variations. Perturbations which amount to relative amplitude 92 changes or horizontal or vertical offsets between the original and delayed phase variations in the SOA-MZI structure lead to power penalties for the output signal. Variation in input signal properties, e.g. extinction ratio can also force the device away from its optimum operating condition pointing to the requirement of active monitoring of input signal metrics and dynamic optimization of the operational parameters of the wavelength converter. 4.6 Difference between DXPM and DISC configurations with respect to sensitivity to input signal extinction ratio As explained in the previous section, the optimum phase-bias for the DXPM wavelength converter moves away from ‘p’ as the input signal’s extinction ratio decreases. This trend has its roots in the fact that the input signal is split unequally between the two SOAs. The signal splitting ratio, S split is a critical parameter that differentiates the DXPM configuration from the DISC. In the DISC, the signal causes cross-phase modulation of the probe in a single SOA which is converted into amplitude modulation by a passive delay interferometer. Thus, the interfering components have identical phase modulation apart from a time delay introduced by the delay interferometer. This is equivalent to a DXPM converter with an S split value of 0.5. Thus, the DISC configuration can be thought of as a DXPM wavelength converter with equal splitting of the input signal between the two arms. 93 Under this condition the phase of the probe carrier wave in the two arms is always identical in the absence of a pump pulse, independent of the 0-level of the input signal. Therefore, complete destructive interference can be achieved using a phase- bias of ‘p’ independent of the input signal extinction ratio. O u t p u t E R ( d B ) 0 10 5 20 15 Phase-bias (p p p p rad) 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 0.9 25 O u t p u t E R ( d B ) 0 10 5 20 15 Phase-bias (p p p p rad) 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 0.9 25 Fig. 4-33. Sensitivity of output signal extinction ratio to MZI phase-bias for delayed-interference signal converters. If the sub-pulses are neglected, the optimum phase-bias remains at ‘p’ independent of the input signal extinction ratio. However, the absence of the extra degree of freedom (S split ) leads to an overshoot of the delayed phase variation that generates a sub-pulse following each main pulse in the output signal. If the sub-pulses are ignored and the output extinction ratio is calculated based on the power level of the 1’s relative to a string of 0’s it is observed that the optimum phase-bias remains at ‘p’ independent of the input extinction ratio as shown in Fig. 4-33. In reality however, the sub-pulses need to be suppressed by shifting the phase-bias away from ‘p’. Since higher input extinction ratios lead to greater cross-phase modulation and larger sub-pulses, the phase-bias needs to be 94 shifted further away from ‘p’ to suppress the sub-pulses. Therefore, the optimum phase-bias moves away from ‘p’ as the input signal extinction ratio increases. This is clearly shown in the results plotted in Fig. 4-34 where the sub-pulse is taken into account while calculating the output extinction ratio. S u b - p u l s e s u p p r e s s i o n ( d B ) 0 4 2 8 6 Phase-bias (p p p p rad) 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 0.90 10 S u b - p u l s e s u p p r e s s i o n ( d B ) 0 4 2 8 6 Phase-bias (p p p p rad) 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 ERin=21 ERin=15 ERin=9 0.90 10 Sub-pulse suppression= power in main pulse power in sub-pulse S u b - p u l s e s u p p r e s s i o n ( d B ) 0 4 2 8 6 Phase-bias (p p p p rad) 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 0.90 10 S u b - p u l s e s u p p r e s s i o n ( d B ) 0 4 2 8 6 Phase-bias (p p p p rad) 0.95 1 1.1 1.05 ERin=21 ERin=15 ERin=9 ERin=21 ERin=15 ERin=9 0.90 10 Sub-pulse suppression= power in main pulse power in sub-pulse Fig. 4-34. Sensitivity of output signal extinction ratio to MZI phase-bias for delayed-interference signal converters if the sub-pulses are included. The optimum phase-bias moves away from ‘p’ as the input signal extinction ratio increases. This dependence of optimum phase-bias on input signal extinction ratio for the DISC is opposite to that observed for DXPM and is a key differentiator between the two configurations. If the input signal’s extinction ratio is monitored to dynamically adjust the phase-bias, the control system needs to take into account this difference between the two configurations. 95 Chapter 5 Design and implementation of a 160 Gb/s optical time- division multiplexing system Optical time division multiplexing (OTDM) [55, 104] is commonly employed as a means of generating data signals with bit-rates in excess of those achievable through purely electronic modulation techniques. State-of-the-art electronic time-division multiplexing (ETDM) has been used to achieve single channel data rates of 107 Gb/s [110] for 100 Gb/s Ethernet applications [93]. However, for higher data-rates e.g. 160 Gb/s, OTDM is the only option available currently. The generic block diagram of an OTDM system is shown in Fig. 5-1. Mode-locked Laser CLK 10 GHz 10 GHz, 2 ps FWHM Modulator DATA 10 Gb/s System under test Demultiplexer Multiplexer Receiver 10 Gb/s 10:160 Gb/s Fig. 5-1. Block diagram of an optical time-division multiplexing system. The transmitter is based around a short-pulse source with a repetition rate equal to the base-rate (individual channel data rate). The base-rate should be low enough to allow modulation using conventional optical modulators (40 Gb/s). The pulse- width should be narrow enough to accommodate the line-rate (multiplexed data rate) 96 with negligible pulse-overlap. For example, for a 160 Gb/s OTDM system, the transmitter may be based on a 10 GHz or 40 GHz pulse source with pulse-widths ~2 ps. The pulses are encoded with data using a base-rate modulator. Following the modulation, the different data streams are combined together with appropriate relative delays to generate the line-rate multiplexed output. The system under test should introduce negligible overall pulse broadening in order to maintain the line- rate RZ nature of the data. At the receiver end, the line-rate data passes through a time-division demultiplexer that switches out one base-rate channel out of the multiplexed data stream. The job of the demultiplexer boils down to generating narrow (width < line-rate bit-slot) switching windows with a repetition rate equal to the base-rate. The temporal location of the switching window relative to the multiplexed data can be tuned, allowing the receiver to recover any of the base-rate channels. The ideal demultiplexer should be able to simultaneously demultiplex all the base-rate channels. Each individual channel is fed to a base-rate receiver which converts the data back into electronic form. The performance of a high speed (80 Gb/s) OTDM system hinges on several critical components. At the transmitter end, various methods to generate short-pulses have been explored [55, 103, 106, 112, 115]. Mode-locked lasers are the most popular short-pulse sources since they offer high extinction ratios (30 dB) and pulse-widths between 1-2 ps. Both semiconductor and fiber-based versions have been used [14, 26]. The system under test, including any inline amplifiers needs to 97 have minimal dispersion to prevent excessive broadening of pulses that may lead to pulse-overlap. Transmission systems require very accurate dispersion compensation since the short-pulses have large spectral widths that may lead to high penalties for small amounts of residual dispersion. At the receiver end, several techniques have been demonstrated to generate narrow switching windows for demultiplexing. Most of these methods rely on optically controlled switching where the interaction of the line-rate signal with a periodic optical switching signal leads to demultiplexing. The nonlinearities exploited include four-wave mixing [70, 80], cross-phase modulation and filtering-assisted cross-gain modulation [90] in SOAs. Wave-mixing in other media e.g. highly nonlinear fiber [48, 51] and electro-absorption modulators [3] has also been used. Typically, optically-induced switching requires another source of narrow pulses repeating at the base-rate. As a popular alternative, electro-absorption modulators (EAMs) which are capable of generating electrically-controlled narrow switching windows [13] have also been used. The inherent nonlinear transfer function of the EAM [54] converts a sinusoidal electrical signal into narrow switching windows with a repetition rate equal to the frequency of the sinusoid. EAMs which generate switching window widths ~5 ps when driven with a 40 GHz electrical clock are commercially available. The demultiplexing technique used should be able to create high-quality switching windows with large extinction ratio and narrow-enough pulse-widths. Typically, a tradeoff is noted between these two requirements. For example, the switching window widths generated by EAMs are inversely proportional to the frequency of the electrical driving clock but the 98 modulation bandwidth of the EAM imposes limitations on the achievable extinction ratio as the drive frequency increases. 5.1 Performance of the transmitter subsystem The design of the 160 Gb/s transmitter is shown in Fig. 5-2. It comprises of a tunable semiconductor mode-locked laser, a 10 Gb/s electro-optic Mach-Zehnder modulator and a passive split-delay-combine multiplexer. Mode-locked Laser CLK Pattern Generator MOD 10 GHz Optical Time Division Multiplexer D D D Dt=(W/2 + 50) ps D D D Dt=(W/4 + 25) ps D D D Dt=(W/8 + 12.5) ps D D D Dt=(W/16 + 6.25) ps W: PRBS Word Length 10 Gb/s 20 Gb/s 40 Gb/s 80 Gb/s 160 Gb/s 10 GHz, 2 ps FWHM EDFA Fig. 5-2. OTDM transmitter comprising of a short-pulse source, modulator and split- delay-combine multiplexer. The laser is locked to the frequency of an external synthesizer. The locking frequency can be varied between 9.8 and 10.8 GHz which includes the native OC- 192 base-rate (9.953 Gb/s) and the 7% overhead forward error correction (FEC)- inclusive base-rate (10.709 Gb/s). The wavelength of the mode-locked laser can be tuned from ~1425 to 1575 nm. For basic system analysis the laser is operated at 99 1550 nm and emits pulses with a full-width at half maxima (FWHM) of ~1.8 ps. The pulse train from the mode-locked laser passes through a lithium niobate electro- optic intensity modulator where it is encoded with PRBS data at the base-rate (chosen to be 10.736 Gb/s) obtained from a bit-pattern generator. Even though the electrical drive signal to the modulator is NRZ in nature, the output base-rate data is very-low duty-cycle RZ since the data is modulated onto the narrow pulses. An electrical phase shifter is used to temporally align the electrical pulses driving the modulator with the optical pulses passing through it to ensure good extinction ratio of the output data. An EDFA amplifies the data to compensate for the loss of the modulator and the multiplexer which follows the EDFA. The multiplexer is of the split-delay-combine kind and consists of four stages, each of which doubles the bit-rate. The splitter in the first stage splits the incoming 10.736 Gb/s signal into two copies which are recombined after one of the copies has been delayed appropriately. The relative delay introduces an overall half-bit (based on the input bit-slot) offset between the two copies so that the output at the end of the stage has a bit-rate of 21.472 Gb/s. However, in order to ensure that the multiplexed output maintains the PRBS nature of the data stream, the delay also needs to include a relative time-shift of half the PRBS word length between the two paths in the multiplexer. For example, if a 2 7 -1 PRBS is used, a 64 bit additional delay is required in one of the paths. At the bit-rate being considered, this amounts to approximately 1 m of fiber. As the PRBS order 100 increases, so does the required fiber length. It is difficult to accommodate long and accurate lengths of fiber in a small form-factor. As a result commercially available split-delay-combine multiplexers are limited to 2 7 -1 PRBS. Even if higher order PRBS data is used at the input to the multiplexer, the output is fairly random in nature but does not meet the strict statistical properties of a true higher order (>7) PRBS. One of the paths in each multiplexer stage also contains a variable attenuator so that the pulse powers in both paths can be equalized. As the original data passes through the different stages of the multiplexer its bit-rate increases from 10.736 to 21.472, 42.944, 85.888, and 171.776 Gb/s. Since both outputs of each splitter are used except for the one at the end of the last stage only a 3 dB loss is incurred apart from the insertion losses of the various components. Since polarization maintaining components are not used in the multiplexer, the output pulses do not follow any polarization pattern relative to each other. Another mode of operation is possible where output pulses are forced to maintain specific polarization states relative to each other. As shown in Fig. 5-2, polarization controllers are added before the multiplexer and in each stage of the multiplexer. A polarizer is connected to the unused port of the final output coupler. Each stage is switched on one at a time and the polarization state of the output pulses arising from the delayed arm is adjusted using the polarization controllers to maximize transmission through the polarizer. Once this procedure is carried out for each stage, the output of the polarizer can be used as a single-polarization 171.776 Gb/s signal. 101 If bit-to-bit alternating polarization is required the polarization controller in the last stage is adjusted to minimize the power transmission of the delayed pulses through the polarizer. The signal emerging from the output port without the polarizer exhibits alternating bit-to-bit polarization. Once the laser is locked to a repetition rate of 10 GHz, the signal quality is analyzed through autocorrelation measurements. Fig. 5-3(a) shows the pulse train as observed using a 40 GHz bandwidth receiver and Fig. 5-3(b) shows the autocorrelation trace of the pulse. Autocorrelation Trace for Output Pulses Time (1.03 ps/div.) Voltage (50 mV/div.) 10 GHz Pulse Width: 1.85 ps FWHM Pulses (40 GHz BW detector) 1 mW Time (50 ps/div.) Optical power (1 mW/div.) (a) (b) Fig. 5-3. (a) 10 GHz short-pulse train from a mode-locked laser observed using a 40 GHz detector. (b) Autocorrelation trace of the pulses: pulse-width of 1.85 ps. 102 The signal is also analyzed in the spectral domain where well-defined modes spaced at 10 GHz are observed as shown in Fig. 5-4(a). A close up of the modes obtained through a high-resolution optical spectrum analyzer is shown in Fig. 5-4(b). Spectrum (0.2 pm res.) Spectrum (10 pm res.) Optical power (5 dBm/div.) Optical power (5 dBm/div.) Wavelength (1 nm/div.) Wavelength (0.02 nm/div.) (a) (b) Fig. 5-4. (a) Mode-locked spectrum of the 10 GHz short pulse train. (b) Close-up of the individual modes showing good spectral quality. In order to measure the pulse-widths and pulse spacing for multiplexed data streams beyond 40 Gb/s, autocorrelators are used. Uniform pulse spacing is critical and the multiplexer delays have to be accurately matched to the original repetition rate of the laser. As shown in Fig. 5-5, the final 160 Gb/s multiplexed data stream shows 103 uniform pulse spacing. The variation in the power of individual autocorrelation peaks arises due to the non-uniformity in the autocorrelation window as determined by the apparatus itself. Autocorrelation Trace for OTDM Pulses 160 GHz Time (10.3 ps/div.) Voltage (30 mV/div.) 80 GHz 40 GHz Fig. 5-5. Autocorrelation traces of 40, 80 and 160 Gb/s signals 5.2 Performance of the receiver subsystem At the receiver end of the system, an optical time-division demultiplexer is required. The job of the demultiplexer is to extract one base-rate channel out of the multiplexed line-rate data stream. This amounts to generating gating windows which repeat at the base-rate and have an ideal width equal to the line-rate bit-slot as shown in Fig. 5-6. The quality of the gating window determines the power penalty added to the system by the demultiplexer. As the ratio between the line-rate and base-rate increases (higher order of multiplexing), the duty cycle of the square wave switching window in the demultiplexer reduces. Designing a demultiplexer with narrow 104 switching windows and high extinction ratios to prevent crosstalk from adjacent time-slots is quite challenging. Receiver Error Detector Optical Time Division Demultiplexer Some form of optical/electronic gating 160 Gb/s data t 0110101001010010111111001010010110101110 t 160 Gb/s input Gating window 10 Gb/s output Ideal window width ~ 6.25 ps Window repetition = 10 GHz Fig. 5-6. Concept of time-domain demultiplexing of high-speed signals. The demultiplexer creates switching windows with width ~ line-rate bit-slot and base-rate repetition frequency. Several techniques have been proposed and demonstrated for 160 Gb/s line-rate demultiplexing. Techniques that exploit fiber based nonlinearities are ultra-fast and use optically controlled switching windows that can be made very narrow using short-pulses from a mode-locked laser as the control signal. However, dispersion induced walk-off restricts the fiber lengths and the corresponding conversion efficiency, requiring high powers to be used. Integrated solutions have focused on semiconductor optical amplifiers (SOAs) and electro-absorption modulators (EAMs). Four-wave mixing (FWM) in either device [70, 103] offers a high-speed nonlinearity but slow carrier dynamics complicate the operation due to pattern dependence issues. Cross-phase modulation in SOA-based interferometers is 105 another feasible solution where differential mode can be used to generate narrow switching windows. EAMs offer the welcome alternative of using electrically controlled switching windows to perform the demultiplexing [13, 16]. This technique relies on the fact that the nonlinear transfer function of an EAM results in narrow switching windows (width << time-period) when the EAM is driven by a sinusoidal electrical signal at the base-rate frequency. 5.2.1 Demultiplexing using a PPLN waveguide Another option worth exploring is to generate narrow gating windows through wavelength conversion in a periodically-poled lithium niobate (PPLN) waveguide. The operation of the PPLN waveguide is described in detail in chapter 2. The 160 Gb/s data signal acts as the pump for the PPLN waveguide while a 10 GHz, 2 ps FWHM pulse train is injected as a signal. The pump undergoes second harmonic generation (SHG) and the product mixes with the signal to generate a wavelength converted output through difference frequency generation (DFG). The 10 GHz pulse train is temporally synchronized with one of the sixteen channels that form the 160 Gb/s data stream and only when there is a pulse present on this channel, the signal pulse gets converted to the output wavelength. By isolating the output wavelength through filtering, the demultiplexed channel is recovered. The PPLN waveguide’s wavelength conversion spectrum for the case of 42.8 Gb/s pump and 10.7 GHz pulse train as the pump is shown in Fig. 5-7. 106 1546.5 1562.5 Wavelength (2 nm/div.) 1554.5 10.7 GHz pulse train (signal) 42.8 Gb/s data (pump) 10.7 Gb/s demultiplexed data Power (5 dB/div.) Fig. 5-7. Wavelength conversion spectrum of a 42.8 Gb/s -to- 10.7 Gb/s demultiplexer using a periodically-poled lithium niobate waveguide. The demultiplexing operation results in a 10.7 Gb/s channel extracted from the original data stream, as shown in Fig. 5-8. Optical Time Division Demultiplexer Periodically Poled Lithium Niobate Waveguide 42.8 Gb/s Data 10.7 GHz Pulse Train Wavelength converted demuxed 10.7 Gb/s Data Time (20 ps/div.) Fig. 5-8. Eye diagram of the demultiplexed output channel The conversion efficiency of the PPLN waveguide increases with the length of the waveguide. However, since the conversion process involves mixing of the pump’s SH component (~777 nm) with the pulse train (~1549 nm), there is significant group 107 velocity mismatch between the waves, if the waveguide length is too long [36, 116]. The waveguide length needs to be short enough to limit the group-velocity mismatch-induced walkoff between the SH and signal waves to a small percentage of the line-rate time-slot. If this condition is not satisfied, significant cross-talk from channels adjacent to the one being demultiplexed is expected. For 160 Gb/s, this length reduces to ~2-3 mm and the conversion efficiency takes a large hit, potentially making this technique difficult to implement unless much higher conversion efficiency waveguides are available. The waveguide used for the 42.8 Gb/s demultiplexing is ~5 cm long and exhibits <15 dB conversion efficiency. Techniques aimed at compensating for group-velocity mismatch [36] may help enable higher speed demultiplexing using PPLN waveguides. 5.2.2 Demultiplexing using electro-absorption modulators Electro-absorption modulators have emerged as a popular device for implementing time-domain signal processing functions. These include short pulse generation [115], demultiplexing [16], clock-recovery [3] and add/drop multiplexing [13]. Optically-controlled nonlinear processes occurring in EAMs, including cross- absorption modulation and four-wave mixing have been used for various applications. In addition, the nonlinear optical power transfer characteristics of EAMs driven by electrical signals have been explored extensively for high speed demultiplexing. If an EAM is driven by a sinusoidal electrical clock, it generates switching windows with widths much narrower than the time period of the driving 108 signal. If a CW beam is passing through the EAM, the output is a short-pulse train with a repetition rate equal to the frequency of the driving signal. However, if the optical input is a high-speed TDM data stream, a single channel can be switched out if the driving frequency matches the base-rate and the switching window widths are narrow enough to induce negligible crosstalk from neighboring channels. The switching window width for an EAM is inversely proportional to the frequency of the driving signal. Therefore, the crosstalk from adjacent channels reduces if a higher base-rate is used. However, the EAM modulation bandwidth is also limited and if the drive frequency exceeds the bandwidth, it will lead to a loss of extinction ratio in the switching window, leading to leakage from adjacent channels. Typically, dual-stage architecture is adopted if the base-rate is significantly lower than the line- rate [13], although some advanced driving techniques that enable single stage demultiplexing have been reported [16]. For example if the base-rate is 10 Gb/s and the line-rate is 160 Gb/s, the demultiplexer comprises of an EAM driven with a 40 GHz clock to generate narrow switching windows capable of extracting a 40 Gb/s channel from the 160 Gb/s data stream. This is followed by a second stage EAM driven by a 10 GHz clock which demultiplexes the 40 Gb/s data stream into a single 10 Gb/s base-rate channel which can be handled by the electronic modules for error- rate measurements and other processing. This complete OTDM system setup is shown in Fig. 5-9. Of course, the switching windows in both stages have to be accurately synchronized (using RF delay lines) to the data stream so that the peaks of 109 the switching windows are temporally-aligned with the peaks of the pulses corresponding to the channel of interest. EA-MOD Rx EA-MOD Optical Time Division Multiplexer D D D Dt=(W/2 + 50) ps D D D Dt=(W/4 + 25) ps D D D Dt=(W/8 + 12.5) ps D D D Dt=(W/16 + 6.25) ps X4 10 GHz 40 GHz RF Delay Lines W: PRBS Word Length 20 Gb/s 40 Gb/s 80 Gb/s 160 Gb/s 10 Gb/s 40 Gb/s 160 Gb/s Optical Time Division Demultiplexer Mode-locked Laser CLK Pattern Generator MOD 10 GHz Error Detector 10 Gb/s 10 GHz, 2 ps FWHM Fig. 5-9. Experimental setup for demultiplexing using electro-absorption modulators. A two-stage design is shown where the first stage switches out an intermediate rate channel which is demultiplexed down to base-rate in the second stage. To determine the quality of the switching windows generated, a CW beam is coupled into the first EAM (driven by a 42.944 GHz sinusoidal electrical clock) and the 42.944 GHz pulse train generated is observed using an autocorrelator. As confirmed through the autocorrelation trace shown in Fig. 5-10, the EAM generates a ~6.1 ps FWHM switching window that repeats at a rate of 42.944 GHz. Since the driving frequency is well beyond the modulation bandwidth (~32 GHz) of the EAM used, the extinction ratio takes a hit. The variation in the amplitude of the individual autocorrelation peaks arises due to the non-uniformity of the autocorrelation window 110 determined by the apparatus itself. Moreover, the autocorrelation window spans ~90 ps and as a result the peaks at the edges are severely attenuated. Autocorrelation window Demux Stage 1 Switching Window Stage 1: 42.944 GHz, 6.1 ps FWHM Time (10.3 ps/div.) V oltage (100 m V /div.) Fig. 5-10. Autocorrelation trace of the switching windows in the first stage of the demultiplexer. The EAM generates a 42.944 GHz, 6.1 ps FWHM switching window. The pulse train is then passed through the second EAM which is driven by a 10.736 GHz electrical clock. The RF delay line for the clock signal is adjusted to ensure that the peak of the sinusoid coincides with one of the pulses inside the EAM. The autocorrelation trace of the output of the second EAM is shown in Fig. 5-11. The trace of the first EAM’s output is also included for comparison. As expected, only one of the four pulses remains while the others are suppressed. Even though the second EAM generates much broader switching windows, since the first EAM has already carved out a narrow pulse, the pulse-width of the single remaining pulse is unchanged. However, the broader window in the second EAM allows some finite 111 amount of crosstalk from the adjacent pulses. This is visible at the floor of the trace in Fig. 5-11. Time (10.3 ps/div.) Voltage (100 m V/div.) Switching Window Stage 1 + 2: 10.736 GHz, 6.1 ps FWHM Demux Stage 1+2 Demux Stage 1 Fig. 5-11. Autocorrelation trace of the overall switching window of the two-stage demultiplexer. The cascaded EAMs generate a 10.736 GHz, 6.1 ps FWHM switching window. 5.3 Demultiplexing of an 80 Gb/s signal using EAMs The cascading of the two EAMs implements a demultiplexer with a switching window width of ~6.1 ps and repetition rate of 10.736 GHz. This window width is sufficiently narrow to demultiplex a signal from 85.888 Gb/s down to 10.736 Gb/s but not good enough for demultiplexing a 171.776 Gb/s signal due to excessive crosstalk. In fact, for demultiplexing an 85.888 Gb/s signal, the first stage can be driven by a 21.472 GHz clock as a narrow enough switching window is generated at this lower driving frequency and the extinction ratio improves because the device operates well within its modulation bandwidth. Fig. 5-12 shows the eye diagrams of 112 the 85.888 Gb/s signal and the four 21.472 Gb/s tributaries obtained after the first stage EAM in the demultiplexer. The EAM is reverse biased at 3 V and driven with a 4 V p-p 21.472 GHz electrical clock. The signals are observed using a 30 GHz receiver as a result of which the 85.888 Gb/s RZ signal looks like an NRZ signal. 85.888 Gb/s 21.472 Gb/s 5 ps 20 ps Ch #2 Ch #3 Ch #4 Demux Stage 1 (21.472 GHz drive) Ch #1 Fig. 5-12. Eye diagrams obtained after the first stage of the demultiplexer that performs 85.888 Gb/s -to- 21.472 Gb/s demultiplexing. The EAM is reverse biased at 3 V and driven with a 4 V p-p 21.472 GHz electrical clock. The demultiplexed eyes show a clear opening indicating high quality operation of the EAM. This signal is then passed through the second stage EAM driven by a 10.736 GHz electrical clock. The eye diagrams of the eight, base-rate (10.736 Gb/s) channels demultiplexed from the 85.888 Gb/s data stream using the dual-stage EAM- based demultiplexer are shown in Fig. 5-13 and a sequence of the corresponding bits is shown in Fig. 5-14. 113 85.888 Gb/s 5 ps Demux Stage 1 (21.472 GHz drive) + Demux Stage 2 (10.736 GHz drive) 20 ps 10.736 Gb/s Ch #2 Ch #7 Ch #8 . . . . Ch #1 4 mW Fig. 5-13. Eye diagrams obtained after the second stage of the demultiplexer. The 21.472 Gb/s signals are stepped down to 10.736 Gb/s. The second EAM is reverse biased at 3.2 V and driven with a 5 V p-p 10.736 GHz electrical clock. 20 ps 10.736 Gb/s Ch #2 Ch #7 Ch #8 . . . . Ch #1 4 mW Fig. 5-14. Bit patterns of all eight base-rate channels obtained after the two-stage demultiplexer. The line-rate signal at 85.888 Gb/s is stepped down to 10.736 Gb/s. 114 Bit-error rate measurements are carried out on the demultiplexed channels. The power penalty of the best demultiplexed channel compared to a back-to-back 10.736 Gb/s signal is ~0.1 dB as shown in Fig. 5-15. These measurements show that the multiplexer and demultiplexer introduce almost negligible penalty into the system. -22 -21 -20 -19 -18 3 4 5 6 7 8 9 10 -Log (BER) Received Power (dBm) Bk-to-bk 10 Gb/s 80-to-10 Gb/s demuxed Fig. 5-15. Bit-error-rate measurements of the 10.736 Gb/s channel demultiplexed from an 85.888 Gb/s signal. The best-case channel shows negligible penalty compared to a back-to-back measurement for a base-rate channel. 5.4 Demultiplexing of a 160 Gb/s signal using EAMs In order to demultiplex a 171.776 Gb/s signal, an optimal combination of switching window width and extinction ratio is needed. If a 42.944 GHz electrical clock is used in the first stage, the extinction ratio reduces drastically due to bandwidth limitations of the EAM while a 21.472 GHz clock results in unacceptably wide switching windows. Both constraints result in crosstalk from adjacent bit-slots. The reverse-bias for the EAM, the drive signal’s peak-to-peak voltage swing and the optical signal’s polarization need to be carefully controlled in order to enable 115 successful demultiplexing of 171.776 Gb/s signals. A non-error-free sample of single-stage demultiplexed eye diagrams (171.776 to 21.472 Gb/s) is shown in Fig. 5-16. Further optimization of the drive conditions and a first stage EAM with narrower pulse-widths is expected to provide error-free performance. Ch #2 Ch #7 Ch #8 . . . . Ch #1 10 ps 4 mW 21.472 Gb/s Fig. 5-16. Eye diagrams obtained for single-stage demultiplexing of a 171.776 Gb/s signal down to eight 21.472 Gb/s signals. The EAM is reverse biased at 3 V and driven with a 4 V p-p 21.472 GHz electrical clock. The cross-talk observed is due to excessively broad switching windows. The use of EAMs is a popular technique for demultiplexing of high-speed data signals and several successful experiments have served to validate it [13, 16, 55, 103, 104]. Nevertheless, the tradeoff between extinction ratio and switching window width as the electrical drive frequency is increased forces careful optimization of drive conditions in order to achieve error-free demultiplexing. 116 Chapter 6 Phase-reconstructive wavelength conversion of OTDM signals using an SOA-MZI to generate high-speed coherent phase-correlated signals Two of the most common methods to increase the data transport capacity per fiber are wavelength division multiplexing (WDM) and time division multiplexing (TDM). In WDM, multiple wavelengths are modulated with data from different channels and are coupled together before being launched over the same fiber while TDM involves time-interleaving of the data from different transmitters. In order to achieve efficient high-speed traffic aggregation, WDM and TDM technologies are used in a complementary fashion. At the same time, technology commercialization is driven by a reduction in the transmission cost per bit. As a result, optical transmission research is aimed at achieving higher bit-rates over longer distances at a reduced cost. With the conventional on-off keyed (OOK) formats, an increase in per-channel data-rates translates into narrower pulse-widths (broader spectra) leading to increased sensitivity to fiber dispersion. At the same time, squeezing multiple channels closer together in the spectral-domain leads to larger penalties from nonlinear effects and narrow filtering. These problems have led to the emergence of ‘advanced modulation formats’ [109] that can potentially enable robust transmission systems with much higher spectral efficiency compared to OOK formats. 117 6.1 Advanced modulation formats Phase-correlated modulation formats have emerged as promising options for next generation transmission systems due to their increased robustness to fiber-based impairments and signal-to-noise ratio degradation [7]. These formats include those that carry information in the phase transitions of a constant envelope signal, e.g. differential-phase-shift-keying (DPSK) and ones which maintain specific bit-to-bit phase relationships even though the information is carried in the intensity transitions, e.g. carrier-suppressed return-to-zero (CSRZ). Figure 6-1 highlights some such advanced modulation formats, their temporal-phase characteristics and their primary advantages. Format Temporal Phase Variation Advantages CSRZ Phase alternates between 0 and p High NL tolerance for adjacent bit-slots PAP-CSRZ Phase alternates between 0 and p High NL tolerance for adjacent pairs of bit-slots GAP-CSRZ Phase alternates between 0 and p Sub-harmonic CLK rec. for adjacent groups of 4 bit-slots DPSK Phase changes between 0 and p Low OSNR requirement based on binary data AMI Phase changes between 0 and p High NL tolerance for successive ‘1’ bits Duobinary Phase changes between 0 and p High CD tolerance for ‘1’ bits separated by odd # of ‘0’ bits Fig. 6-1. Advanced modulation formats, their temporal-phase characteristics and their primary advantages. 118 Since these formats rely on specific phase relationships between bits, their generation requires some mechanism for phase modulation. Conventional generation techniques are based on the Mach-Zehnder modulator (MZM) which enables both intensity and phase modulation [109]. However if the single-channel data-rates desired are in excess of those achievable through commercial MZMs, optical time-division multiplexing (OTDM) is required. OTDM involves interleaving optical pulses of one data stream with another data stream to form a single high-speed signal. Although this approach is valid for conventional on-off keying (OOK), it does not maintain phase relationships between adjacent bits of the multiplexed output [62] and is thus not readily usable for generating high-speed phase-correlated signals. As shown in Fig. 6-2, in a lab environment, a split-delay- combine multiplexer is used to generate high speed OTDM signals. The bit-rate doubles after every stage of the multiplexer, but bit-to-bit phase relationships are lost. The primary reason for this is the drift in the fiber delays used in the multiplexer. Even for short PRBS (2 7 -1) the delays required are too long to be realized in an integrated structure, making temperature control very difficult. Vibration and temperature changes can easily cause the fiber lengths to change by 10’s of nm, large enough to induce a fractional change in the phase of the optical carrier at conventional communication wavelengths. This lack of phase-coherence manifests itself as the absence of well-defined tones in the multiplexed spectrum as shown in Fig. 6-2. 119 Mode-locked Laser MOD Optical Time Division Multiplexer D D D Dt=(W/2 + 50) ps D D D Dt=(W/4 + 25) ps D D D Dt=(W/8 + 12.5) ps D D D Dt=(W/16 + 6.25) ps W: PRBS Word Length 160 Gb/s 10 GHz, 2 ps FWHM 10 Gb/s 20 Gb/s 40 Gb/s 80 Gb/s Power (5 dB/div.) Wavelength (1 nm/div.) t t Loss of phase coherence No phase relationship between adjacent pulses 10 Gb/s 80 Gb/s Fig. 6-2. Loss of bit-to-bit phase relationship in OTDM signals as observed through spectral instability. Moreover, spectral instability is observed as the relative powers of the peaks in the spectrum change rapidly over time. Since conventional OTDM fails, a module that is capable of converting incoherently-multiplexed OOK signals into high-speed coherent phase-modulated signals is desired. 6.2 Generation of high-speed phase-correlated signals Generation of high speed phase-correlated signals has been previously demonstrated using nonlinear polarization rotation in highly nonlinear fiber (HNLF) [64]. A CW probe light is propagated through the HNLF and a polarizer at the output is arranged 120 such that it blocks the light. When a co-propagating pump pulse is injected into the HNLF it induces cross-phase modulation on the probe, leading to a rotation of its polarization state. The polarizer at the output converts this polarization modulation into intensity modulation. Thus, the intensity information of the pump signal is transferred onto the probe wavelength. Since the polarization modulation results purely from the intensity variations of the pump signal, the pump can be an incoherently time-division-multiplexed signal. At the same time the phase of the output probe pulses can be controlled through the polarization of the pump pulses. If the polarization of the pump is flipped by 90°, the phase of the probe output is changed by ‘p’. In this way, intensity and polarization information of the incoherent, high-speed pump signal is translated into intensity and phase modulation of a new coherent carrier wave enabling the generation of high-speed phase coherent signals. Since the technique relies on the ultra-high-speed Kerr nonlinearity [62] data-rates in the 100’s of Gb/s regime are possible and CSRZ signal generation has been shown at 320 Gb/s [85]. However, this method requires a long fiber length to achieve suitable amount of polarization rotation which leads to walkoff between the pump and probe waves. To prevent the walkoff from affecting the performance of the module, the pump and probe wavelengths need to be specifically positioned relative to the zero- dispersion wavelength of the fiber. Moreover, input signal polarization needs to be carefully controlled to obtain accurate [0,p] phase relationship between the output pulses. Also, high average powers (~20 dBm) are required to achieve adequate cross-phase modulation and stimulated Brillouin scattering needs to be suppressed 121 which requires additional equipment. As an alternative, it is desirable to develop an integrated module that can convert incoherent OTDM signals into high-speed phase- correlated signals. The popular nonlinear device for integrated optical signal processing modules is the semiconductor optical amplifier (SOA). Several nonlinear processes occur in SOAs some of which are described in chapter 2. For the application being considered, the following features are desired · Nonlinearity dependent on input signal power variations but independent of input signal phase variations · Potential for >40 Gb/s data rates · Reasonable input signal power requirements · Polarization independence · Flexibility in choosing input and output wavelength One of the processes that meet these requirements is differential cross-phase modulation (DXPM) in the semiconductor optical amplifier-Mach Zehnder interferometer (SOA-MZI) structure. Recent work [101] has shown that the SOA- MZI can be used for wavelength conversion of DPSK signals, opening up the possibility of exploiting it for phase-processing of incoherent signals. The aim is to develop a reconfigurable module capable of generating multiple high-speed phase- modulated formats, as depicted in Fig. 6-3. 122 Phase-correlated signal generator Multiple low-rate OOK signals CSRZ PAP-CSRZ GAP-CSRZ DPSK AMI Duobinary Integrated Polarization-insensitive Low input signal power Wavelength flexibility Fig. 6-3. Multiplexing of OOK signals into a single phase-modulated signal 6.3 Coherent phase control through DXPM in an SOA-MZI The operating principles of DXPM in an SOA-MZI have been described in detail in chapter 4. In order to explore its use for phase modulation, an understanding of the dynamics of the device down to the level of carrier phase variations is required. As shown in Fig. 6-4 an SOA-MZI structure comprises of two SOAs placed in the arms of a symmetric MZI. A phase shifter in one of the arms enables control over the interference conditions at the output coupler of the MZI. The input coupler of the MZI is used to split the power of a CW laser (probe) between the two arms. Each SOA’s input is connected to another coupler for injecting the pump (control) signals. Under ideal operating conditions, both SOAs are biased with equal currents and the phase shifter is adjusted to provide a phase shift of ‘p’ for the probe wavelength. As a result, in the absence of any control signals, the amplified probe output from the SOAs cancels out due to destructive interference. This situation is depicted in Fig. 6-4(a) where the probe carrier in the upper arm at the output coupler is represented by a red sinusoid while that in the lower arm is shown as a blue sinusoid. 123 SOA 2 SOA 1 Filter OFF OFF CW Probe Phase (p p p p) Probe carrier Probe carrier SOA 2 SOA 1 Filter ON OFF CW Probe Phase (p) SOA 2 SOA 1 Filter OFF ON CW Probe Output carrier Phase (p) LOW HIGH F F F F = 0 HIGH F F F F = p p p p Relative p p p p phase change Destructive interference Output LOW Constructive interference Output HIGH Phase = 0 Constructive interference Output HIGH Phase = p p p p (a) (b) (c) Output Output carrier XPM XPM Fig. 6-4. (a) Destructive interference in the SOA-MZI. (b) Constructive interference with output phase ‘0’. (c) Constructive interference with output phase ‘p’. The carrier after interference is not shown since ideally it has zero power. As shown in Fig. 6-4(b), if the control signal injected in to the upper arm is ‘ON’, it causes a phase change of ‘p’ for the probe carrier wave through the process of cross-phase modulation. This leads to perfect constructive interference at the output coupler. The phase of the probe carrier at the output (black) of the MZI is the same as that of the carrier in the lower arm (after the phase shifter). Note that the phase of the carrier in the upper arm after the control signal-induced shift is also the same. However, if the upper arm is unperturbed and the lower arm’s control input causes a ‘p’ phase shift, the situation shown in Fig. 6-4(c) is produced. In this case, again there is perfect constructive interference but the phase of the output probe carrier is 124 out of phase by ‘p’ relative to the output in Fig. 6-4(b). Thus, the phase of the output probe carrier is determined by the particular control signal (upper or lower) that perturbs the system. A control pulse in the upper arm will produce an output pulse due to constructive interference just the way a control pulse in the lower arm would. But there is a relative phase difference of ‘p’ between the probe output pulses for these two cases. Carrier Amplitude (a.u.) 2 0 -2 2 0 -2 2 0 -2 2 0 -2 2 0 -2 2 0 -2 Time (Time period) 0 2 0 2 Upper DF DF DF DF=0.5p p p p Lower DF DF DF DF=0.5p p p p DF DF DF DF=0 Upper DF DF DF DF=0.7p p p p Lower DF DF DF DF=0.7p p p p DF DF DF DF=0 Lower armUpper arm Output Lower armUpper arm Output Perfect destructive interference XPM in upper arm XPM in lower arm p p p p phase difference p p p p phase difference Fig. 6-5. Phase properties of the output signal generated through cross-phase modulation. A relative phase difference of ‘p’ exists between the two output carriers corresponding to XPM in the upper and lower arm, no matter how small the actual value of the phase-shift induced by the pump. A quick analysis reveals that the control pulses need not induce a ‘p’ phase shift, which is not easy to achieve with reasonable pump powers. As long as the amounts of phase shift induced by control pulses in the upper and lower arms are equal, the probe output pulses will be equal in amplitude and out of phase by ‘p’. Of course, 125 the peak power in the output probe pulses will reduce with a reduction in control- induced phase shifts. This can be better understood through Fig. 6-5, where the carriers in the upper (red) and lower (blue) arms are shown along with the resultant carrier after interference (black) for two different values of XPM-induced phase shifts. The output carrier amplitude is smaller if the XPM-induced phase shift is smaller. However a relative phase difference of ‘p’ is observed between the two output carriers corresponding to XPM in the upper and lower arm, no matter how small the actual value of the phase-shift. The SOA-MZI structure effectively operates as an optically-controlled dual-drive Mach-Zehnder modulator. The above description assumes that the control pulses cause an instantaneous phase change in the SOAs. In reality, there is a finite time over which the phase change occurs and the slow carrier recovery in the SOAs plays a big role in determining the performance of the device. To alleviate the slow carrier recovery effects, differential cross-phase modulation (DXPM) is employed [61]. For every control pulse that is injected into the upper (lower) arm, a delayed and suitably attenuated copy of it is injected into the lower (upper) arm. This technique allows the slow recoveries in the two arms to coincide leading to a narrow output pulse whose width is determined only by the time delay between the copies of the control pulses. As a result, the bit- rate of the control signals can be increased beyond the restrictions imposed by the carrier recovery time. Ultimately, nonlinear patterning emerges as the limiting factor which leads to output pulse amplitude fluctuations. To summarize the concept, 126 DXPM in an SOA-MZI structure is exploited to create narrow switching windows for a new coherent carrier (probe) based on the intensity information of the input signals (pumps). At the same time, the ‘p’ phase-bias between the two arms of the MZI allows us to phase modulate the output signal by dynamically reversing the roles of the push and pull arms of the MZI. 6.3.1 Generation of 80 Gb/s CSRZ signals In order to verify the phase modulation capabilities of the SOA-MZI, simulations are performed for the simplest phase-correlated format, i.e. carrier-suppressed return-to- zero (CSRZ). CSRZ signals carry information encoded in the form of RZ pulses. However, a phase change of ‘p’ is introduced for every other bit. As a result the phase of the signal alternates between ‘0’ and ‘p’ for successive bits. This leads to reduced nonlinear interaction between adjacent pulses when the signal is transmitted over fiber. As shown in Fig. 6-6, the phase-correlated signal generator should convert multiple RZ input channels into a single multiplexed CSRZ data stream. From the temporal phase profile it is clear that output pulses originating from even- numbered channels have ‘0’ phase while those from odd-numbered channels have ‘p’ phase. As described earlier, this can be achieved by injecting pulses from even- numbered channels into the top arm of the SOA-MZI while the odd-numbered channels are coupled into the lower arm. 127 10 Gb/s Ch#1 10 Gb/s Ch#8 t t Power Phase 0 p p p p Phase correlated signal generator 80 Gb/s CSRZ 0110101001010010111111001000 0110101001010010111111001000 t t t t t t t Ch#2 Ch#3 Ch#4 Ch#5 Ch#6 Ch#7 Phase changes by ‘p p p p’ for every other bit 8X10 Gb/s RZ OTDM Fig. 6-6. Conversion of 8X10 Gb/s RZ signals into an 80 Gb/s CSRZ signal. In the simulations performed using a commercial software package, the SOA parameters are adjusted to obtain a 10-90% gain recovery time of ~15 ps and the differential delay is fixed at 5 ps to obtain ~5 ps FWHM pulses at the output. SOA 2 SOA 1 Filter 10 Gb/s Ch#1,3,5,7 CW Probe Phase (p) 10 Gb/s Ch#2,4,6,8 t Power Phase 0 p p p p 80 Gb/s CSRZ Phase changes by ‘p p p p’ for alternate bits Fig. 6-7. Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent CSRZ output. 128 As shown in Fig. 6-7 for a case of eight 10 Gb/s RZ (pulse-width ~3 ps) channels being multiplexed to generate an 80 Gb/s CSRZ data stream, the channels are arranged in such a way that the interleaved pulses from channels 1,3,5 and 7 are injected into the top arm while those from channels 2,4,6 and 8 perturb the bottom arm. All input pulses generate output pulses leading to a multiplexed 80 Gb/s output. However pulses which originate in the top arm are out of phase by ‘p’ relative to the ones which originate in the bottom arm. Since the input channels alternate between the arms, the phase of the output bits also alternates between ‘0’ and ‘p’ leading to carrier suppression as seen in the output spectrum in Fig. 6-8. Relative Power (dB) 0 60 30 Wavelength (nm) 1553.5 1555 1556.5 80 GHz Output Original carrier Fig. 6-8. Spectrum of the 80 Gb/s coherent CSRZ output, obtained through simulations. The original carrier position is shown in blue. Tone spacing of 80 GHz is observed. The original narrow linewidth probe carrier before modulation is shown in blue to provide a reference for the tone positions. Fig. 6-9 shows the intensity and phase variation of the 80 Gb/s CSRZ output signal. 129 Power (mW) Phase (rad.) -p p p p p p p p 0 0 20 10 30 Time (ps) 0 100 200 Fig. 6-9. Intensity and phase variations for the 80 Gb/s coherent CSRZ output. Phase alternates between 0 and ‘p’ for adjacent bit-slots. The phase of the ‘1’ bits is the key factor in improving tolerance to nonlinearities since the deleterious effects arise from pulse-overlap. The constant phase for a long string of 0’s will not degrade the signal as much since the power in the 0’s is minimal. If one observes a string of 1’s it can be seen that phase changes by ‘p’ for every alternate pulse. Some residual nonlinear pattern dependence in the form of output pulse power variation is observed. Several techniques have been proposed to mitigate this nonlinear pattern dependence and may be employed in conjunction with the SOA-MZI structure. Other variations of the CSRZ format are generated by changing the injection sequence of the low-rate tributaries into the module. An example of such a format is pairwise alternating phase (PAP)-CSRZ which exhibits greater tolerance to intra- channel four-wave mixing (IFWM) [86]. The phase of PAP-CSRZ signals alternates 130 between ‘0’ and ‘p’ for successive pairs of bits. To generate PAP-CSRZ data format, input channels are paired up and alternate pairs are injected into the two arms of the SOA-MZI as shown in Fig. 6-10. SOA 2 SOA 1 Filter 10 Gb/s Ch#1,2,5,6 CW Probe Phase (p) 10 Gb/s Ch#3,4,7,8 t Power Phase 0 p p p p 80 Gb/s PAP-CSRZ Phase changes by ‘p p p p’ for alternate pairs of bits Fig. 6-10. Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent PAP-CSRZ output. The change in periodicity of the in-phase components squeezes the spectral tones closer, leading to the spectrum shown in Fig. 6-11. Relative Power (dB) 0 60 30 Wavelength (nm) 1553.5 1555 1556.5 40 GHz Output Original carrier Fig. 6-11. Spectrum of the 80 Gb/s coherent PAP-CSRZ output, obtained through simulations. The original carrier position is shown in blue. Tone spacing of 40 GHz is observed. 131 It should be noted that these spectral characteristics are a direct indication of the coherent nature of the output signal and are made possible by specific bit-to-bit phase relationships of a single modulated carrier. A short sequence of output bits along with the corresponding temporal phase variation is shown in Fig. 6-12. Power (mW) Phase (rad.) -p p p p p p p p 0 0 20 10 30 Time (ps) 0 100 200 Fig. 6-12. Intensity and phase variations for the 80 Gb/s coherent PAP-CSRZ output. Phase alternates between 0 and ‘p’ for adjacent pairs of bit-slots. As expected, a string of consecutive 1’s exhibits phase changes for every alternate pair of bits. The tones can be squeezed even closer together by coupling the channels into groups of four and injecting alternate groups into the two arms of the SOA-MZI as shown in Fig. 6-13. This leads to the generation of groupwise alternating phase (GAP)-CSRZ signals. This signal format adds further tolerance to fiber-based nonlinear effects [84] allowing higher powers to be launched for fiber transmission and increasing received optical signal-to-noise values. Moreover, the spectrum reveals (Fig. 6-14) 20 GHz tone spacing for an 80 Gb/s signal with alternate pairs of tones being suppressed relative to their neighbors. 132 SOA 2 SOA 1 Filter 10 Gb/s Ch#1,2,3,4 CW Probe Phase (p) 10 Gb/s Ch#5,6,7,8 t Power Phase 0 p p p p 80 Gb/s GAP-CSRZ Phase changes by ‘p p p p’ for alternate sets of 4 bits Fig. 6-13. Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent GAP-CSRZ output. Relative Power (dB) 0 60 30 Wavelength (nm) 1553.5 1555 1556.5 20 GHz Output Original carrier Fig. 6-14. Spectrum of the 80 Gb/s coherent GAP-CSRZ output, obtained through simulations. The original carrier position is shown in blue. Tone spacing of 20 GHz is observed with alternate pairs of tones being suppressed. This property can be exploited for narrow band filtering of the pair of tones closest to the center and obtaining a beat signal after detection to recover a sub-harmonic clock [84] from the high data rate signal. This filtering based clock recovery method is a simpler alternative to other complicated schemes based on nonlinear optical devices. 133 A representative sequence of bits showing the temporal phase variations is presented in Fig. 6-15. For a long string of 1’s, the phase flips after every four bits. Power (mW) Phase (rad.) -p p p p p p p p 0 0 20 10 30 Time (ps) 0 100 200 Fig. 6-15. Intensity and phase variations for the 80 Gb/s coherent GAP-CSRZ output. Phase alternates between 0 and ‘p’ for adjacent sets of four bit-slots. As verified through simulations, the SOA-MZI structure can be used to generate various CSRZ formats. The output phase-correlative properties can be reconfigured simply by changing the pattern of injection of the lower rate input channels. 6.3.2 Generation of 80 Gb/s DPSK signals Differential phase-shift keying (DPSK) has emerged as one of the most popular advanced modulation formats. It involves encoding information in the phase of a constant power signal (NRZ-DPSK) or in the phase of a pulse train (RZ-DPSK). This constant envelope property makes it tolerant to fiber nonlinear effects that arise from pattern dependent intensity variations. Moreover, balanced detection of DPSK 134 signals provides a 3 dB benefit in terms of the OSNR required to achieve a certain BER at the receiver compared to OOK modulation schemes. RZ-DPSK signals are composed of a pulse train where the phase of the pulses changes between ‘0’ and ‘p’ to represent the data being transmitted. The data needs to be pre-coded to enable differential detection wherein each bit’s phase is compared to the phase of the following bit, instead of using a local phase reference as is the case for coherent detection. Time division multiplexing of RZ-DPSK signals amounts to time-interleaving since only the phase relationships between pulses of each tributary are maintained and arbitrary phase jumps are encountered between adjacent pulses of the multiplexed output [63]. P o w e r (a .u .) P h a s e (ra d .) -p p p p p p p p 0 Time (ps) 0 50 100 P o w e r (a .u .) P h a s e (ra d .) -p p p p p p p p 0 Time (ps) 0 50 100 Pulse from Ch #1 Pulse from Ch #8 (a) (b) Fig. 6-16. (a) Incoherently multiplexed 80 Gb/s OTDM DPSK signal. Adjacent bits possess random relative phase. (b) The random distribution of the carrier phase in the multiplexed 80 Gb/s data is highlighted using blue colored markers. This condition is shown in Fig. 6-16 for the case of eight 10 Gb/s DPSK channels being incoherently multiplexed to form an 80 Gb/s data stream. The output intensity 135 profile represents an 80 GHz pulse train. However, there is no well-defined phase relationship between the pulses from one channel and those from another. The relative phases of the pulses in the multiplexed stream are randomly distributed as is clear from Fig. 6-16(b) where the intensity and phase profiles from the previous figure have been reproduced and blue colored markers have been added to highlight the phase value for each pulse at the position of its peak intensity. Due to this random phase relationship between adjacent pulses, a DPSK demodulator (delay interferometer) for the multiplexed data-rate is not suitable. Only pulses from the same original channel can be interfered with each other to recover the data. Thus, in our example, a 12.5 ps delay interferometer (DI) cannot be used to demodulate the 80 Gb/s data stream. If such a time-interleaved 80 Gb/s DPSK signal passes through an 80 Gb/s DPSK demodulator, the signals on the destructive and constructive ports don’t exhibit well-defined on/off states, leading to eye closure as shown in Fig. 6-17. D D D Dt = 12.5 ps Phase (p p p p) 80 Gb/s DPSK Demodulator Bal. Rx Closed Eye Power (a.u.) Phase (rad.) -p p p p p p p p 0 Time (ps) 0 50 100 OTDM DPSK - Random phase jumps between pulses Fig. 6-17. Unsuccessful demodulation of an incoherently multiplexed 80 Gb/s DPSK signal using an 80 GHz delay interferometer. The signals on the destructive and constructive ports do not exhibit well-defined on/off states, leading to eye closure. 136 In order to generate a genuine high speed DPSK signal, phase coherence needs to be maintained while transferring the combined information from the input tributaries to the output as a phase modulated signal. This can be achieved by using DXPM in the SOA-MZI structure. The 80 Gb/s data to be transmitted is pre-coded (pre-coding can be performed at lower rates [7]) and converted into an 80 Gb/s RZ data stream composed of individual tributaries which do not bear any phase relationship to each other. The pulses in this data stream correspond to the pre-coded ‘1’ bits. Similarly another OTDM data stream is created with the inverse data. These pulses corresponds to the pre-coded ‘0’ bits. The job of the phase-correlated signal generator is to convert this incoherent OTDM data into a pulse train, while assigning ‘0’ phase to the pulses corresponding to pre-coded ‘0’ bits and ‘p’ phase to pulses corresponding to pre-coded ‘1’ bits. As shown in Fig. 6-18 this can be achieved by injecting the 80 Gb/s OTDM stream corresponding to the pre-coded ‘1’ bits into the top arm while injecting the inverse data stream synchronously into the lower arm. SOA 2 SOA 1 Filter 80 Gb/s Pre-coded 1’s CW Probe Phase (p) t Power Phase 0 p p p p 80 Gb/s DPSK Phase changes are determined by pre-coded data F F F F=0 for 0’s & F F F F=p p p p for 1’s 80 Gb/s Pre-coded 0’s t Power t Power Fig. 6-18. Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent RZ-DPSK output. 137 Since there is exactly one input pulse perturbing the module in every bit-slot, the output on the probe wavelength is a pulse train. However, if the output pulse was initiated due to XPM in the top arm it bears a phase of ‘0’ while if it was initiated due to XPM in the lower arm it exhibits ‘p’ phase. Thus the module generates an output pulse train with a pulse-to-pulse phase variation governed by the 80 Gb/s pre- coded data. An example for 8 bits ‘01001101’ at 80 Gb/s is shown in Fig. 6-19. Phase (rad.) -p p p p p p p p 0 Time (ps) 0 50 100 Power (a.u.) 0 1 0 0 1 1 0 1 Phase (rad.) -p p p p p p p p 0 Time (ps) 0 50 100 Power (a.u.) Input: 80 Gb/s Pre-coded OTDM bits Output: 80 Gb/s Phase-Reconstructed DPSK bits Fig. 6-19. Intensity and phase variations for the 80 Gb/s coherent RZ-DPSK output. Phase changes are determined by the pre-coded OTDM data stream that perturbs the SOA-MZI. The example is for an 8-bit input sequence ‘01001101’. The output is a pulse train and the phase variation is ‘0p00pp0p’ confirming the phase coherent transfer of information. This 80 Gb/s DPSK signal can be demodulated using a 12.5 ps delay interferometer and reveals an open eye after 138 balanced detection as shown in Fig. 6-20. The optical spectrum of the output DPSK signal is shown in Fig. 6-21. Open Eye Phase (rad.) -p p p p p p p p 0 Time (ps) 0 50 100 Power (a.u.) Phase-reconstructed DPSK - [0,p p p p] phase relationship between pulses D D D Dt = 12.5 ps Phase (p p p p) 80 Gb/s DPSK Demodulator Bal. Rx Fig. 6-20. Successful demodulation of a coherent 80 Gb/s DPSK signal using an 80 GHz delay interferometer. The signals on the destructive and constructive ports exhibit well-defined on/off states and a clear eye opening is observed after balanced detection. Changing the polarity of data at the receiver’s ports is easily achieved by generating a pseudo-CSRZ-DPSK signal by imposing an alternating phase modulation on top of the RZ-DPSK data based modulation. This is done by considering the 80 Gb/s OTDM input as being composed of two 40 Gb/s data streams and injecting the pulses corresponding to ‘1’ bits of Ch#1 and those corresponding to ‘0’ bits of Ch#2 in to the top arm. The roles of the two channels are reversed in the bottom arm. The power and phase variations for an 8-bit output sequence for RZ-DPSK and CSRZ- DPSK signals are compared in Fig. 6-22. Compared to the phase profile of the DPSK signal, the CSRZ-DPSK signal exhibits a phase-flip for every alternate bit. 139 Relative Power (a.u.) 0 60 30 Wavelength (nm) 1553.5 1555 1556.5 Output Original carrier Fig. 6-21. Spectrum of the 80 Gb/s coherent RZ-DPSK output, obtained through simulations. The original carrier position is shown in blue. Phase (rad.) -p p p p p p p p 0 Time (ps) 0 50 100 Power (a.u.) RZ-DPSK Power (a.u.) Phase (rad.) -p p p p p p p p 0 Time (ps) 0 100 200 CSRZ-DPSK (a) (b) Fig. 6-22. (a) Intensity and phase profiles of an 8 bit pattern of a coherent 80 Gb/s RZ-DPSK signal generated using the SOA-MZI scheme. (b) Intensity and phase profiles of the same 8 bits with the injection scheme altered to generate CSRZ- DPSK. Alternate bits exhibit a ‘p’ phase shift relative to the phase profile of the DPSK signal. 140 It should be noted that the pulse-width of both these signals is the same since it is governed by the differential delay between the push and pull pulses in the DXPM process. Thus, the signals are not equivalent to the conventional RZ-DPSK and CSRZ-DPSK signals described in the literature [33, 109]. The primary effect of switching from RZ- to CSRZ-DPSK is that the data polarity of the signals appearing at the output ports of the demodulator is reversed. 6.3.3 Generation of 80 Gb/s AMI and duobinary signals The signals at the two output ports of a DPSK demodulator possess specific bit-to-bit phase relationships. The output at the destructive port is called an alternate-mark- inversion (AMI) signal and it exhibits a ‘p’ phase change for every pulse. The output at the constructive port is called the duobinary signal and it exhibits a ‘p’ phase change for every pulse that is separated by an odd number of 0’s from the previous pulse. These types of signal have gained a lot of attention recently. In particular, duobinary has been shown to be extremely tolerant to tight filtering [57] and robust to residual chromatic dispersion [58] since it possesses a narrow optical spectrum. AMI on the other hand exhibits high tolerance to fiber-based nonlinear effects [8, 9]. Various techniques have been proposed [7, 31, 56] to generate these signals directly, instead of generating a DPSK signal and passing it through a DI. One of the methods to generate AMI signals involves pre-coding the data before driving the modulator and performing a delay-and-subtract operation on the 141 modulated optical signal. The SOA-MZI structure described earlier is capable of providing this functionality. The pre-coded signal is injected into the top arm and a 1-bit delayed copy of it is injected into the bottom arm, as shown in Fig. 6-23. SOA 2 SOA 1 Filter 80 Gb/s Pre-coded data CW Probe Phase (p) t Power Phase 0 p p p p 80 Gb/s AMI Phase changes by ‘p p p p’ for alternate ‘1’ bits 80 Gb/s Pre-coded data 1 bit delayed t Power Power t Fig. 6-23. Scheme for signal injection into the SOA-MZI for generating 80 Gb/s coherent AMI output. The SOA-MZI effectively operates as an XOR gate in the intensity domain. For the case of two consecutive ‘1’ bits, the signal and its 1-bit delayed version exhibit simultaneous pulses. These pulses induce the same exact amount of XPM in both arms which cancels out and no output pulse is generated. As a result the pre-coding process is reversed allowing direct detection to be used at the receiver. However, if pump pulses are not injected simultaneously into the two arms (as would be the case for isolated ‘1’ bits), two cases emerge. If there is a pulse in the top arm but not in the bottom arm, an output pulse is generated with a phase of ‘0’. However, the presence of a pulse in the bottom arm and not in the top arm, leads to an output pulse with a phase of ‘p’. In this way, the delay-and-subtract operation leads to alternating phases for ‘1’ bits. A sample intensity and phase profile for AMI signal generation 142 using the SOA-MZI structure is shown in Fig. 6-24 and the corresponding spectrum is shown in Fig. 6-25. Power (a.u.) Phase (rad.) -p p p p p p p p 0 Time (ps) 0 100 200 Fig. 6-24. Intensity and phase variations for the 80 Gb/s coherent AMI output. Phase changes by ‘p’ for every ‘1’ bit. Relative Power (a.u.) 0 60 30 Wavelength (nm) 1553.5 1555 1556.5 80 GHz Fig. 6-25. Spectrum of the 80 Gb/s coherent AMI output, obtained through simulations. The original carrier position is shown in blue. Duobinary can potentially be generated by following the same injection pattern as AMI and using the constructive port of the SOA-MZI, instead. However, under such conditions, the SOA-MZI is performing constructive interference in the unperturbed 143 state and therefore the output extinction ratio is determined by how close to the perfect destructive interference the device is pushed when pump pulses are injected. Thus, the output extinction ratio is critically dependent on the phase-swings induced in the SOAs. 6.3.4 Pulse-width control of phase-correlated signals and transmultiplexing The differential mode of operation and the special features of the carrier dynamics in the SOAs enable some additional capabilities for this technique of generating phase- correlated signals. These features apply to the generation of any of the modulation formats described in this chapter. Since the output pulse-width is determined by the time-delay between the push and pull pulses in the DXPM process, the module is capable of output pulse-width control, adding another degree of freedom to tailor the signal' s properties for optimum fiber transmission [113]. This pulse-width tuning is shown in Fig. 6-26 for the case of 80 Gb/s DPSK generation. Time (ps) 0 25 50 Power (a.u.) 0 1 3 ps FWHM 7 ps FWHM Fig. 6-26. Output pulse-width control enabled through the differential delay in the DXPM process. The example shown here is for an 80 Gb/s RZ-DPSK signal. 144 Since the cross-phase modulation effect is relatively independent of the signal wavelength as long as the wavelengths lie in the vicinity of the SOA gain peak, it is conceivable that the input channels that need to be multiplexed may be on different wavelengths. The device can potentially act as a transmultiplexer, converting lower rate WDM inputs to a single high-speed phase coherent TDM signal while providing the flexibility of choosing the output format. Fig. 6-27 summarizes the generation technique employed for the various modulation formats discussed in this chapter. Format Signal Injection Pattern Spectrum CSRZ PAP- CSRZ GAP- CSRZ Upper arm: Channel #1, 3, 5, 7 Lower arm: Channel #2, 4, 6, 8 Upper arm: Channel #1, 2, 5, 6 Lower arm: Channel #3, 4, 7, 8 Upper arm: Channel #1, 2, 3, 4 Lower arm: Channel #5, 6, 7, 8 40 GHz 40 GHz 20 GHz 20 GHz AMI DPSK Upper arm: Pre-coded Channel #1-8 Lower arm: 1-bit Delayed Pre- coded Channel #1-8 Upper arm: Pre-coded Channel #1-8 Lower arm: Bit-inverted Pre- coded Channel #1-8 80 GHz 80 GHz 80 GHz 80 GHz Fig. 6-27. Spectra of 80 Gb/s coherent phase modulated formats generated using the SOA-MZI. The pattern of injection of the low-rate RZ tributaries is used to reconfigure the output format. 145 The output data format is reconfigured by changing the pattern of injection of the lower rate input channels that are to be multiplexed. The spectral properties of each signal confirm the phase-coherence of the generated outputs. 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Fejer, "Femtosecond pulse second harmonic generation under large depletion conditions in long PPLN waveguides," presented at Conference on Lasers and Electro-Optics Europe - Technical Digest, Baltimore, MD, 2001, pp. 547. 159 Appendix A MATLAB code for simulating carrier dynamics in semiconductor optical amplifiers File: main.m % MATLAB base workspace variables % % - Simulation parameters % delt_ps :: double number % time sampling step expressed in ps % % num_samples :: double number % number of signal samples in time domain % % time :: double vector [num_samples 1] % time sample values expressed in ps % % - Input signals % % pump_in :: complex vector [num_samples polarization_mode] % optical signal pump_in time domain samples % % probe_in :: complex vector [num_samples polarization_mode] % optical signal probe_in time domain samples % % - Output signals % % converted_out :: complex vector [num_samples polarization_mode] % optical signal converted_out time domain samples % % - Component parameters % % pumpwave :: double number % parameter pumpwave expressed in nm % % probewave :: double number % parameter probewave expressed in nm 160 % % bias1 :: double number % parameter bias1 expressed in mA % % bias2 :: double number % parameter bias2 expressed in mA % % probesplit :: double number % % probecoup :: double number % % pumpsplit :: double number % % phaseshift :: double number % parameter phaseshift expressed in rad % % delay :: double number % parameter delay expressed in ps % global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm iteration lambda y=0.892; % molar fraction of Arsenide in the active region x=0.47*y; % lattice match, x: molar fraction of Gallium in the active region % active region geometry lc=600e-6; % central active region length lt=100e-6; % tapered active region length l=lc+lt; % mean length (approx.) d=0.4e-6; % active region thickness w=0.4e-6; % central active region width confine=0.45; % optical confinement factor kg=0.9e-10; % bandgap shrinkage coefficient (in eVm) % refractive index n1=3.22; % InGaAsP active region refractive index n2=3.167; % InP region refractive index dn1wrtdn=-3.6e-26; % dn1/dn---differential of active region refractive index wrt carrier density (in m^-3) 161 neq0=3.22; % equivalent refractive index at zero carrier density dneqwrtdn=-1.34e-26; % dneq/dn---differential of equivalent refractive index wrt carrier density % coupling incouploss=3; % input coupling loss (in dB) outcouploss=3; % output coupling loss (in dB) % reflectivity R1=5e-5; % input facet power reflectivity R2=5e-5; % output facet power reflectivity r1=sqrt(R1); % input facet field reflectivity r2=sqrt(R2); % output facet field reflectivity % absorption k0=6200; % carrier independent absorption loss coeff. (in m^-1) k1=7500e-24; % carrier dependent absorption loss coeff. (in m^2) % recombination arad=1e7; % linear radiative recombination coeff. (in s^-1)orig 1e7 brad=5.6e-16; % bimolecular radiative recombination coeff. (in m^3*s^-1) anrad=7*3.5e8 % linear nonradiative recombination coeff. due to traps (in s^-1) bnrad=0.0e-16; % bimolecular nonradiative recombination coeff. (in m^3*s^-1) caug=3e-41; % auger recombination coeff. (in m^6*s^-1) dleak=0.0e48; % leakage recombination coeff. (in m^13.5*s^-1) % bandgap a=1.35; % bandgap energy quadratic coeff. a,b,c. b=-0.775; c=0.149; % mass me=4.1e-32; % effective mass of electron in the CB mhh=4.19e-31; % effective mass of a heavy hole in the VB mlh=5.06e-32; % effective mass of a light hole in the VB % general constant clight=3e8; % speed of light h=6.626e-34; % Planck' s constant hbar=h/(2*pi); % Planck' s constant divided by 2pi 162 k=1.3806e-23; % Boltzmann' s constant temperature=300; % absolute temperature e=1.6e-19; % simulation constants lambda=[pumpwave;probewave] % signal wavelengths (in nm) nu=(clight/1e-9)./lambda; % convert to frequency ns=length(lambda); % number of signals nz=20; % number of sections n=ones(1,nz); % carrier density vector q=zeros(1,nz); % setting up initial rate of change of carrier density vector km=20; % constant for determining resonant freqs for noise (dependent on SOA gain BW) nm=40; % constant for determining resonant freqs for noise (dependent on SOA gain BW) timestep=1; % in ps deltat=timestep*1e-12; % end of constants listing fixed intermediate parameters for simulation ra=arad+anrad; % ra to rd are coefficients of the polynomial in n that represents the recombination rate rb=brad+bnrad; rc=caug; rd=dleak; % main program begins if delt_ps<timestep downratio=timestep/delt_ps; else downratio=1; end % Initializing the average optical signal variable opt_signal_data_avg = complex(zeros(num_samples, polarization_mode), ... zeros(num_samples, polarization_mode)); opt_signal_data_avg = pump_in; opt_signal_data_avg = opt_signal_data_avg + probe_in; % Assigning output(s) 163 converted_out = opt_signal_data_avg; probeanglefull=angle(probe_in); pumpanglefull=angle(pump_in); runnumber=0; for soanumber=1:1:2 if soanumber==1 probepower=probesplit*abs(probe_in(1:round(downratio):num_samples)).^2; pumppower=pumpsplit*abs(pump_in(1:round(downratio):num_samples)).^2; bias=bias1*1e-3; else probepower=(1-probesplit)*abs(probe_in(1:round(downratio):num_samples)).^2; pumppower=(1-pumpsplit)*abs(pump_in(1:round(downratio):num_samples)).^2; bias=bias2*1e-3; end initprobepower=probepower(1); % intial probe power in mW initpumppower=pumppower(1); % initial pump power in mW pintran=[initpumppower;initprobepower]; [n,srateposavg,sratenegavg,nrateposavg,nratenegavg,sratepos,nratepos,nunoise,epos] =steadystate(pintran,bias); srateposavgtran=srateposavg; sratenegavgtran=sratenegavg; nrateposavgtran=nrateposavg; nratenegavgtran=nratenegavg; ntran=sum(n)/nz; srateouttran=(1-R2)*sratepos(:,nz+1); knoisefactor=noisenormfactor(noisediscretefreq(n),n); noiserate=2*10^(-outcouploss/10)*(1-R2)*knoisefactor(:,1).*nratepos(:,nz+1); noisefreq=nunoise(min(find(nunoise>=lower_frequency*1e12)):1:max(find(nunoise <=upper_frequency*1e12))); nrateouttran=noiserate(min(find(nunoise>=lower_frequency*1e12)):1:max(find(nun oise<=upper_frequency*1e12))); 164 dneqwrtdnprime=(n1*confine/(neq0*(2-confine)))*dn1wrtdn; neq=neq0+dneqwrtdnprime*n; neqsum=sum(neq); effrefrac=neqsum/nz; qtran=zeros(1,nz); sample=2; while sample <= length(probepower) recomterm=rd*n.^5.5+rc*n.^3+rb*n.^2+ra*n; if ns==1 q=(bias/e/d/l/w)-recomterm- confine/d/w*gm(nu,n).*(srateposavg+sratenegavg)... - 2*confine/d/w*sum(gm(noisediscretefreq(n),n).*noisenormfactor(noisediscretefreq( n),n).*(nrateposavg+nratenegavg)); else q=(bias/e/d/l/w)-recomterm- confine/d/w*sum(gm(nu,n).*(srateposavg+sratenegavg))... - 2*confine/d/w*sum(gm(noisediscretefreq(n),n).*noisenormfactor(noisediscretefreq( n),n).*(nrateposavg+nratenegavg)); end %calculate new value of carrier density n=(n+q*deltat); %call elecfield ppump=pumppower(sample); pprobe=probepower(sample); pintran=[ppump;pprobe]; pintran=10*log10([ppump;pprobe]); eintran=sqrt(((10 .^((pintran-incouploss)/10))/1000)./(h*nu)); [epos,eneg,gaincoeff] = elecfield(nu,n,eintran); sratepos=(abs(epos)).^2; srateneg=(abs(eneg)).^2; srateposavg=(sratepos(:,1:nz)+sratepos(:,2:nz+1))/2; sratenegavg=(srateneg(:,1:nz)+srateneg(:,2:nz+1))/2; %call sponrate 165 [nratepos,nrateneg] = sponrate(noisediscretefreq(n),n); nrateposavg=(nratepos(:,1:nz)+nratepos(:,2:nz+1))/2; nratenegavg=(nrateneg(:,1:nz)+nrateneg(:,2:nz+1))/2; ntran=[ntran,sum(n)/nz]; srateouttran=[srateouttran,(1-R2)*sratepos(:,nz+1)]; knoisefactor=noisenormfactor(noisediscretefreq(n),n); knoisefactor2=spline(noisediscretefreq(n),knoisefactor(:,1),noisefreq); noiserate2=2*10^(-outcouploss/10)*(1- R2)*knoisefactor2(:,1).*spline(noisediscretefreq(n),nratepos(:,nz+1),noisefreq); nrateouttran=[nrateouttran,noiserate2]; dneqwrtdnprime=(n1*confine/(neq0*(2-confine)))*dn1wrtdn; neq=neq0+dneqwrtdnprime*n; neqsum=sum(neq); effrefrac=[effrefrac,neqsum/nz]; sample=sample+1; end samplesdone=1 poutnoise=0.5*h*repmat(noisefreq,1,length(time))' .*interp1(time(1:round(downratio ):num_samples),nrateouttran' ,time,' linear' ,' extrap' ); noisephase=repmat(2*pi*(center_frequency*1e12- noisefreq),1,length(time)).*repmat(time' ,length(noisefreq),1); % pumpsoaphase=interp1(time(1:round(downratio):num_samples),2*pi*effrefrac*nu(1 )*l/clight,time,' linear' ,' extrap' ); probesoaphase=interp1(time(1:round(downratio):num_samples),2*pi*effrefrac*nu(2 )*l/clight,time,' linear' ,' extrap' ); poutpump=interp1(time(1:round(downratio):num_samples),0.5*h*nu(1)*srateouttra n(1,:),time,' linear' ,' extrap' ); poutprobe=interp1(time(1:round(downratio):num_samples),0.5*h*nu(2)*srateouttra n(2,:),time,' linear' ,' extrap' ); pump_out=sqrt(poutpump*1000).*exp(complex(0,pumpanglefull)).*exp(- complex(0,pumpsoaphase)); probe_out=sqrt(poutprobe*1000).*exp(complex(0,probeanglefull)).*exp(- complex(0,probesoaphase)); 166 noise_out=sum(sqrt(poutnoise' *1000).*exp(- complex(0,noisephase)).*exp(complex(0,2*pi*rand(size(poutnoise' )))))' ; if soanumber==1 soa_outfirst=probe_out+noise_out+pump_out; soa_outfirstprobe=probe_out; phasesoa1=probesoaphase; else soa_outsecond=zeros(num_samples,1); temppower=zeros(round(delay/delt_ps)+num_samples,1); temppower(round(delay/delt_ps)+1:round(delay/delt_ps)+num_samples)=sqrt(poutp robe*1000); temppower(1:round(delay/delt_ps))=sqrt(poutprobe(num_samples- round(delay/delt_ps)+1:num_samples)*1000); tempphase=zeros(round(delay/delt_ps)+num_samples,1); tempphase(round(delay/delt_ps)+1:round(delay/delt_ps)+num_samples)=probesoaph ase; tempphase(1:round(delay/delt_ps))=probesoaphase(num_samples- round(delay/delt_ps)+1:num_samples); soa_outsecond=temppower(1:num_samples).*exp(- complex(0,tempphase(1:num_samples))).*exp(complex(0,probeanglefull))+noise_ou t+pump_out; soa_outsecondprobe=temppower(1:num_samples).*exp(- complex(0,tempphase(1:num_samples))).*exp(complex(0,probeanglefull)); phasesoa2=tempphase(1:num_samples); end end % phasediff(:,runnumber)=phasesoa1-phasesoa2; converted_out=sqrt(probecoup)*soa_outfirst+sqrt(1- probecoup)*(soa_outsecond*exp(complex(0,phaseshift))); converted_outprobe=sqrt(probecoup)*soa_outfirstprobe+sqrt(1- probecoup)*(soa_outsecondprobe*exp(complex(0,phaseshift))); % End of file %__________________________________________________________________ 167 File: steadystate.m function [n,srateposavg,sratenegavg,nrateposavg,nratenegavg,sratepos,nratepos,nunoise,epos] =steadystate(pin,bias) % Wideband Semiconductor Optical Amplifier Steady State Numerical Model global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm iteration lambda % simulation constants nu=(clight/1e-9)./lambda; % convert to frequency pin=10*log10(pin); ein=sqrt(((10 .^((pin-incouploss)/10))/1000)./(h*nu)); n=ones(1,nz); % carrier density vector q=zeros(1,nz); % setting up initial rate of change of carrier density vector weight=1; % initial weight in steps towards convergence weight=weight*ones(1,nz); % setting up initial weight vector tolerance=.01; % tolerance for steady state values at end of simulation % end of constants listing % fixed intermediate parameters for simulation ra=arad+anrad; % ra to rd are coefficients of the polynomial in n that represents the recombination rate rb=brad+bnrad; rc=caug; rd=dleak; % main program begins % calculating initial carrier density biasterm=bias/(e*d*l*w); % the contribution of bias current to carrier density in the rate equation p=[rc rb ra -biasterm]; % polynomial equation for initial carrier density 168 r=roots(p); % find roots for this polynomial ninitial=findmax(r); n=ninitial*n; nrateposavg=zeros(nm,nz); nratenegavg=zeros(nm,nz); iteration=0; tcheck=1; qold=zeros(1,nz); tic; while tcheck==1 iteration=iteration+1; % electric field for signal [epos,eneg,gaincoeff] = elecfield(nu,n,ein); sratepos=(abs(epos)).^2; srateneg=(abs(eneg)).^2; srateposavg=(sratepos(:,1:nz)+sratepos(:,2:nz+1))/2; sratenegavg=(srateneg(:,1:nz)+srateneg(:,2:nz+1))/2; % spontaneous emission noise photon rate [nratepos,nrateneg] = sponrate(noisediscretefreq(n),n); nunoise=noisediscretefreq(n); nrateposavg=(nratepos(:,1:nz)+nratepos(:,2:nz+1))/2; nratenegavg=(nrateneg(:,1:nz)+nrateneg(:,2:nz+1))/2; %q_new calculation; ra=arad+anrad; % ra to rd are coefficients of the polynomial in n that represents the recombination rate rb=brad+bnrad; rc=caug; rd=dleak; recomterm=rd*n.^5.5+rc*n.^3+rb*n.^2+ra*n; %Calculating the new amount of Q if ns==1 qnew=(bias/e/d/l/w)-recomterm- confine/d/w*gm(nu,n).*(srateposavg+sratenegavg)... - 2*confine/d/w*sum(gm(noisediscretefreq(n),n).*noisenormfactor(noisediscretefreq( n),n).*(nrateposavg+nratenegavg)); 169 else qnew=(bias/e/d/l/w)-recomterm- confine/d/w*sum(gm(nu,n).*(srateposavg+sratenegavg))... - 2*confine/d/w*sum(gm(noisediscretefreq(n),n).*noisenormfactor(noisediscretefreq( n),n).*(nrateposavg+nratenegavg)); end %Updating weight and carrier density vectors weight=(sign(qold).*sign(qnew)-1).*weight/4+weight; nnew=(sign(qnew)+1).*n.*(1+weight)/2+(1-sign(qnew)).*n./(1+weight)/2; if iteration>1 %deviations maxdevn=max(abs((nnew-n)./n)); maxdevsratepos=max(max(abs((srateposavg- oldsrateposavg)./oldsrateposavg))); maxdevsrateneg=max(max(abs((sratenegavg- oldsratenegavg)./oldsratenegavg))); maxdevnratepos=max(max(abs((nrateposavg- oldnrateposavg)./oldnrateposavg))); maxdevnrateneg=max(max(abs((nratenegavg- oldnratenegavg)./oldnratenegavg))); if (max([maxdevn maxdevsratepos maxdevsrateneg maxdevnratepos maxdevnrateneg]) < tolerance) % if tolerance is met quit iteration tcheck=0; end end %update oldsrateposavg=srateposavg; oldsratenegavg=sratenegavg; oldnrateposavg=nrateposavg; oldnratenegavg=nratenegavg; qold=qnew; n=nnew; end % End of file %__________________________________________________________________ 170 File: elecfield.m % function name: elecfield % calculate electric field in both pos and neg directions by solving a set % of simultaneous linear differential equations % input parameter: signal frequencies vector: nu (column), carrier density % vector: n (row), signal input electric fields vector: ein (column) % output parameter: positive electric field matrix: epos, negative % electric field matrix: eneg, gain coefficient matrix: gaincoeff function [epos,eneg,gaincoeff] = elecfield(nu,n,ein) global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm bias % initialization epos=zeros(1,nz+1); eneg=zeros(1,nz+1); A=zeros(2*(1+nz),2*(1+nz)); B=zeros(2*nz+2,1); gaincoeff=gm(nu,n); %gain matrix losscoeff=alpha(n); ratio=0.68; %scale factor on RHS of diff eq A(2*nz+1,nz+1)=-r2; A(2*nz+1,2*nz+2)=1; A(2*nz+2,1)=1; A(2*nz+2,nz+2)=-r1; for i1=1:length(nu) A=zeros(2*(1+nz),2*(1+nz)); B=zeros(2*nz+2,1); for i=1:nz temp=(.5*(confine*gaincoeff(i1,i)-losscoeff(i)))*l/nz; A(i,i)=-1-temp*ratio; A(i,i+1)=1-temp*(1-ratio); A(i+nz,i+nz+1)=1-temp*(1-ratio); A(i+nz,i+nz+2)=-1-temp*ratio; end A(2*nz+1,nz+1)=-r2; A(2*nz+1,2*nz+2)=1; A(2*nz+2,1)=1; A(2*nz+2,nz+2)=-r1; B(2*nz+2,1)=(1-r1)*ein(i1); 171 E=inv(A)*B; if i1==1 epos=E(1:nz+1)' ; eneg=E(nz+2:2*nz+2)' ; else epos=[epos;E(1:nz+1)' ]; eneg=[eneg;E(nz+2:2*nz+2)' ]; end end % End of file %__________________________________________________________________ 172 File: sponrate.m % function name: sponrate % calculate noise photon rates in both pos and neg directions by solving a set % of simultaneous linear differential equations % input parameter: noise frequencies vector: nunoise (column), carrier density % vector: n (row), % output parameter: positive noise photon rate matrix: noisepos, negative % noise photon rate matrix: noiseneg, function [noisepos,noiseneg] = sponrate(nunoise,n) global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm bias [gaincoeff,gaincoeffp]=gm(nunoise,n); Rsp=confine*gaincoeffp*km*noisefreqspacing(n); alphavect=k0+confine*k1*n; ratio=0.68; for i1=1:length(nunoise) A=zeros(2*(1+nz),2*(1+nz)); B=zeros(2*nz+2,1); for i=1:nz temp=(confine*gaincoeff(i1,i)-alphavect(i))*l/nz; A(i,i)=-1-temp*ratio; A(i,i+1)=1-temp*(1-ratio); A(i+nz,i+nz+1)=1-temp*(1-ratio); A(i+nz,i+nz+2)=-1-temp*ratio; %change it back to -temp end A(2*nz+1,1)=1; A(2*nz+1,nz+2)=-R1; A(2*nz+2,nz+1)=R2; A(2*nz+2,2*nz+2)=-1; B=[Rsp(i1,:)' ;-Rsp(i1,:)' ;0;0]*l/nz; noise=inv(A)*B; if i1==1 noisepos=noise(1:nz+1)' ; noiseneg=noise(nz+2:2*nz+2)' ; else noisepos=[noisepos;noise(1:nz+1)' ]; noiseneg=[noiseneg;noise(nz+2:2*nz+2)' ]; end end % End of file %__________________________________________________________________ 173 File: alpha.m % function name: alpha % calculate material loss coeff. (alpha, which is modeled as a linear function of carrier density) % input parameter: carrier density vector: n (row) % output parameter: losscoefficient vector: losscoeff (row) function losscoeff=alpha(n) global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm bias % real function body losscoeff=k0+confine*k1*n; % End of file %__________________________________________________________________ 174 File: gm.m % function name: gm % calculate gain coefficient matrix for all wavelengths in each section % input parameter: signal or noise freq vector: nu (column), carrier density vector: n (row) % output parameter: gaincoefficient matrix: gaincoeff, gain component: % gainacoeffgain, absorption component: gaincoeffabsorption function [gaincoeff,gaincoeffgain,gaincoeffabsorption]=gm(nu,n) global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm bias % real function body tau=1./(arad+brad*n); % radiative carrier recombination lifetime is dependent on n eg0=e*0.774;%(a+b*y+c*y^2); % bandgap energy with no injected carriers deltaegn=e*kg*n.^(1/3); % bandgap shrinkage due to the injected carrier density egn=eg0-deltaegn; % bandgap energy ea=(h*nu*ones(1,nz)-ones(length(nu),1)*egn)*mhh/(me+mhh); eb=-(h*nu*ones(1,nz)-ones(length(nu),1)*egn)*me/(me+mhh); nc=2*(me*k*temperature/(2*pi*hbar^2))^(3/2); mdh=(mhh^(3/2)+mlh^(3/2))^(2/3); nv=2*(mdh*k*temperature/(2*pi*hbar^2))^(3/2); smalldelta=n/nc; p=n; epsilon=p/nv; efcvect=k*temperature*(log(smalldelta)+smalldelta.*(64+0.05524*smalldelta.*(64+ sqrt(smalldelta))).^(-1/4)); efvvect=- k*temperature*(log(epsilon)+epsilon.*(64+0.05524*epsilon.*(64+sqrt(epsilon))).^(- 1/4)); efc=ones(length(nu),1)*efcvect; efv=ones(length(nu),1)*efvvect; fcv=1./(exp((ea-efc)/(k*temperature))+1); % Fermi-Dirac distribution in the Conduction Band 175 fvv=1./(exp((eb-efv)/(k*temperature))+1); % Fermi-Dirac distribution in the Valance Band gpart1=(clight^2)./(4*sqrt(2)*pi^(3/2)*n1^2*(nu.^2)*ones(1,nz)*diag(tau)); gpart2const=(2*me*mhh/(hbar*(me+mhh)))^(3/2); gpart3=sqrt(nu*ones(1,nz)-ones(length(nu),1)*egn/h); gaincoeff=(gpart1.*gpart3).*(fcv-fvv)*gpart2const; gaincoeffgain=((gpart1.*gpart3).*fcv).*(1-fvv)*gpart2const; gaincoeffabsorption=((gpart1.*gpart3).*(1-fcv)).*fvv*gpart2const; % End of file %__________________________________________________________________ 176 File: noisediscretefreq.m % function name: noisediscretefreq % calculation of discrete noise frequencies % input parameter: carrier density vector: n (row) % output parameter: noise frequencies vector: nunoise (column) function nunoise=noisediscretefreq(n) global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm bias % nu0 calculation eg0=e*.774;%(a+b*y+c*y^2); % bandgap energy with no injected carriers deltaegn=e*kg*n.^(1/3); % bandgap shrinkage due to the injected carrier density egn=eg0-deltaegn; % bandgap energy nuc=max(egn)/h; % basis freq nubasis=noisefreqspacing(n); divide=nuc/nubasis; nu0=ceil(divide)*nubasis; i=(1:nm)' ; nunoise=nu0+(i-1)*km*nubasis; % End of file %__________________________________________________________________ 177 File: noisefreqspacing.m % function name: noisefreqspacing % calculate the noise longitudinal mode freq spacing % input parameter: carrier density vector: n (row) % output parameter: noise freq spacing : deltanum (number) function deltanum=noisefreqspacing(n) global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm bias % trapezoidal integration deltaz=l/nz; dneqwrtdnprime=(n1*confine/(neq0*(2-confine)))*dn1wrtdn; neq=neq0+dneqwrtdnprime*n; %neq=neq0+dneqwrtdn*n; neqsum=sum(neq); deltanum=clight/(2*neqsum*deltaz); % End of file %__________________________________________________________________ 178 File: noisenormfactor.m % function name: noisenormfactor % calculation of noise normalization factors % input parameter: noise frequencies vector: nunoise (column), carrier density vector: n (row) % output parameter: noise normalization factors matrix: knoisefactor (each % column is the same i.e. same factor for each section for a given wavelength function knoisefactor=noisenormfactor(nunoise,n) global y x lc lt l d w confine kg n1 n2 dn1wrtdn neq0 dneqwrtdn incouploss outcouploss R1 R2 r1 r2 k0 k1 arad brad anrad bnrad caug dleak a b c global me mhh mlh clight h hbar k temperature e ns nz km nm bias gaincoeff=gm(nunoise, n); losscoeff=ones(length(nunoise),1)*alpha(n); gs=(exp((sum((confine*gaincoeff-losscoeff)' ))*l/nz))' ; gamma=4*sqrt(R1*R2)*gs./((1-gs*sqrt(R1*R2)).^2); knoisevect=1./sqrt(1+gamma.^2); knoisefactor=knoisevect*ones(1,nz); % End of file %__________________________________________________________________

Abstract (if available)

Abstract The past decade has witnessed tremendous growth in telecommunication network traffic. The ever-increasing demand for bandwidth has been tackled primarily through wavelength-division-multiplexing technology. However, with the emergence of multimedia applications, the high-capacity transport capability offered by optical-fiber systems has started to move away from the network core towards the end users. This trend has led to diverse networks with critical interoperability needs. As single channel data rates increase and wavelength channel spacing continues to reduce in order to enable cost-effective, high spectral efficiency links, the work load on the conventional electronic signal processing elements in the network routers is building up. Signal processing in the optical domain can potentially alleviate this bottleneck if the properties unique to the optical domain are leveraged efficiently to assist conventional electronic processing methodologies. Ultra-high speed capability along with the potential for format-transparent and multi-channel operation make optical signal processing an attractive technology poised to make a big impact on future optical networks.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Kumar, Saurabh (author)

Core Title Optical signal processing for high-speed, reconfigurable fiber optic networks

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 11/09/2006

Defense Date 10/20/2006

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag fiber optics,nonlinear optics,OAI-PMH Harvest,optical communication,optical logic,optical signal processing,optical switching

Language English

Advisor Willner, Alan E. (committee chair), Bickers, Nelson Eugene, Jr. (committee member), Dapkus, P. Daniel (committee member), Steier, William H. (committee member)

Creator Email skumar@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m128

Unique identifier UC1134525

Identifier etd-Kumar-20061109 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-22041 (legacy record id),usctheses-m128 (legacy record id)

Legacy Identifier etd-Kumar-20061109.pdf

Dmrecord 22041

Document Type Dissertation

Rights Kumar, Saurabh

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu