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Designable nonlinear power shaping photonic surfaces
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Designable nonlinear power shaping photonic surfaces
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Content
Designable nonlinear
power shaping photonic
surfaces
A DISSERTATION SUBMITTED TO THE FACULTY OF THE USC
GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF
PHILOSOPHY (ELECTRICAL ENGINEERING –
ELECTROPHYSICS)
Roshni Biswas
December 2015
2
Dedication
In memory of my uncle and aunt, Samir Kumar Datta and Kalyani Datta for their
unending love, support and inspiration...
3
Acknowledgements
First, I would like to express my deepest gratitude to my advisor, Professor Michelle L. Povinelli,
for her unwavering support throughout my tenure as a graduate student at USC. Her command
on the research subject matter and professional guidance enriched my graduate experience
and helped prepare me for a life outside school. Her inquisitive and positive spirit pushed the
quality of my work during my PhD, and for this I am forever grateful. She also made tireless
efforts in improving my oral presentation skills, which I have benefited from greatly. Next, I
would like to acknowledge the help I received from my first mentor at USC, Dr. Mehmet
Solmaz. His experimental proficiency helped me immensely as I began my research at USC.
During our GUV project, I also received a great deal of help from Dr. Camilo Mejia with optical
simulations. I am also thankful to Dr. Luis Javier Martinez, from whom I learnt SOI fabrication
processes and optical characterization procedures; his passion and knowledge regarding this
subject matter was invaluable to my PhD. I extend thanks to my labmate, Dr. Chenxi Lin, who
helped me tremendously in the beginnings of my non-linear optics project. I would like to
acknowledge the contributions from Dr. Eric Jaquay and Dr. Jing Ma in various phases of my
research. I would like to express my appreciation for Dr. Ningfeng Huang, who started his PhD
alongside me, and whose sparks of brilliance helped me solve problems critical to my research.
It was really a pleasure working with Duke Anderson and spending hours in the lab solving
optical setup and fabrication issues. He always volunteered to proof-read my technical writings,
for which I am grateful. Also, it was wonderful to work with my junior labmates Shao-Hua Wu
4
and Aravind Krishnan. I extend my best wishes to Duke, Shao-Hua and Aravind for their careers
ahead. I would say that I have been extremely lucky to have had labmates like all of you, who
made this arduous journey a fun-filled, and fulfilling one.
I want to express my gratitude to Professor Noah Malmstadt for making our
collaboration with his group in the GUV projects a successful one. Shalene Sankhagowit, from
the Malmstadt group, was an amazing research partner to work alongside.
I would also like to extend my thanks to Dr. Donghai Zhu whose untiring efforts kept
(and keep) the cleanroom running. I would like to thank the HPCC and its staff for
computational resources, without which, the computations in this thesis would not be possible.
I would also like to acknowledge the generous support from various funding agencies during my
PhD: the USC Viterbi Fellowship and the National Science Foundation.
I want to express sincere thanks to Professor P. Daniel Dapkus and Professor Stephen
Cronin for serving on my PhD Qualification Exam committee. My deepest regards goes to
Professor Wei Wu and Professor Noah Malmstadt for being in both my PhD Qualification and
Defense committee.
I am enormously indebted to my parents, Mallika Biswas and Chittaranjan Biswas, and
my husband, Dipankar Das, for their unconditional love and support in my life and also during
my PhD.
5
Contents
Chapter 1 : Introduction ...................................................................................................... 12
1.1 Systems showing non-linear transmission ............................................................................... 12
1.2 Photonic Crystal Slabs: Guided Resonance Modes .................................................................. 13
1.3 Absorptive guided resonance modes in silicon PCS ................................................................ 14
1.4 Non-linear optical response using guided resonance modes .................................................. 15
1.5 Demonstration of thermo-optically induced nonlinearity in silicon ........................................ 18
1.6 Thesis Outline........................................................................................................................... 20
Chapter 2 : Photonic surfaces for designable nonlinear power shaping ................................. 21
2.1 The Key Concept ...................................................................................................................... 21
2.2 Design of absorptive resonances: ............................................................................................ 22
2.3 Fabrication of two-dimensional photonic crystal .................................................................... 23
2.4 Fabrication of membrane ........................................................................................................ 25
2.5 Experimental setup and device characterization..................................................................... 27
2.6 Spectral shift at monitor wavelength ...................................................................................... 28
2.7 Non-linear power transmission ............................................................................................... 29
2.8 Discussion................................................................................................................................. 32
Chapter 3 : Enhancing the size of response........................................................................... 34
3.1 Background .............................................................................................................................. 34
3.2 Free-standing membrane ........................................................................................................ 35
3.3 Fabrication of carrier free-standing membrane on carrier handle.......................................... 36
3.4 Comparison between membrane on glass substrate and free-standing one ......................... 37
3.4.1 Spectral Shift Analysis................................................................................. 37
3.4.2 Non-linear transmission response ............................................................. 39
3.5 Isolate device from unpatterned silicon .................................................................................. 39
Chapter 4 : Time response of the non-linear transmission .................................................... 41
4.1 Laser induced thermal time scale ............................................................................................ 41
4.2 Coupled mode theory (CMT): Analytical form of absorption and transmission spectrum ..... 42
4.3 Determination of coefficients of the coupled mode theory expression ................................. 43
4.4 Analytical form for absorption and transmission spectrum from fitted parameters .............. 44
6
4.5 Transient heat transport in photonic crystal slab .................................................................... 45
4.5.1 Temperature rise: finite element methods modeling ................................ 47
4.5.2 Transmission change with temperature rise .............................................. 49
4.5.3 Comparison with silicon slab of equal thickness ........................................ 49
4.5.4 Finite Element Methods modeling results ................................................. 51
4.6 Maximizing non-linear response time and size ....................................................................... 53
4.6.1 Effect of the thermal conductivity on the response .................................. 53
4.6.2 Effect of the laser operating wavelength detuning on the response ........ 54
4.6.3 Effect of absorption Q on the size of the response.................................... 55
4.7 Experimental Verification ........................................................................................................ 56
4.7.1 Reasons for mismatch in theoretically and experimentally trends ........... 58
4.8 Enhancing the response by thermally isolation decreasing thermal conductivity .................. 59
4.9 Discussion................................................................................................................................. 61
Chapter 5 : Photonic Crystal Nano-heaters - Application in biological environment .............. 62
5.1 Comparison of absorption spectrum of a PCS and gold disk array .......................................... 63
5.2 Experimental validation in water ............................................................................................. 65
Chapter 6 : Future Work ...................................................................................................... 67
6.1 Size of response enhancement by optimizing Q ...................................................................... 67
6.2 Fabrication of photonic crystal infilled with gold .................................................................... 68
6.3 Preliminary simulation results ................................................................................................. 70
Chapter 7 : Conclusion ......................................................................................................... 72
Appendix A .......................................................................................................................... 73
A.1 Absorption and transmission spectrum shift of silicon slab with temperature ...................... 73
References .......................................................................................................................... 75
7
List of figures
Figure 1-1: Non-linear power input (P in) and output (P out) trends in a) saturable absorbers b) power
limiter c) inverter ........................................................................................................................................ 12
Figure 1-2: Schematic of a photonic crystal slab illuminated with normally incident radiation b)
transmission spectrum of a loss-less, non-dispersive photonic crystal slab as a function of normalized
frequency .................................................................................................................................................... 13
Figure 1-3: a) Refractive index (left axis) and absorption length (right axis) of crystalline silicon from
[1] b) Absorption due to a GRM in a silicon PC slab with lattice constant 380nm and hole size 95nm .... 15
Figure 1-4: Lousse et al (a) - (d) : (a) Schematic photonic crystal slab (b) Transmission spectrum (c)
Bistability observed when operation at Point a (d) (c) Bistability is observed when operation at
Point b; Ngo et al (e) - (g) : (a) 2D Photonic Crystal slab (f) Reflection spectrum for etch depth h and
layer thickness h (g) Bistable response for the device with etch depth 20nm and layer thickness
320nm; Zhang et al (h) - (j) : (h) SEM of fabricated 1D LiNbO3 Photonic Crystal Slab (i) Transmission
Spectrum of the fabricated device (j) Temporal response of probe transmission ..................................... 16
Figure 1-5: Almeida et al (a) - (b): (a) SEM of fabricated ring resonator (b) Bistable response with
microwatts of input power; Uesugi et al (c) - (d) : (c) SEM of the photonic crystal cavity (d) Radiation
efficiency (power radiated by the cavity) as a ............................................................................................ 19
Figure 2-1: a) Schematic of power-shaping surface and transmission spectrum of a guided resonance
mode for increasing incident laser powers; b) Transmission schematic for three characteristic laser
wavelengths ................................................................................................................................................ 22
Figure 2-2: a) Transmission and b) Absorption spectrum of silicon photonic crystal membranes with
lattice constant 420nm and three different radius values 63nm, 67nm and 70nm. For all the three
cases the laser wavelength (dotted line) is placed red-shifted from the resonance. ................................ 23
Figure 2-3: Schematic of fabrication steps of 2D photonic crystal and SEM of fabricated device ............. 24
Figure 2-4: a) Patterning membrane on SOI b) Dislodging patterned membrane by under etching the
buried oxide layer c) Transfer of the membrane to a circular glass slide ................................................... 26
Figure 2-5: Schematic of experimental setup ............................................................................................ 27
Figure 2-6: a) Transmission spectrum of 2D PC with lattice constant 380nm and hole diameter 95nm.
b) Spectral shift at monitor wavelength range, red and blue dashed lines correspond to original and
shifted resonances at 986 nm and 1015 nm............................................................................................... 28
8
Figure 2-7: a) Transmission spectrum for patterned and un-patterned silicon membrane and b) non-
linear power transmission corresponding to each device .......................................................................... 31
Figure 3-1: (a) and (d) SEM, (b) and (e) transmission spectrum, (c) and (f) steady state heat
distribution of stack and ladder device respectively .................................................................................. 35
Figure 3-2: Free standing nano-membrane positioned on perforated silicon substrate ........................... 35
Figure 3-3: Fabrication steps of free standing photonic crystal membrane ............................................... 36
Figure 3-4: Device on glass substrate a) white light spectrum b) spectral shift at monitor wavelength;
Free standing c) white light spectrum d) spectral shift at monitor wavelength ........................................ 38
Figure 3-5: Nonlinear power transmission with laser power for free-standing membrane
and membrane on glass substrate .............................................................................................................. 39
Figure 3-6: Device Isolation from unpatterned silicon a) schematic representation b) fabricated device
before membrane release from SOI ........................................................................................................... 40
Figure 4-1: Timescales of various electron and lattice processes in laser-excited solids. The schematic
represents a direct bandgap material. The time scales are equally applicable to silicon. Figure
reprinted from [58] ..................................................................................................................................... 41
Figure 4-2:a) Schematic of a photonic crystal slab illuminated with normally incident radiation b)
transmission spectrum of a loss-less, non-dispersive photonic crystal slab as a function of wavelength
and the corresponding fit to the analytical form derived from coupled mode theory .............................. 44
Figure 4-3: a) Transmission and c) absorption through PCS (a = 470nm and d = 160nm),
b) Transmission and d) absorption through an unpatterned silicon slab. Dotted line on the
transmission plots shows the position of the laser wavelength ................................................................. 45
Figure 4-4: Spatial profile of the temperature distribution after the laser pulse was turned
on for 17.4μs. The color bar represents temperature rise in Kelvin and the length scale is in nm............ 47
Figure 4-5: Left column and right column denote the PCS and unpatterned Silicon slab respectively (a)
and (b) Power absorbed (c) and (d) Temperature rise (e) and (f) Transmission as a function of time ..... 51
Figure 4-6: Variation of turnaround time with thermal conductivity k ...................................................... 53
Figure 4-7: Variation of response time with laser detuning from the resonance ...................................... 54
9
Figure 4-8 : (a) Absorption spectrum (b) Total absorbed power as a function of time (c) Temperature
variation of the device with time (d) Temporal response of transmission for the different absoprtive
quality factor ............................................................................................................................................... 56
Figure 4-9: a) Transmission spectrum of the fabricated device b) Transmission change as a function of
time ............................................................................................................................................................. 57
Figure 4-10: Microscope of image of a free standing silicon membrane with devices. The bottom right
device has trenches around it to improve thermal isolation ...................................................................... 59
Figure 4-11: a) Spectrum of devices with and without trenches around it b) Temporal response of the
transmission for the device without trenches c) Temporal response of the transmission for the device
with trenches .............................................................................................................................................. 60
Figure 5-1: Absorption spectrum of a gold nanoparticle array and a photonic crystal slab ...................... 64
Figure 5-2: (a) Transmission Spectrum (dotted line shows the laser operating wavelength),
(b) Non-linear transmission with laser power (c) Spectral shift at monitor wavelength for device
operating in water (d) Spectral shift at monitor wavelength for device operating in heavy water .......... 65
Figure 6-1: a) Temperature rise ( ΔT) (b) Maximum and minimum value of transmission observed in
the temporal response of transmission change as a function of the ratio of γ abs and γ rad ......................... 67
Figure 6-2: Fabrication of photonic crystal in-filled with gold .................................................................... 69
Figure 6-3: PCS with lattice constant 430 nm and radius 86nm a) Transmission and b) Absorption
spectrum. .................................................................................................................................................... 70
Figure 6-4: Electric field intensity profile through the center of the hole in one unit cell of the photonic
crystal a) without gold infilling in the holes and b) holes filled with 7nm thin gold layer. Devices are
illuminated normally with a plane colorbar represents electric field intensity in V
2
/m
2
........................... 71
Figure A.1: (a) Absorption and (b) Transmission spectrum of a 340 nm unpatterned silicon
slab. Dotted lines shows the position of the operating laser wavelength…………………………………74
10
Abstract
This dissertation involves the design of nonlinear input-output power responsive
surfaces based on absorptive resonances of nanostructured silicon membranes. We have
demonstrated that various power transmission trends can be obtained by placing a photonic
resonance mode at the appropriate detuning from the operating laser wavelength. In this work,
we used nanostructures to achieve arbitrary power response curves. We designed and
fabricated a flexible non-linear power transmission surface based upon a common silicon
microphotonic platform which can be tailored to obtain any desirable power relationship
between the input and the output. We have experimentally demonstrated non-linear optical
transmission of lasers (operating at 808 nm and 980nm) through silicon based photonic crystal
slabs. In this case we chose to operate at wavelengths where silicon is partially absorptive
(~800-1100nm). Since the photonic crystal slabs supports guided resonance modes (GRMs), the
absorption is enhanced near these resonances. The non-linear operation of the photonic crystal
slab is thus due to the resonantly enhanced thermo-optic effect of silicon. These results
illustrate the possibility of designing different nonlinear power trends within a single materials
platform at a given wavelength of interest.
In the next part of our work, we demonstrate a mechanism to enhance this current non-
linear behavior. The temperature rise in the structure for a fixed amount of input power is
11
directly proportional to the thermal conductivity of the material. We artificially decreased the
thermal conductivity of our structures via microfabrication techniques and hence increased the
resultant temperature which in turn magnified the non-linear response.
The resonantly enhanced absorption results in huge amount of local heating and
thereby causes a large temperature rise. In the third part of this thesis, we theoretically
calculated the temperature rise and its temporal response. The theoretical predictions were
then matched with experiments by observing the temporal response of the non-linear
transmission. We observed a large sudden temperature rise due the presence of the
absorptive resonance. This structure can therefore provide an alternative to gold nanoparticle
arrays which are extensively used for local heat generation in various lab-on-chip applications.
This includes chemical assays, vapor generation, microfluidic mixing and enhanced catalytic
effects. We also conducted the experiments in water in order to provide a proof of concept of
the efficacy of these structures as local heaters in biological environments.
12
Chapter 1 : Introduction
1.1 Systems showing non-linear transmission
The ability to design arbitrary relationships applications between input power and
output power would fundamentally impact a large range of in optics and photonics. Saturable
absorbers, for example, exhibit decreased absorption with increasing light intensity, where
transmission increases with input power (Figure 1-1 (a)). The non-linear absorption in saturable
absorbers has been extensively used for laser pulse shaping [2-6]. The opposite case, where
transmission decreases with input power, yields an optical inverter (Figure 1-1 (c)) [7]. Flat
output above a certain threshold power is characteristic of an optical limiter (Figure 1-1(b)) [8,
9].
Typically, however, these nonlinear input-output power relationships are all provided by
different materials and device designs. Moreover, approaches based on the electronic states of
a material are constrained to operate at particular wavelengths corresponding to electronic
transitions. In this work, we propose a mechanism for designing arbitrary input-output power
Figure 1-1: Non-linear power input (P in) and output (P out) trends in a) saturable absorbers b)
power limiter c) inverter
13
relationships in a single materials platform. Our approach, based on resonant electromagnetic
modes of periodic absorptive surfaces, can flexibly be tailored for operation at a wavelength of
interest. The key element of this approach is the presence of a guided resonance mode [5, 6] in
a partially absorptive system. As a prototypical example, we will be considering thermo-
optically induced non-linearity in 2D photonic-crystal slabs in silicon.
1.2 Photonic Crystal Slabs: Guided Resonance Modes
Photonic crystal slabs, featuring two dimensional (2D) arrays of periodic structures[10],
has been the focus of extensive research [11]. The existence of standing Bloch modes, also
known as guided resonance modes, in these structures has been an active area of research [12].
We can understand the origin of these resonances in the following manner. Light incident from
air (low permittivity medium) onto a uniform silicon slab (high permittivity medium) cannot
couple to the guided modes in the slab (possessing an in-plane translational symmetry) due to
the conservation of in-plane wave vector [13]. However, when the slab is punctured with array
Figure 1-2: Schematic of a photonic crystal slab illuminated with normally incident radiation
b) transmission spectrum of a loss-less, non-dispersive photonic crystal slab as a function of
normalized frequency
14
of holes, the translational symmetry is reduced, and the in-plane wave vector is conserved only
up to the reciprocal lattice vector, thus allowing incident light to couple to guided modes of the
slab. These guided resonance modes interfere with the Fabry Perot oscillations of the slab
giving rise to Fano shaped resonances on a smoothly varying background [12, 14]. Of these
guided modes, Γ-point modes of the slabs, excited by a normally incident plane wave with
appropriate symmetry properties [15], are particularly interesting for a plethora of applications.
The transmission spectrum of a non-dispersive loss-less photonic crystal slab (Figure 1-2 (a))
illuminated by a normally incident beam is illustrated in Figure 1-2(b). Due to the resonantly
enhanced optical near-field, these devices are extensively used as filters [16, 17] and sensors
[18, 19]. They have also been used for enhancement of fluorescence in dyes [20, 21], single
molecules [22], and colloidal quantum dots [23]. Properly designed modes in these structures
also leads to enhanced coupling of normally incident light. Therefore, these modes can
significantly improve the light extraction from semiconductors [24], LEDs [25, 26] and lasers [20,
27-30]. However, most of the silicon based PC slabs focus on guided resonance modes in the
optical communication band, where silicon is non-absorptive, resulting in very high quality (Q)
factor modes [31].
1.3 Absorptive guided resonance modes in silicon PCS
Recently, however, due to the proliferation of the photovoltaics research, there has
been interest in exploiting guided resonance modes in the absorptive regime of silicon. Too
high of absorption in the substrate destroys the resonance, due to the loss associated with
increased absorption. However, silicon is moderately absorptive between the wavelength
ranges of 365nm to 1127nm; this range corresponds to the separation between silicon's direct
15
and indirect band-gap energy (Figure 1-3(a)). This region of low absorptivity leads to the
existence of resonance modes [32-34] which have moderately high quality factors (a few
hundred). Due to the resonantly enhanced electric field within the substrate, the guided
resonance modes are associated with enhanced absorption (Figure 1-3(b)) which is exploited in
photovoltaic applications. This suggests that one should be able to achieve resonantly-
enhanced thermo-optic effects in this regime utilizing these modes. This is of particular interest
for achieving nonlinear transmission in the current work.
1.4 Non-linear optical response using guided resonance modes
Nonlinear response of guided resonance modes in photonic crystal slabs has been
studied previously in the optical communication band. But the non-linear coefficient of silicon
(e.g. Kerr coefficient of silicon at 1550 nm is 0.45×10-
13
cm
2
/W) in this wavelength range is too
low to produce any appreciable response. Thus in order to produce significant non-linear
response, researchers used highly non-linear materials like chalcogenides (e.g. As2S3) [35, 36] or
lithium niobate (LiNbO3) [37]. Increased Kerr non-linearity in these materials has shown
Figure 1-3: a) Refractive index (left axis) and absorption length (right axis) of crystalline
silicon from [1] b) Absorption due to a GRM in a silicon PC slab with lattice constant
380nm and hole size 95nm
16
different non-linear behavior including optical switching and bistability. For example, some
Figure 1-4: Lousse et al (a) - (d) : (a) Schematic photonic crystal slab (b) Transmission
spectrum (c) Bistability observed when operation at Point a (d) (c) Bistability is observed
when operation at Point b; Ngo et al (e) - (g) : (a) 2D Photonic Crystal slab (f) Reflection
spectrum for etch depth h and layer thickness h (g) Bistable response for the device with etch
depth 20nm and layer thickness 320nm; Zhang et al (h) - (j) : (h) SEM of fabricated 1D LiNbO3
Photonic Crystal Slab (i) Transmission Spectrum of the fabricated device (j) Temporal
response of probe transmission
17
early theoretical work by Lousse et al. [35], involves the exploitation of guided resonance
modes to obtain optical bistability. Their structure (Figure 1-4(a)) consists of two dimensional
array of holes in a triangular lattice. The holes are etched on a three layer structure where a
layer of Kerr non-linear material (As 2S 3) is sandwiched between two layers of a linear material
(Silicon). They observed (Figure 1-4(c) and (d)) different bistable curves depending on the
detuning of the operation point (Point a and b) with respect to the location of the resonant
wavelength (Figure 1-4(b)). More recently, Ngo et al. [36] also showed bistable response
exploiting guided resonance modes in a chalcogenide (As 2S 3) based photonic crystal slab (Figure
1-4(e)). They varied the quality factor of the resonances by changing the etch depth and the
thickness of the slab as depicted in the reflection spectrum shown in Figure 1-4(f). The bistable
response for the device with the highest quality factor is shown in Figure 1-4(g), which shows a
switching threshold of ~0.1 GW/cm
2
. An ultrafast tunable Fano resonance was observed
experimentally in a lithium niobate (LiNbO 3) based 1D photonic crystal structure[37]. Figure
1-4(h) shows the SEM of the fabricated device and the corresponding transmission spectrum is
shown in Figure 1-4(i). They employed a pump probe method (pump and probe operating at
the same wavelength but the probe power is 1% of the pump) to observe the temporal
response of the probe transmission change as the resonance moves past the operating
wavelength (1500nm), due to induced spectral shift from the pump power. A pump power of
30MW/cm
2
is required to induce the non-linear effects. However, it should be noted that the
materials having large Kerr non-linearity are not compatible with standard CMOS technology
and the switching threshold for these devices ranges from tens of MW/cm
2
to a few GW/cm
2
.
18
Current state-of-the-art-technologies exploiting optical non-linear effects [38-42] focus
on the optical communication band. However, efforts are seldom considered to shift the
operation wavelength to regions near the indirect bandgap of silicon. This region is of practical
importance as it is where linear absorption can be exploited to induce non-linearity through the
thermo-optic effect of silicon.
1.5 Demonstration of thermo-optically induced nonlinearity in silicon
Thermo-optic effects in silicon can give very strong nonlinearities, as has been
demonstrated by several groups using various resonator systems. The Lipson group [43] has
demonstrated bistability at telecommunication wavelengths using microring resonators Figure
1-5(a)) by exploiting the thermo-optic nonlinearity of silicon. The quality factors of these
resonators are estimated to be on the order of a few thousand, and hence the switching
threshold goes down to a few microwatts. The bistable response is depicted in Figure 1-5 (b),
and the markers define the curve points related to the transmission spectrum shown in the
inset. Thermo-optic bistability was also observed by Uesugi [44] and co-workers in ultra-high Q
silicon based photonic crystal cavities Figure 1-5 (c)) operating in the telecommunication band.
The sharp transition (Figure 1-5 (d)) of the radiated power from the cavity with increasing input
power is a signature of the bistable response [39, 45, 46] for these devices. Several other
groups [39, 40, 47-53] have also exploited thermo-optic nonlinearity in high Q photonic crystal
cavities to induce bistable response. The low switching threshold observed in these devices is
attributed to their ultra-high quality factor. Thermo-optically induced bistability involving Fano
resonances has also been experimentally demonstrated in photonic crystal cavities [45]. The
19
switching threshold was shown to be reduced further by depositing 2D materials like graphene
on silicon [54].
However, coupling to the cavity modes is not straight forward and requires special
optics. Free space optics provides a more suitable platform to extend the non-linear
functionality of silicon to large scale parallel optical networks. In all of these previously
mentioned cases, the thermo-optic effect was resulting from two photon absorption (TPA)
processes. Here, in this work linear absorption effects are directly exploited which will have an
enhanced effect. In addition, the structures we use function as nonlinear, power-shaping
Figure 1-5: Almeida et al (a) - (b): (a) SEM of fabricated ring resonator (b) Bistable response
with microwatts of input power; Uesugi et al (c) - (d) : (c) SEM of the photonic crystal cavity
(d) Radiation efficiency (power radiated by the cavity) as a
20
surfaces: due to their 2D periodicity, they can provide nonlinear power transmission over
extended areas.
1.6 Thesis Outline
As mentioned before, the key element of this approach is the presence of a guided
resonance mode in a partially absorptive system. As a prototypical example, 2D photonic-
crystal slabs in silicon are considered. In Chapter 2, it will be shown, that resonantly enhanced
absorption can be used to design increasing, decreasing, or nonmonotonic output transmission
as a function of input power, all within the same materials platform. The nonlinear power
response results from a shift in the resonance mode due to absorptive heating, in combination
with the thermooptic effect. Chapter 3 deals with the method of maximizing the effect by
thermally isolating the structures. In Chapter 4, a theoretical foundation is laid to numerically
calculate the temperature rise in the structures and obtain its temporal response. Based on the
conclusions drawn from Chapter 4, we can envision these structures as nanoheaters. In Chapter
5, first a comparison of these structures is made with existing gold nanorod array which are
proven to extremely efficient nanoheaters. The nonlinear behavior of these devices are then
shown in a biocompatible medium (water in this case), to prove the successful operation of the
devices as a nanoheater for biological applications. Finally, Chapter 6 concludes the thesis by
providing some directions to relevant future work.
21
Chapter 2 : Photonic surfaces for
designable nonlinear power shaping
A version of this Chapter was published as reference [55].
2.1 The Key Concept
To demonstrate the idea of nonlinear power shaping, photonic crystal slabs featuring a
two dimensional array of holes was employed. The key concept we propose is shown in Figure
2-1. We considered a normally incident laser on the photonic-crystal slab, as shown in the inset
to Figure 2-1(a). The slab is designed to support a guided resonance mode in the wavelength
range of interest. The transmission spectrum is shown schematically in Figure 2-1(a). The low-
power spectrum is plotted with a red line (labeled P = 0). As the incident laser power is
increased, the light absorbed in the slab increases, heating the material. Due to the thermo-
optic effect, the refractive index changes with temperature, shifting the resonance to higher
wavelengths. This effect is shown schematically in the Figure 2-1(a) for powers P2 > P1 > 0.
The power-dependent transmission will depend on the position of the resonance
relative to the laser wavelength. For λlaser= λA, the laser is close to the low-power resonance dip.
In this case, the transmission increases with increasing laser power, as plotted in Case A of
Figure 2-1(b). For λlaser= λB, the transmission decreases and then increases with increasing
power (Case B), and for λlaser= λA, (Case C), the transmission decreases. In practice, for a given
laser wavelength of interest the lattice constant and hole size of the photonic crystal slab can
be designed to place the low-power resonance at the appropriate detuning from the laser
wavelength, yielding Case A, B, or C as desired.
22
Figure 2-1: a) Schematic of power-shaping surface and transmission spectrum of a guided
resonance mode for increasing incident laser powers; b) Transmission schematic for three
characteristic laser wavelengths
2.2 Design of absorptive resonances:
To demonstrate the three general ingredients for nonlinear power shaping shown in
Figure 2-1(b), we designed and fabricated photonic-crystal slabs in silicon. The operation
wavelength was 808nm where silicon is partially absorptive. We designed and simulated the
optical properties of various photonic crystal slabs with absorptive resonance near this
operating wavelength using the finite domain time difference method (Lumerical Solutions®).
The transmission and absorption spectrum of a representative silicon photonic crystal slab on
23
glass substrate is shown in Figure 2-2(a) and (b). The detunings from the operating wavelength
(808nm) is varied by changing the hole size and keeping the lattice constant fixed at 420nm. As
evident in Figure 2-2(b), the guided mode resonances are associated with absorption
enhancement which in turn leads to enhanced thermo-optic nonlinearity.
2.3 Fabrication of two-dimensional photonic crystal
The simulated devices are fabricated in Keck Photonics Cleanroom Laboratory at USC.
The process begins with a silicon-on-insulator wafer with the following layers: 340 nm Si device
layer, 2 μm buried oxide layer, 600 μm silicon handle layer. After solvent and O 2 plasma
cleaning, an HF dip is performed to remove the native oxide. Electron beam resist is spin coated
onto the wafer at 3,000 rpm for 60 seconds, resulting in a layer approximately 300 nm thick.
The resist is Poly(methyl methacrylate), i.e. PMMA, with a 4% concentration of anisole and a
molecular weight of 950K. The sample is baked at 160 °C for 70 minutes to evaporate the
Figure 2-2: a) Transmission and b) Absorption spectrum of silicon photonic crystal
membranes with lattice constant 420nm and three different radius values 63nm, 67nm and
70nm. For all the three cases the laser wavelength (dotted line) is placed red-shifted from
the resonance.
24
solvent. The samples are then exposed in the Raith e-Line 150 system using an acceleration
voltage of 30 kV and an aperture of 10 μm, which produces a current of approximately 32 pA.
The exposed pattern is created in the Raith software using proximity-corrected doses and a
curved-features exposure mode.
After exposure the samples are then developed in a 1:3 mixture of methyl isobutyl
ketone (MIBK) to isopropyl alcohol (IPA) for 45 seconds. This developing is followed by a rinse in
IPA for 45 seconds. Etching is done in the Oxford DRIE system using a modified Bosch process
with the following parameters: 33.0 sccm of SF 6 (etchant), 57.0 sccm of C 4F 8 (polymer coating
for protecting sidewalls), 20 mT chamber pressure, 30 W inductively-coupled plasma (ICP)
power, 600 W reactive ion etching (RIE) power, 52 seconds etching time. The modified Bosch
Figure 2-3: Schematic of fabrication steps of 2D photonic crystal and SEM of fabricated device
25
etching recipe was developed following the guidelines in [56] and produces smooth, vertical
sidewalls. An example of a fabricated device is shown in Figure 2-3.
2.4 Fabrication of membrane
After the fabrication of the photonic crystal pattern, we used the method described in
[57] to fabricate a photonic crystal membrane. We used standard ultraviolet (UV)
photolithography to define a 6mm×6mm square membrane region in the silicon device layer, as
shown in Figure 2-4(a). The central square part of the membrane has measured dimensions of
500 μm ×500 μm and was aligned to overlap with the photonic crystal patterns. The remainder
of the membrane was patterned with an array of circular access holes (40 μm in diameter, 500
μm in pitch) to facilitate the wet chemical etching of the buried oxide layer in hydrofluoric acid.
Samples were spin coated with AZ5214E positive photoresist at 3000 rpm for 45 seconds and
then the resist was soft baked at 100⁰C for 2 mins. The pattern was transferred to the resist by
exposing the coated sample to UV light (100mJ/cm
2
) in a mask aligner (Karl Suss MJB-3). The
photoresist was then developed in AZ400K (1:4 concentration) and post baked at 170⁰C for 2
mins. ICP-RIE etching was used to transfer the membrane pattern to the sample, using the
same recipe described above. The remaining photoresist was removed by ultra-sonication in
acetone followed by oxygen plasma. In order to release the silicon membrane from the handle
silicon substrate, we immersed the sample in hydrofluoric acid (concentration, 52%, Avantor-
Macron Fine Chemicals) for 5-6 hours to completely remove the buried oxide layer. The
released membrane remained weakly adhered to the underlying silicon handle wafer due to
surface tension. When transferred to deionized water, the membrane quickly detaches from
the substrate and floats, as shown in Figure 2-4(b). The membrane is then picked up using a
26
circular glass slide, 1 inch in diameter, which can later be threaded into a lens tube with 1 inch
internal diameter to facilitate the subsequent optical measurement process.
Figure 2-4: a) Patterning membrane on SOI b) Dislodging patterned membrane by under
etching the buried oxide layer c) Transfer of the membrane to a circular glass slide
27
2.5 Experimental setup and device characterization
The experimental setup is shown in Figure 2-5. The sample is mounted on a translation
stage for positioning. A laser (808nm) and/or white light source (Ocean Optics HL-2000) can be
used as input excitations. The light is focused through a microscope objective onto the sample.
The transmitted light is collected by a second microscope objective and passes through a beam
splitter. The path connected to the spectrometer (Ocean Optics USB 4000) contains a notch
filter centered at 808nm to remove the IR laser light. The path connected to the photodetector
contains a band pass filter centered at 808nm to remove the majority of the white light. .
Figure 2-5: Schematic of experimental setup
28
We first characterized the resonance modes of our devices by measuring the low-power
transmission spectra with the white light source and spectrometer (Ocean Optics USB 4000).
The spectrum for a device with 95nm diameter holes and a lattice constant of 380nm is shown
in Figure 2-6(a). The spectrum shows several prominent dips, corresponding to resonant modes.
The mode at 803nm lies closest to the laser wavelength of 808nm. A fit of the transmission
spectrum yielded a quality factor of 216.
2.6 Spectral shift at monitor wavelength
We verified the spectral shift of the GRM due to induced nonlinearities in silicon with
increasing laser power at a monitor wavelength range (825nm - 1050nm). This is achieved by
illuminating the sample simultaneously with a broadband white light source and the laser. The
transmitted light after filtering through a notch filter (centered at 808nm) is fed to a
spectrometer (Ocean Optics USB 4000). Figure 2-6(a) shows the transmission spectrum of a 2D
Figure 2-6: a) Transmission spectrum of 2D PC with lattice constant 380nm and hole diameter
95nm. b) Spectral shift at monitor wavelength range, red and blue dashed lines correspond to
original and shifted resonances at 986 nm and 1015 nm
29
photonic crystal membrane with a square array of holes (diameter 95nm and lattice constant
380nm) etched on to silicon. This resonant position represents case B in Figure 2-1(a), where
the resonance is red-detuned from the laser wavelength (808nm). Figure 2-6(b) shows the
optical transmission in the monitor wavelength range for three different laser powers
(integrated power on a beam with spot size 80 microns). The systematic shift of the location of
the GRM with increasing laser power is illustrated and the reduction of quality factor due to
enhanced absorption can also be observed. For example, the guided resonance mode located
at 987nm undergoes a shift of 11nm and 29nm when the integrated laser power is 149mW and
340mW, respectively. With the fractional change in wavelength being proportional to the
fractional change in refractive index, a spectral shift of 29nm at 927nm wavelength corresponds
to a shift of 23nm at 808nm wavelength.
2.7 Non-linear power transmission
To illustrate the three, representative nonlinear trends shown in Figure 2-1, we used
three devices with resonances at different wavelengths. Device I has a hole diameter of 120nm
and a lattice constant of 400nm, and device II has a hole diameter of 114nm and a lattice
constant of 380nm. Device III is the same as in Figure 2-6.
The low-power transmission spectra for all three devices are shown in Figure 2-7(a). The
dashed line indicates the laser wavelength. All three devices have prominent resonant dips
within the spectral range shown. For comparison, we also plot the transmission through the
unpatterned silicon device layer. We next measure the laser power transmission for each of the
devices as a function of laser power.
30
For device I, the resonant dip is very close to the laser wavelength (~807nm),
corresponding to Case A. As the laser power is increased, the transmission increases, as shown
in Figure 2-7(b). We may interpret this trend in terms of a shift of the low-power transmission
spectrum to higher wavelength. For powers greater than ~190mW, the transmission decreases
again. This is due to the shifting of the lower-wavelength resonance (initially at 783nm in Figure
2-7(a)) towards the laser wavelength. This behavior corresponds to Case C in Figure 2-1(b).
Considering the spectral shift (24nm) at the monitor wavelength (903 nm) for this device at
346mW laser power, we estimated a spectral shift of 21.5nm at 808nm (assuming the fractional
shift in wavelength, Δλ /λ. is same at both the wavelengths). This confirms the shift of the
resonance at 783nm in the vicinity of the laser wavelength.
For device II, the resonance is initially at a lower wavelength than the laser. The laser
power transmission, shown in Figure 2-7(b), decreases and then increases again, similar to Case
B in Figure 2-1(b). Device III also has a resonance at lower wavelength than the laser, but it lies
closer to the laser wavelength than Device II. A similar nonlinear transmission trend is observed,
but the turn-around power (separating decreasing and increasing transmission regimes) is
smaller than for Device II. At much larger powers, the transmission decreases again, due to
lower-wavelength resonances (Case C).
31
These results show that we can use patterning to create very large nonlinearities in
optical power transmission. Moreover, we can design the structure to obtain either increasing
or decreasing transmission as a function of input power. In comparison, the nonlinearities in
unpatterned silicon are weak. For comparison, we plot the laser power transmission for the
unpatterned silicon device layer in Figure 2-7(b). The transmission change is minimal, compared
to the large changes seen for the photonic-crystal devices.
Figure 2-7: a) Transmission spectrum for patterned and un-patterned silicon membrane
and b) non-linear power transmission corresponding to each device
32
2.8 Discussion
The operating wavelength we choose for this study, 808nm, corresponds to energy
greater than the bandgap of silicon. We expect the effects of linear absorption to be larger than
those of free carrier dispersion (due to carriers generated by either linear or two-photon
absorption). Linear absorption results in the thermalization of free carriers, heating the
silicon[58]. Due to the positive thermo-optic coefficient of silicon, the refractive index increases
with temperature and shifts the resonances to higher wavelength. Free carrier dispersion will,
in contrast, shift the resonances to lower wavelength[44]. From the experimental results, we
may conclude that thermal effects indeed dominate.
The large spectral shifts induced by enhanced thermo-optic effect that we observe can
be attributed to several factors. The temperature rise ( ΔT) of the device is related to the
absorbed power (Pabs) and the thermal resistance (Rth) by the equation
abs th
T P R . The
electromagnetic field intensity in the photonic crystal slab is resonantly enhanced, increasing
absorption, Pabs. As an example, for device I, we found that the simulated absorption at the
resonant wavelength is 28%, compared to 1.2% for unpatterned silicon slab. In addition, Rth,
which is inversely proportional to the thermal conductivity, depends on the geometry of the
device. The thermal conductivity of the photonic crystal slab is lower than an unpatterned slab.
Tang et al [59] reported a 60% decrease in thermal conductivity for holey silicon membranes
with a porosity of 13%, compared to non-holey membranes of similar thickness. The porosity of
our devices is about 5%. The reduced thermal conductivity thus results in a larger temperature
rise than for the unpatterned slab. Moreover, for unit temperature rise, the resonant shape of
33
the photonic-crystal transmission spectrum gives rise to a larger transmission change than the
relatively featureless spectrum of the unpatterned one.
In conclusion, we have proposed a method for using absorptive resonances to obtain
strongly nonlinear, designable optical transmission. In particular, we demonstrate the use of
silicon photonic-crystal slabs to obtain increasing, decreasing, or nonmonotonic transmission as
a function of laser power. The ability to achieve all three trends within a single materials
platform points the way to highly flexible capabilities in shaping the nonlinear power response.
In this work, we have presented silicon structures at near infrared wavelengths as one
prototypical system. However, the use of absorptive resonances for nonlinear power shaping
should extend to a wide range of materials systems and wavelengths, given only certain very
general conditions on the strength of the absorptive and thermooptic effects. We thus expect
that the fundamental concept proposed here could find application in areas as diverse as pulse
shaping, power limiting, dynamic range adjustment, and optical logic.
34
Chapter 3 : Enhancing the size of
response
3.1 Background
The size of the non-linear response of the effect studied in this thesis will depend on the
conduction of heat away from the device. Hence, the lower the effective thermal conductivity
of the structure, the higher the size of the effect will be. The converse will be true if we increase
the conductivity. As previously studied by the Notomi group [49], the switching threshold of the
thermo-optic bistability in a silicon photonic crystal cavity was reduced drastically by thermally
isolating the devices. In this work, they considered two different geometries: stack (Figure
3-1(a)) and ladder (Figure 3-1(d)) 1D photonic crystal cavities. As evident from the Figures, the
suspended ladder geometry is more thermally isolated than the stack where the structure is
resting on the substrate. The transmission spectrum (Figure 3-1(b) and (e)) clearly suggests the
onset of the bistability for the ladder geometry at a much lower power compared to the stack
(Figure 3-1(e) and (f)). This is also attributed in part to the higher Q of the cavity mode.
However the simulated steady state heat distribution confirms the reduction in effective
thermal conductivity of the ladder geometry.
Hence, in this chapter, we will increase the thermal isolation of the device in order to
magnify the size of the response. As will be seen in a later chapter, this thermal isolation will
also directly influence the response time of the devices.
35
Figure 3-1: (a) and (d) SEM, (b) and (e) transmission spectrum, (c) and (f) steady state heat
distribution of stack and ladder device respectively
3.2 Free-standing membrane
The photonic crystal slabs employed in the previous chapter were resting on glass. So in
order to increase the thermal isolation and enhance the effect we fabricated free standing
Figure 3-2: Free standing nano-membrane positioned on perforated silicon substrate
36
photonic crystal membranes (Figure 3-2). Due to the increased thermal isolation of the
suspended devices, the power required to achieve non-linear transmission will be lowered.
3.3 Fabrication of carrier free-standing membrane on carrier handle
Figure 3-3: Fabrication steps of free standing photonic crystal membrane
37
The membrane is now made free-standing by positioning it on a perforated window on
a silicon wafer host surface (Figure 3-2). An approach similar to the one described in [57] is
followed (Figure 3-3). To achieve the free standing membrane, we started with a plain [100]-
oriented silicon wafer having a nitride coating (100nm) on both the front and back side of the
wafer. We then defined a window pattern (0.6 cm in diameter) using UV photolithography on
the back side of the wafer and performed electron cyclotron resonance reactive ion etching
(RIE) of the nitride using CF 4 gases. After stripping off the photoresist using acetone, we
conducted a wet chemical etching of silicon in 30% by weight KOH solution. After the KOH
solution etches the entire silicon wafer, the top nitride layer is removed in hydrofluoric acid.
Finally, a thin layer (~50 nm) of thermal oxide will be grown on the surface of the perforated
silicon wafer in a thermal furnace. This oxidation step is required in order to position the
membrane on surface of the host substrate efficiently.
3.4 Comparison between membrane on glass substrate and free-standing one
3.4.1 Spectral Shift Analysis
We designed and fabricated free standing devices, having resonances near the
operating wavelength of the laser (808nm). We recorded the spectral shift in the monitor
wavelength range, similar to the one described in Section 2.6. The current device supports a
resonance at 809nm and is compared to the device I (Figure 2-7(a) from Chapter 2) which
exhibits resonance at 807nm. It should also be mentioned that the quality factor for both
devices is around 200, which accounts for similar field enhancement inside the photonic crystal
structure. As is evident from Figure 3-4, to shift the resonance by 17nm in Device I (positioned
on glass substrate) requires an input power of 242mW, whereas for the free standing
38
membrane, only 53mW of laser power can cause a spectral shift of 15nm. In both cases, the
beam spot size is kept constant (beam waist of 40μm) in order to have the same incident field
intensity.
Figure 3-4: Device on glass substrate a) white light spectrum b) spectral shift at monitor
wavelength; Free standing c) white light spectrum d) spectral shift at monitor wavelength
39
3.4.2 Non-linear transmission response
The enhanced response of the free standing membrane is further validated by
measuring the non-linear response of the device with increasing laser power and comparing it
with the device on a glass substrate (Figure 3-5).
Figure 3-5: Nonlinear power transmission with laser power for free-standing membrane and
membrane on glass substrate
3.5 Isolate device from unpatterned silicon
Since the effective thermal conductivity is a strong function of the geometry and the
structural parameters of the device, we took one further step to it. We isolated the device from
the rest of the silicon membrane by patterning trenches around the device and using arms to
connect the device (Figure 3-6(a)) to the un-patterned silicon. The trenches can be defined in
the same photolithography step as the one defining the membrane area mask. Figure 3-6(b)
shows a microscope image of such a device (at this stage the membrane is not yet released
from the SOI).
40
Figure 3-6: Device Isolation from unpatterned silicon a) schematic representation b)
fabricated device before membrane release from SOI
41
Chapter 4 : Time response of the non-
linear transmission
In this chapter, we intend to analyze the time scale associated with the thermo-optic
effect in silicon photonic crystal slab devices. The thermal response time for silicon based
devices reported in literature varies from a few nanoseconds [60-62] to miliseconds [47]
depending on the structure and operating power. The time scale for the thermo-optic effect is
also highly dependent on the structure.
4.1 Laser induced thermal time scale
Upon laser irradiation, free carriers are generated through the absorption of photons
and impact ionization. Si being an indirect band gap material, carrier generation is accompanied
Figure 4-1: Timescales of various electron and lattice processes in laser-excited solids. The
schematic represents a direct bandgap material. The time scales are equally applicable to
silicon. Figure reprinted from [58]
42
predominantly by momentum conservation. This is followed by a thermalization process
through carrier – carrier scattering or carrier – phonon scattering events, eventually leading to
a Fermi- Dirac distribution of the free carriers. The excess free carriers are then removed from
the system through recombination (Auger, surface, and defect) and diffusion processes, and
eventually the lattice and free carriers reach thermal equilibrium, raising the temperature of
the material. The time scale of each of the processes is depicted in Figure 4-1 [58, 63].
In order to gain more physical understanding on the underlying processes and their
temporal response, we solved the 3D transient heat transport equation in the photonic crystal
slabs coupled with the full 3D electromagnetic simulations.
4.2 Coupled mode theory (CMT): Analytical form of absorption and
transmission spectrum
First, following the method described in [64], we obtained the analytical forms of the
absorption and transmission spectra of photonic crystal slabs. The following expressions,
representing the absorption A( ω ) and transmission T ( ω ) spectra as a function of frequency ω,
are derived using coupled mode theory [65-67] which takes into account both the direct (Fabry
Perot mode) and indirect transmission (guided resonance mode) pathways in a photonic crystal
slab.
22
0
2
rad abs
rad abs
A
, (4-1)
2 2
0
22
0
d abs d d rad
rad abs
t t r
T
,
(4-2)
43
γrad and γabs represents decay rates due to radiative coupling and material absorption
respectively. ω0 corresponds to the resonant frequency. Using perturbation theory [68], we
can estimate γabs in terms of real (n) and imaginary (k) part of the refractive index of silicon and
is represented by the following expression
0
2
abs
k
n
. ξ denotes the fraction of the modal
energy contained within the dielectric. td and rd are the transmission and reflection coefficients
in the direct pathway.
4.3 Determination of coefficients of the coupled mode theory expression
In order to determine the coefficients (td, rd, γrad ) in the Equation (4-1) and( 4-2), we first
consider a lossless nondispersive medium and perform a full 3D electromagnetic simulation
using finite difference time domain method (Lumerical®). The refractive index of the medium is
chosen to be the refractive index of silicon at the operating wavelength [1]. Our simulated
structure consists of an infinite 2D array of holes with periodicity 470nm and diameter 160nm
(Figure 4-2(a)). The thickness of the slab is chosen to be 340nm. One unit cell of the structure is
simulated and periodic boundary conditions are employed to emulate the infinite case. The
symmetry of the electromagnetic fields is also considered in order to reduce the computational
space by 4X. The structure is illuminated normally by a plane wave. For these structures we will
be choosing our operating wavelength to be 976nm and so we design the modes around that
wavelength. The obtained transmission spectrum is then fitted to the functional form
represented in Equation (4-2) using a nonlinear curve fitting algorithm [69]. Thus the fit
parameters td, rd, and γrad are obtained. It should be noted that γabs is zero in this case. The
44
transmission spectrum obtained from FDTD simulations and the corresponding fit to the
analytical form derived from coupled mode theory are shown in Figure 4-2(b).
4.4 Analytical form for absorption and transmission spectrum from fitted
parameters
Based on the fitted parameters and the calculated γabs (as described in section 4.2), an
analytical form for absorption and transmission spectrum is obtained using coupled mode
theory from Equation (4-2) and (4-1). The analytically obtained results are then validated with
FDTD simulations and a good match between theory and simulations is obtained as depicted in
Figure 4-3 (a) and (c). In the following section (4.5.3), a comparison of the size and time
response of the nonlinearity will be made between the resonant case (the photonic crystal slab)
and a nonresonant case (unpatterned silicon slab of same thickness). Hence, the relatively
Figure 4-2:a) Schematic of a photonic crystal slab illuminated with normally incident
radiation b) transmission spectrum of a loss-less, non-dispersive photonic crystal slab as a
function of wavelength and the corresponding fit to the analytical form derived from
coupled mode theory
45
featureless transmission and absorption spectrum of an unpatterned silicon slab arising from
the Fabry-Perot modes of the slab of thickness 340nm is shown in Figure 4-3 (b) and (d).
Figure 4-3: a) Transmission and c) absorption through PCS (a = 470nm and d = 160nm), b)
Transmission and d) absorption through an unpatterned silicon slab. Dotted line on the
transmission plots shows the position of the laser wavelength
4.5 Transient heat transport in photonic crystal slab
In the following section, the transient response of the non-linear behavior is considered. We
developed a 3D model for the heat transport across the photonic crystal slab. Next we consider
the case where the photonic crystal slab is normally illuminated with a laser pulse operating at
46
a wavelength detuned, towards higher wavelength, from the resonance (Figure 4-3(a)). As the
device absorbs the incident laser power (Pabs), the temperature T of the slab increases
following the transient 3D heat transport model given in Equation (4-3).
p abs
T
C k T P t
t
, (4-3)
where ρ, Cp and k represent respectively the density, heat capacity at constant pressure and
thermal conductivity of the slab. This temperature rise induces a shift in the resonant frequency
( ω0) towards lower frequency ( ω0
'
) (higher wavelength), following Equation (4-4), due to
positive thermo-optic effect of silicon:
'
0
0 0 0
0
n
t T t T
nT
, (4-4)
where the derivative represent the thermo-optic coefficient of silicon at a temperature T0. n0
denotes the refractive index at room temperature T0. Thus at any point in time t, the resonant
frequency is determined by the current temperature of the slab. Therefore, we expect as the
resonance approaches the laser operating frequency ωop, the absorption in the slab increases.
Hence the absorbed power Pabs, calculated using Equation (4-1), will assume a Lorentzian form
as a function of time as the resonance moves through the laser wavelength. Equation (4-3)
provides the functional form of Pabs:
2
2
'
0
2
abs rad
abs in
op abs rad
P t P
t
,
(4-5)
47
where Pin denotes the power of the input laser pulse.
4.5.1 Temperature rise: finite element methods modeling
Next equation (4-3) is solved to obtain the temperature rise ( ΔT) as a function of time (t)
using finite element methods (COMSOL®). We assumed an initial detuning (towards higher
wavelength) of 4nm of the laser operating wavelength from the position of the resonance. We
Figure 4-4: Spatial profile of the temperature distribution after the laser pulse was turned on
for 17.4μs. The color bar represents temperature rise in Kelvin and the length scale is in nm
48
simulated a 2D axis-symmetric structure where a rectangle of cross-section 340nm x 0.5mm is
rotated around its smaller axis. Therefore in essence our structure is a disk of thickness h =
340nm with a radius r = 0.5mm. Since we are considering a free-standing silicon membrane in
air, the top and bottom surface of the structure are considered to be thermally insulated. The
lateral surface of the structure (side walls of the disk) is maintained at room temperature. A
heat source with a Gaussian spatial extent is positioned at the center of the disk. The beam
width w0 of the Gaussian source is chosen to be 5μm.
The product of the density and heat capacity terms in Equation (1) are set by multiplying
the values for bulk silicon with the volume fill fraction (0.91) of the photonic crystal slab
considered in our study. However, for our structures due to nanopatterning [59, 70], the
thermal conductivity cannot be approximated by the classic Eucken model [71], since the pitch
and thickness of the photonic crystal slab is similar to the mean free path of phonons (~300nm)
in silicon [72]. There have also been reports of drastic reduction of thermal conductivity of free
standing membranes [73] due to defects introduced during fabrication processes. The effect of
dislocations on the in-plane thermal conductivity of thin free-standing semiconductor slabs has
been studied in [74]. To approximately model the effect of the holes on the thermal conductivity,
we assumed a value (50 W/m.K [59]) between that of bulk silicon (130 W/m.K [72]) and the
values reported in the literature for holey silicon membranes (1.73 W/m.K [59]) with higher air
filling fractions than in our structure.
It should also be noted that the Pabs from Equation (4-5) is substituted in Equation (4-3).
Pin is calculated assuming a Gaussian profile of the beam across the structure (in the xy plane in
49
Figure 4-4) and uniform absorption along the length of the structure (along z). Hence Pin is
given by
0
2
0
in
P
P
hw
, where P0 is the total input power of the laser beam. The simulated
temperature profile across the disk structure is shown in Figure 4-4, after the beam has been
turned on for 17.4 μs.
4.5.2 Transmission change with temperature rise
Following the discussion in the previous sub-section, it is clear that as the temperature
rises the position of the resonant wavelength moves in and out of the operating laser
wavelength. Therefore the transmission Ttrans of the laser pulse through the PCS will have a
temporal form resembling the Fano lineshape of the original transmission spectrum [75]. Using
Equation (4-2) we can establish the temporal response of the transmitted pulse through the
photonic crystal slab, which is provided in the equation below:
2
2
'
0
2
2
'
0
()
d abs d op d rad
trans
op rad abs
t t t r
Tt
t
.
(4-6)
4.5.3 Comparison with silicon slab of equal thickness
In order to substantiate the effect of the resonantly enhanced absorption, we also
studied a nonresonant system, the case of an unpatterned silicon slab. In this case the
absorption and hence Pabs is dictated by the low quality factor Fabry-Perot resonances lacking
the sharp resonance shape. The transmission and absorption spectrum of an unpatterned
silicon slab of similar thickness (340nm) is shown in Figure 4-3 (d) and (e). The spectrum is
almost flat in the wavelength range considered in our simulations. Therefore, any shift in the
50
spectrum due to the thermo-optic effect, induced by a strong laser pulse, is negligible.
Appendix A describes the method used to obtain analytical forms for transmission and
absorption spectrum for Fabry Perot modes as a function of time. Also it should be noted that
while solving the heat transport equation for the unpatterned slab case we considered the bulk
conductivity of silicon which is an order of magnitude higher compared to conductivity of the
photonic crystal slab.
51
4.5.4 Finite Element Methods modeling results
The results of the finite element method simulations are illustrated in Figure 4-5 where
we have considered three different power levels for the input pulse (130mW, 100mW and
Figure 4-5: Left column and right column denote the PCS and unpatterned Silicon slab
respectively (a) and (b) Power absorbed (c) and (d) Temperature rise (e) and (f)
Transmission as a function of time
52
70mW). The device parameters are similar to the one described in Section (4-2). As mentioned
previously, the absorbed power has a Lorentzian temporal response (Figure 4-5 (a)). In contrast,
we obtained a flat temporal response for absorption in case of an unpatterned slab (Figure 4-5
(b)). The abrupt rise in the temperature (Figure 4-5 (b)) (~110 K with a 130mW input power) is
due to the presence of the resonance which yields a sharp rise in the absorbed power as
depicted in Figure 4-5 (a). As expected, such a sudden temperature rise is absent in the case of
the unpatterned slab structure (non-resonant case) (Figure 4-5 (d)). The transmission change as
a result of this abrupt temperature rise, which occurs as the resonance moves through the laser
operating wavelength, is shown in Figure 4-5 (e). Following Equation (4-6), the temporal
response of the transmission yields a Fano shape, and it undergoes a huge transmission change
from about 1% to 58%. On the contrary, the transmission remains virtually same for the case of
the unpatterned slab structure.
It should be noted from Figure 4-5 (c) that the response time at which the sudden
temperature rise occurs and consequently when the transmission excursion (Figure 4-5 (b))
happens is dependent on the pulse power. This can be clearly explained from Equation (4-3).
Increasing the input pulse power leads to a sharper rise in Tt . Thus with faster temperature
rise, the speed at which the resonance is brought closer to the operating laser wavelength is
enhanced.
53
4.6 Maximizing non-linear response time and size
In the following section we will study the effect of tuning various physical parameters:
thermal conductivity, absorptivity, and laser detuning, on the size and time of the non-linear
response. Here, we define the response time as the time when the temporal response of the
transmission reaches its minimum. At this juncture, we have a sudden temperature rise, and
also the absorption reaches its maximum.
4.6.1 Effect of the thermal conductivity on the response
Reduction in thermal conductivity not only maximizes the non-linear effect (Chapter 3)
but also decreases the response time. The dependence is shown in Figure 4-6, where we have
Figure 4-6: Variation of turnaround time with thermal conductivity k
54
varied thermal conductivity in the simulations keeping all the other parameter the same as in
Section (4.4). This follows directly from the heat transport Equation (4-3). Reducing thermal
conductivity inhibits heat transport, thereby causing higher and faster temperature rise. As
proposed in Chapter 3, thermal isolation is a way to reduce conductivity, however decreasing
the fill fraction or reducing the thickness of the photonic crystal slab can also have similar
effects [59].
4.6.2 Effect of the laser operating wavelength detuning on the response
As seen in Chapter 2, the non-linear transmission is a strong function of laser detuning and we
were able to obtain various transmission profiles depending on the detuning. In this subsection, we will
analyze the effect of laser detuning on the response time. Clearly, the smaller the detuning of the laser
wavelength from the resonance, the faster will be the response time. Again, our parameter space is
same as described in Section (4.4), only the laser detuning is varied. The results are illustrated in Figure
4-7, where with our current configuration we can achieve a minimum response time of 14 ns with a
detuning of 1nm.
Figure 4-7: Variation of response time with laser detuning from the resonance
55
4.6.3 Effect of absorption Q on the size of the response
In this section we will be studying the effect of the varying the absorption Q (absorption
decay rate γabs) on the size of the non-linear response. Maximum absorption (50%) is obtained
when the absorptive and the radiative decay rates are matched i.e. γabs= γrad [76]. However, this
condition does not guarantee a maximum temperature rise in the system nor a maximum
transmission change. As is evident in Figure 4-8(c), in order to maximize the temperature rise,
we should choose an optimum absorption Q so that at the laser detuning, the absorption is
maximum ( γabs= 10γrad in this case) (Figure 4-8(a)). Though the peak absorbed power Figure
4-8(b) for the two other cases ( γabs= γrad and γabs= 0.25 γrad ) is at least two times greater than the
( γabs= 10γrad ) case, what dictates the temperature rise is the integrated power. It should be
pointed at, that the maximum temperature rise is accompanied by the fastest response time
(which is also indicative of how quickly the system reaches equilibrium). Clearly as the
absorptive Q continues to increase, the system will no longer support any resonance. γabs=
100γrad is a case where the absorption destroys the resonance.
The situation is different if we observe the maximum transmission excursion as
illustrated in Figure 4-8(d). In this case, lowering the absorption Q will result in the highest
transmission change ( γabs= 0.25γrad). Evidently, the response time is slowest for this case.
However, again there is also a lower bound on the absorption Q below which the effect will be
negligible.
56
Figure 4-8 : (a) Absorption spectrum (b) Total absorbed power as a function of time (c)
Temperature variation of the device with time (d) Temporal response of transmission for the
different absoprtive quality factor
4.7 Experimental Verification
In order to experimentally verify the theoretical predictions, we fabricated free standing
silicon based 2D photonic crystal membrane following the methods elucidated in Chapter 3 and
4. The fabricated structure is similar to our simulated structure considered in Section (4.4) with
lattice constant 470nm and hole diameter 160nm. We then characterize the transmission
spectrum of the device by using a broad band white light source in conjunction with a
57
spectrometer (Ocean Optics USB 4000). The transmission spectrum of the fabricated device is
depicted in Figure 4-9(a). The device has a resonance around 968nm. The resonant wavelength
and the quality factor of the resonance are obtained by fitting the transmission lineshape to a
characteristic Fano shape. The fit corresponds to a quality factor of 300. The obtained quality
factor is far less than the simulated structure, and the deviation is attributed to the finite
numerical aperture of the objective (both incidence and collection). This corresponds to an
angular spread of about ±10 degrees, degrading the quality factor of the mode. We next
illuminated the sample with a near infra-red diode laser operating at 976nm. The laser is
pigtailed with a single mode fiber that has a mode field diameter of 8µm. This results in a
Gaussian beam with spot size of 10µm on the sample with a 10X microscope objective
(Mitutoyo NIR MPlan Apo). The laser output is modulated using a laser diode controller
(Thorlabs) with a square pulse. The modulation frequency is 1 KHz and the duty cycle is 20%.
Figure 4-9: a) Transmission spectrum of the fabricated device b) Transmission change as a
function of time
58
The rise time of the laser pulse is approximately 1µs. The transmitted laser pulse is collected by
another 10X objective and fed to a fiber coupled trans-impedance amplifier (Thorlabs). The
response time of the amplifier is of the order of a few picoseconds. The temporal response of
the transmitted pulse through the photonic crystal slab is depicted in Figure 4-9(b), which
resembles the line shape of the original transmission curve. Therefore both the experiment and
theory reveal the same trends of the temporal response of the transmission. This trend
therefore confirms the fact that the resonant wavelength moves through the laser wavelength
due to the temperature rise in the photonic crystal slab. The experiments also confirm the
tuning of the response time with laser power, i.e. increasing input power leads to faster
response time.
4.7.1 Reasons for mismatch in theoretically and experimentally trends
As evident, in Figure 4-9, the experiment deviates from the theoretical prediction in a
number of different ways. First, the experimentally observed response time differs from the
one obtained in simulations. In the experiments, the laser wavelength has a larger detuning
from the resonant wavelength compared to the simulations. Also, the actual thermal
conductivity of the photonic crystal slab can be lower than the effective thermal conductivity
considered in the simulations, as elaborated in the previous section. Second, the sharp
transition in transmission observed in simulations is absent in the experimentally observed
trends (occurring over 20μs compared to 1μs in simulations). This can be attributed to the
decrease in quality factor of the resonance with increasing temperature. In our simulations we
did not consider the change in absorption coefficient of silicon with temperature. With
59
increasing temperature, the absorption increases, thereby lowering the quality factor of the
mode. This lowering of the quality factor also causes the maximum transmission (36%) value
observed in the temporal response of transmission (Figure 4-9(b)) to be lower than the
observed maximum value (40%) in the transmission spectrum (Figure 4-9(a)).
4.8 Enhancing the response by thermally isolation decreasing thermal
conductivity
As demonstrated in Figure 4-6, decreasing the thermal conductivity of the structure
would decrease the response time. Following the method described in Chapter 3, we further
decreased the conduction of heat away from the device by defining trenches around it. We
defined the trenches using ebeam lithography. We made two identical devices with the same
lattice constant and hole size (same ebeam dose), where one had trenches around it and the
other did not. A microscope image of such a device is shown in Figure 4-10. The device on the
lower left corner has the same device parameters as the one which has trenches defined
Figure 4-10: Microscope of image of a free standing silicon membrane with devices. The
bottom right device has trenches around it to improve thermal isolation
60
around it (bottom right). The trenches appear in red in the Figure 4-10. Figure 4-11 illustrates
the results. The transmission spectra of the two devices are shown in Figure 4-11 (a). The
resonances are closely aligned and have identical quality factors, which ensure that the only
difference between the two devices is their thermal conductivity. Figure 4-11 (b) and (c) show
the temporal response of the transmission change for the same set of laser power levels. It is
clearly evident that the response time is increased by at least a factor of three by decreasing
Figure 4-11: a) Spectrum of devices with and without trenches around it b) Temporal
response of the transmission for the device without trenches c) Temporal response of the
transmission for the device with trenches
61
the thermal conductivity. In this case, the laser output is modulated using a laser diode
controller using a square pulse with a modulation frequency of 200Hz and a 10% duty cycle.
4.9 Discussion
We have theoretically demonstrated the nonlinear heating effects in a silicon photonic
crystal slab. Due to the presence of the guided resonance mode, the heating is enhanced
compared to a slab of silicon of equal thickness. The enhanced heating results in a sharp and
sudden temperature rise. The temperature rise time can be tailored by increasing the input
power and also by positioning the resonance closer to the laser wavelength. The thermal
conductivity of the structure can also be tuned to tailor the response. The sudden temperature
is accompanied by an abrupt temporal response of the transmission change through the device.
Experiments are performed to observe this temporal response of the transmission change.
In essence, we demonstrated a photonic crystal based nanoheater which yields a
sudden temperature rise (hundreds of Kelvin) and the response time of this nanoheater can be
tailored by physical means.
62
Chapter 5 : Photonic Crystal Nano-heaters
- Application in biological environment
Plasmonic resonance exhibited by metal nanoparticles is accompanied with strong
absorption of light (both visible and infra-red) [77-80]. Therefore metal nanoparticles, when
illuminated with laser beam, can efficiently convert the laser energy to thermal energy. The
enhanced localized heat generation by a single nano-particle or a network of them has been
successfully employed in photo-thermal therapies [81, 82], catalysis [83, 84]and heat assisted
magnetic recording [85]. In order to successfully utilize these particles in the biological
transparency window (800nm - 1200nm) [86], researchers have used various complex sizes and
shapes of these nanoparticles [87]. This allows them to push the localized plasmon resonance
towards higher wavelengths.
The electromagnetic field enhancement associated with the excitation of plasmon
resonances of individual nanoparticles can be further increased by constructing an array of
metal nanoparticles. A strong dipolar coupling between the metal nanoparticles produces large
electromagnetic enhancement, which in turn increases the absorption cross-section of the
structure [88-90]. In addition to enhanced absorption, an arrayed system provides the
opportunity for parallel processing of nanoscale processes, reducing the signal to noise ratio.
Several biological applications have successfully employed the plasmonic heating associated
with illuminating a metal nanoparticle array with an infrared laser. A few such examples involve
nanochemistry [91] , heterogeneous catalysis [83], biosensing [92, 93], nanoscale heat
63
generation [94, 95], and thermally induced convective flows that set up microfluidic mixing [96,
97].
In this chapter we propose to extend the use of the absorptive resonances of a photonic
crystal slab as an alternative to metal nanoparticles. There have been studies related to use of
alternate solutions to gold and silver nanoparticle, for example using titanium nitride
nanoparticles [98, 99] which have a larger absorption cross-section. Also these structures can
withstand higher temperature changes without shape deformation (due to their higher melting
point).
As shown in the previous Chapters our device is capable of achieving moderate to high
temperature rise, similar to what has been achieved using metal nanoparticles with comparable
laser power density.
As demonstrated in Chapter 4, the heating time scale can be tuned in our structures
from tens of nanosecond to microseconds, similar to that reported for metal nanoparticles [80,
100, 101]. The real advantage of our structure over metal nanoparticle array is the tailoring of
the response time depending on its application without changing the actual structure.
5.1 Comparison of absorption spectrum of a PCS and gold disk array
In the following section, we will be comparing the absorption spectrum of a gold disk
array with the photonic crystal slab studied in Chapter 4. As a reference, we will be using the
gold disk arrays studied in [89]. We will be studying the structure having the largest absorption
cross-section, namely the structure with lattice constant 640nm and gold disk radius of 80nm.
We performed FDTD simulations to compute the absorption spectrum. The results are shown in
64
Figure 5-1. The peak absorption is similar in both cases, but the full width at half maximum is
much larger for the gold nanoparticle array compared to the photonic crystal slab. Due to the
induction of the thermo-optic optic non-linearity the photonic crystal slab structure
experiences a sudden temperature rise, whereas the temperature rise of the gold nanoparticle
array always follows an exponential rise, with the time constant dictated by the size of the
structure [98, 100, 101]. However, it should be noted that both the gold disk arrays [94] and the
photonic crystal slab [66, 67] structures are capable of achieving 100% absorption with a back
reflector when the Q matching conditions are satisfied.
Figure 5-1: Absorption spectrum of a gold nanoparticle array and a photonic
crystal slab
65
5.2 Experimental validation in water
In order to experimentally validate our proposal and the working of our devices in
biological environment, we fabricated photonic crystal slabs with resonances around 808nm in
water. The steady state non-linear behavior of these devices was examined. The devices were
Figure 5-2: (a) Transmission Spectrum (dotted line shows the laser operating wavelength), (b)
Non-linear transmission with laser power (c) Spectral shift at monitor wavelength for device
operating in water (d) Spectral shift at monitor wavelength for device operating in heavy
water
66
positioned on glass because the free-standing membrane will break in water. We performed
experiments both in water and heavy water (whose absorption is two orders of magnitude
lower than water). Figure 5-2 illustrates the results. The spectrum of the device (Figure 5-2 (a))
shows that the position of the resonance is around 805nm for both water and heavy water. In
spite of higher absorptivity of water compared to heavy water, both the resonance modes
show similar quality factors. We also observed similar non-linear transmission change due to
thermo-optic effect for both the systems Figure 5-2 (b)). This suggests that absorption in silicon
is dominating over the absorption in water and hence most of the absorption occurs in silicon.
However the spectral shift is not as pronounced as observed in Chapter 2. This is because the
thermo-optic coefficient of silicon and water go in opposite directions and hence there is a net
reduction in spectral shift (Figure 5-2 (c) and (d)). The spectral red shift also confirms the
dominance of the thermo-optic effect of silicon.
67
Chapter 6 : Future Work
6.1 Size of response enhancement by optimizing Q
In this chapter, as a part of the future extension of our current work, I propose to
optimize the non-linear response by modifying the absorption Q of the photonic crystal slabs.
As demonstrated in Section 4.6, the maximum temperature or the maximum non-linear
transmission change can be obtained by tuning the absorption Q (reciprocal of decay rate γ abs),
which is shown in a more systematic way in Figure 6-1. Here we used the same simulation
parameters as described in Chapter 4 but varied the absorption Q (Section 4.6.3). It is evident
from Figure 6-1 (a), that the temperature rise has a maximum, corresponding to an optimal Q.
However the optimum Q is different for the maximum non-linear transmission excursion as
illustrated in Figure 6-1 (b).
Figure 6-1: a) Temperature rise ( ΔT) (b) Maximum and minimum value of
transmission observed in the temporal response of transmission change as a function
of the ratio of γabs and γrad
68
One way to increase the absorption is to evaporate very thin layers (5-10 nm) of gold on
the photonic crystal slab. However the gold will also enhance the effect in the regions where
silicon is less absorptive near the band-gap or even above the band-gap. Since the resonances
in this range have substantially higher Qs lowering the quality factor by a few percent will not
degrade the resonance. Following this approach, we can achieve the peak temperature shown
in Figure 6-1.
However, it should be mentioned that in the optical communication band, researchers
use very high Q photonic crystal cavities to induce non-linearity in the system. The non-linearity
there is predominantly due to the thermo-optic effect resulting from two-photon absorption.
Inclusion of ultra-thin gold layers will provide another mechanism to induce nonlinearity in this
bandwidth without requiring the design of ultra-high Q cavity modes.
In order to optimize the effect, I propose to fill only the holes of the photonic crystal
with gold. In this way gold will act as isolated heating elements and will also have lower thermal
conductivity compared to a continuous film. In order to demonstrate this idea, we aim to
design and fabricate PCSs infilled with gold which have resonance modes near and above the
band-gap of silicon.
6.2 Fabrication of photonic crystal infilled with gold
The fabrication procedure depicted in Figure 6-2 is very similar to the steps described in
Chapter 2. Since the etch selectivity of PMMA to silicon in our etching recipe is 1:1.8, after
etching 340nm of silicon, we will still have 110 nm of ebeam-resist left on silicon. However,
here, we will partially etch the holes leaving a few nm of silicon device layer. This thin buffer
69
layer of silicon will prevent losing the deposited gold during the under etching of the buried
oxide. After etching the sample, we will evaporate a very thin layer of gold (one to seven
nanometers in steps of one nanometer) using an e-beam metal evaporator. The metal from the
unwanted parts is then removed by lift-off of the PMMA in acetone and the resulting final
device will have a gold disk located inside the holes of the PCS. This step is followed by the
under etching of the buried oxide to release the membrane. This final etching step is essential
in order to achieve thermal isolation.
Figure 6-2: Fabrication of photonic crystal in-filled with gold
70
6.3 Preliminary simulation results
I performed FDTD simulations of a PCS where holes are filled with varying thicknesses of
gold. The transmission spectrum of a bare PCS shown in Figure 6-3 (a) (black curve), with a
lattice constant 430 nm and hole size 86nm, displays a resonance at 971 nm. This resonant
mode has a quality factor of 1125 and maximum absorption at the resonance is ~45%. The
holes of this structure are then in-filled with different thicknesses of gold, 5 nm and 7 nm. In
these two cases the quality factor drops to 592 and 462 respectively. However, the maximum
absorption at the resonance points in these two cases also increases to 49% and 54.5%
respectively.
The increased absorption can also be attributed partly to the mode profile (Figure 6-4)
which shows substantial electric field intensity in the hole region of the photonic crystal slab. It
should also be noted that in the structure filled with gold, there are two processes contributing
to the thermo-optic effect. One is the free carrier generation in the silicon slab and the second
Figure 6-3: PCS with lattice constant 430 nm and radius 86nm a) Transmission and b)
Absorption spectrum.
71
is the absorption in gold. Gold being in thermal contact with the slab increases the temperature
of the surrounding slab. We can also model the thermal transport of the photonic crystal in-
filled with gold using COMSOL, using a similar model to the one described in Chapter 4 and
study the time response of the effect.
As mentioned before, the idea of infilling of holes in the photonic crystal with gold can
be extended to achieve nonlinear effects in the optical communication band. However, gold is
extremely absorptive in this region, and even one nanometer of gold layer can destroy the
resonance. As reported previously, the gold nanoparticle arrays support coupled plasmon mode
where the resonance is a function of the particle size and the lattice constant [102]. We can
engineer a device, where the position of the photonic crystal resonance mode is near the
coupled plasmon mode and forms a hybrid mode. Ensuring optimal overlap between the two
modes will preserve the quality factor of the photonic crystal mode while utilizing the gold disks
as nanoheaters
Figure 6-4: Electric field intensity profile through the center of the hole in one unit cell
of the photonic crystal a) without gold infilling in the holes and b) holes filled with
7nm thin gold layer. Devices are illuminated normally with a plane colorbar represents
electric field intensity in V
2
/m
2
72
Chapter 7 : Conclusion
In this thesis we have proposed a method for using absorptive resonances to obtain
strongly nonlinear, designable optical transmission. In particular, we demonstrated the use of
silicon photonic-crystal slabs to obtain increasing, decreasing, or nonmonotonic transmission as
a function of laser power. The ability to achieve all three trends within a single materials
platform points the way to highly flexible capabilities in shaping the nonlinear power response.
We thus expect that the fundamental concept proposed here could find application in areas as
diverse as pulse shaping, power limiting, dynamic range adjustment, and optical logic.
We have also demonstrated methods to enhance the response size by thermal isolation.
Thermal isolation has a direct impact on the size and the time of the response which has been
experimentally validated in the current work.
Finally, we provided the first demonstration of a nanoheater structure based on laser
illumination of a nanopatterned silicon membrane. Our approach provides an alternative to
traditional plasmonic nanoheaters and is suitable for operation within the biological
transparency window. We expect that the devices presented here, which are compatible with
low-cost CMOS fabrication, will find application in a variety of lab-on-a-chip experiments,
including catalysis, optofluidics, and manipulation of cells and DNA.
73
Appendix A
A.1 Absorption and transmission spectrum shift of silicon slab with
temperature
The Fabry Perot modes of a 340nm thick free standing silicon membrane is obtained using the
transfer matrix method. The transmission and absorption spectrum of such a silicon membrane
is shown in Figure A.1. Both the spectra are fitted to parabolic expressions.
Figure A.1: (a) Absorption and (b) Transmission spectrum of a 340 nm unpatterned silicon
slab. Dotted lines shows the position of the operating laser wavelength
From the fitted parameters, we can express absorption A and T as a function of temperature
ΔT. In the following expression ωop represents initial operating frequency (which in our
simulations corresponds to an operating wavelength of 976 nm).
2
16 32
0.15608 1.75 10 4.93 10
op op
A T T T
(A.1)
2
14 30
15.5196 1.57 10 4.06 10
op op
T T T T
(A.2)
74
A non-zero ΔT cause a spectral shift towards lower frequency (higher wavelength) and the
spectral shift as a function of time t is obtained using the following:
0
0
0
,
n
T T T t T
nT
(A.3)
75
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Abstract (if available)
Abstract
This dissertation involves the design of nonlinear input-output power responsive surfaces based on absorptive resonances of nanostructured silicon membranes. We have demonstrated that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the operating laser wavelength. In this work, we used nanostructures to achieve arbitrary power response curves. We designed and fabricated a flexible non-linear power transmission surface based upon a common silicon microphotonic platform which can be tailored to obtain any desirable power relationship between the input and the output. We have experimentally demonstrated non-linear optical transmission of lasers (operating at 808 nm and 980nm) through silicon based photonic crystal slabs. In this case we chose to operate at wavelengths where silicon is partially absorptive (~800-1100nm). Since the photonic crystal slabs supports guided resonance modes (GRMs), the absorption is enhanced near these resonances. The non-linear operation of the photonic crystal slab is thus due to the resonantly enhanced thermo-optic effect of silicon. These results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest. ❧ In the next part of our work, we demonstrate a mechanism to enhance this current non-linear behavior. The temperature rise in the structure for a fixed amount of input power is directly proportional to the thermal conductivity of the material. We artificially decreased the thermal conductivity of our structures via microfabrication techniques and hence increased the resultant temperature which in turn magnified the non-linear response. ❧ The resonantly enhanced absorption results in huge amount of local heating and thereby causes a large temperature rise. In the third part of this thesis, we theoretically calculated the temperature rise and its temporal response. The theoretical predictions were then matched with experiments by observing the temporal response of the non-linear transmission. We observed a large sudden temperature rise due the presence of the absorptive resonance. This structure can therefore provide an alternative to gold nanoparticle arrays which are extensively used for local heat generation in various lab-on-chip applications. This includes chemical assays, vapor generation, microfluidic mixing and enhanced catalytic effects. We also conducted the experiments in water in order to provide a proof of concept of the efficacy of these structures as local heaters in biological environments.
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Biswas, Roshni
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Core Title
Designable nonlinear power shaping photonic surfaces
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Viterbi School of Engineering
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Doctor of Philosophy
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Electrical Engineering
Publication Date
09/21/2015
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07/29/2015
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coupled mode theory
finite element methods
photonic crystals
photothermal effects
plasmonic heating
thermo-optic nonlinearity