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Metasurfaces in 3D applications: multiscale stereolithography and inverse design of diffractive optical elements for structured light

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Metasurfaces in 3D applications: multiscale stereolithography and inverse design of diffractive optical elements for structured light

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Content Metasurfaces in 3D Applications: Multiscale Stereolithography and Inverse Design of Diractive Optical Elements for Structured Light by Yuanrui Li A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Electrical Engineering) August 2019 Copyright 2019 Yuanrui Li Dedication This dissertation is dedicated to my Dad, Mom and Ran for your love and support. ii Acknowledgements First and foremost, I would like to thank my advisor Prof. Wei Wu for his guidance in both research and daily life. The knowledge and philosophy I received from him is invaluable. I would like to thank the rest of professors in my qualifying exam and dissertation committee, Prof. Yong Chen, Prof. Han Wang, Prof. Stephen B. Cronin, and Prof. Andrea Armani, for their kind suggestions and advice. Besides, I would like to thank all the collaborators during my research. I want to thank Prof. Yong Chen and Huachao Mao for the support in 3D printing rmware, Prof. Luhar and Mark Hermes for the help in uid dynamic measurement and knowledge, Prof. Jongseung Yoon and Haneol Lim for the help in TiO 2 thin lm deposition. I would also like to thank all of our research group members including but not limited to Dr. Yuhan Yao, Dr. He Liu, Dr. Yifei Wang, Boxiang Song, Pan Hu, Hao Yang, Buyun Chen, Deming Meng, Yunxiang Wang, Tse-Hsien Ou, Zerui Liu, Leo Yeh. All the works during my Ph.D. include collaboration and hardworking of everyone. Also, many great ideas were created during discussions with them. My research projects would not be what they are today without their help. Last but not least, I would like to thank my family. I can't thank my parents enough for raising me and providing me a happy environment as I grew up. Especially, I would like to thank my wife who appeared at the beginning of my Ph.D. and has been supporting me during tough times. I could not nish this Ph.D. without her. iii Table of Contents Dedication ii Acknowledgements iii Dissertation Overview xvii Topic 1: Multiscale Stereolithography 2 Abstract 2 Chapter 1: Introduction of 3D Printing Technologies 4 1.1 Advantages of 3D Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Stereolithography(SLA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Fused Deposition Modeling(FDM) . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Powder Bed Fusion(PBF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Chapter 2: A Trade-o in Stereolithography: Resolution vs. Throughput 9 Chapter 3: Multiscale Stereolithography 13 3.1 Variable Laser Beam Prole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Design and Characterization of Resonance Grating Filter . . . . . . . . . . . . 18 3.3 Hardware Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 iv 3.4 Adaptive Layer Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Chapter 4: Multiscale Printing of Articial Shark Skin 30 4.1 Brief Introduction of Functional Surfaces in Nature . . . . . . . . . . . . . . . . 30 4.2 Mechanism of Fluid Drag Reduction Eect from Shark Skin Texture . . . . . . 31 4.3 Previous Studies on Fabricating Articial Shark Skin . . . . . . . . . . . . . . . 33 4.4 Multiscale Printing of Articial Shark Skin Texture . . . . . . . . . . . . . . . . 34 4.5 Pipe Flow Measurement Result and Discussion . . . . . . . . . . . . . . . . . . 42 Chapter 5: Multiscale Printing of Articial Lotus Leaf 46 Summary 47 Topic 2: Inverse Design of Diractive Optical Elements for Structured Light 50 Abstract 50 Chapter 6: Introduction to 3D Sensing Techniques 51 6.1 Time of Flight Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 6.2 Structured Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Chapter 7: Inverse Diractive Optical Elements Design and Simulation 58 7.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 7.2 Design consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7.3 Methods of Design and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 60 Chapter 8: Introduction to Diractive Optical Element and Free Space Prop- agation 66 8.1 Diractive Optical Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 v 8.2 Free Space Propagation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 8.2.1 From Vector Diraction to Scalar Diraction . . . . . . . . . . . . . . . . 68 8.2.2 Rayleigh-Sommerfeld Diraction Formula . . . . . . . . . . . . . . . . . . 70 8.2.3 Paraxial Approximation to Rayleigh-Sommerfeld Diraction . . . . . . . . 72 8.2.4 Fresnel Diraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 8.2.5 Fraunhofer Diraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Chapter 9: Introduction to Numerical Optimization 76 9.1 Gradient Descent and Newton's method . . . . . . . . . . . . . . . . . . . . . . 76 9.2 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Chapter 10: Design Case No. 1: Encoded Dot Pattern 82 Chapter 11: Design Case No. 2: Periodic Dot Array Pattern 87 Chapter 12: Optical Characterization 90 Summary 94 Topic 3: Nonlinear Metamaterial over Multiple Wavelength Ranges 96 Abstract 96 Chapter 13: Background and Motivation 97 13.1 Evolution of Radio Communication and Optical Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 13.2 Superheterodyne Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Chapter 14: Non-linear Metamaterial 100 vi 14.1 Origin of Optical Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 14.2 Optical Metamaterial Design, Fabrication and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chapter 15: Future Works 106 Summary 112 Reference List 113 Appendix A Conference Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Appendix B Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Appendix C DOE optimization script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 vii List of Figures 1.1 Schematics of a typical stereolithography system. [6] . . . . . . . . . . . . . . . . . 6 1.2 Schematics of a fused deposition modeling setup [7] . . . . . . . . . . . . . . . . . . 7 1.3 One type of powder bed fusion 3D printing: Selective Laser Melting(SLM) setup [8] 8 2.1 Items printed by dierent 3D printing technologies which is vastly dierent in part size and resolution. Left: Item from Nanoscribe which has 200 nm resolution and sub 1 cm part size. [10] Middle: Item from Formlabs which has 100 m resolu- tion and about 10 cm part size. [11] Right: Auto part from Oak Ridge National Laboratory which has above 1mm resolution and meters in part size. [12] . . . . . 9 2.2 Relationship between 3D printing resolution and overall part size for several current technologies. Observe that the larger the part size is, the worst the feature resolu- tion will be. This is a tradeo between resolution and throughput. Data sourced from commercial products, Formlab Form 1, Envisiontec Ultra 3SP, Envision Aria and publications. [13{17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 The eect of resolution increase on the total number of voxel required. In this case, printing resolution is improved to 1/10 of the original. To ll the same amount of volume, we need 10 3 smaller voxels. In general, a linear increase of resolution results in a cubic growth of the number of voxel. . . . . . . . . . . . . . . . . . . . 11 2.4 Resin ow process. Denote the liquid pressure asP , layer thickness ash and width of the area needs to be coated as b. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 viii 3.1 Structures in nature that has multiscale features. a) Human lung with micro air- ways and blood vessel. [19] b) Human bone structures. [20] c) Shark skin with micro texture that has uid drag reduction eect. [21] d) Lotus leaf with micro hairs that create super-hydrophobicity. [22] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Multiscale model slicing of a digital model. a) the sample input 3D sculpture model. The model has very high surface smoothness. The resolution for the surface is at least 3 orders of magnitude smaller than the overall object size. b) the model is sliced into layers. c) Every layer is separated into high resolution part and low resolution part. d) in the vertical direction, the high resolution part has a smaller layer thickness while the low resolution part has a larger layer thickness . . . . . . 14 3.3 Schematics of beam prole switching process with resonance grating lter. The optical lter has dierent transmission property for dierent wavelength. For 1 = 445 nm the lter is transparent and gives and larger laser spot (300 m) on the resin bottom surface. For 2 = 405 nm, only the center area is transparent. The lter works as an aperture and gives a smaller ( 25 m) laser spot on the resin surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Staking multiple layers of grating lters can give a library of shapes. As one layer of grating structure is optically thin, after one layer is nished, more layers can be fabricated on top of it. Each layer can shape the beam prole of a specic wavelength. In this way, by using multiple wavelengths and layers, a library of beam shapes can be contained on a single piece of substrate. These shapes are self- aligned when lithography is done. Therefore, no misalignment can be introduced when wavelength changes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.5 SEM image of the grating area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.6 FDTD simulation showing electric eld distribution with 405 nm light incident from the bottom. Very little energy is transmitted. . . . . . . . . . . . . . . . . . . 19 ix 3.7 Fabrication process of the resonance grating lter. The lter started with a fused silica substrate with a layer of TiO 2 sputtered on top. Then nanoimprint lithog- raphy was used to transfer the grating pattern onto UV resist. After that, a Cr mask was created by metal deposition and lift-o. Then reactive ion etching was conducted to etch TiO 2 to form grating structure. Next, photolithography was done to cover the whole surface while only exposing the center area with a 25 m diameter. Finally, the exposed gratings are etched away by RIE and the photoresist was removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.8 Simulated and experimental transmission spectrum of the resonance grating. . . . 21 3.9 3D diagram of the complete multiscale stereolithography setup. Two lasers have wavelength of 405 nm and 445 nm respectively. . . . . . . . . . . . . . . . . . . . . 23 3.10 Diagram of the simplied optical path in the multiscale stereolithography setup. The part after the lter works as an imaging system. The transparent part on the lter acts as an emitting object. The resin surface at the bottom of the resin tank acts as an image plane. The laser beam prole after passing through the lter is imaged to the resin surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.11 Illustration of adaptive layer thickness in multiscale SLA process. Each layer of input digital model is separated into high resolution thickness and low-resolution thickness. High resolution part is printed with a small layer thickness (Green). Low resolution part is printed with a large layer thickness(red). . . . . . . . . . . . 25 x 3.12 A comparison of traditional xed layer process and adaptive layer process. To print one layer in the xed layer process, build platform has to move up and down for a long distance( 1mm) to let the fresh liquid resin ow underneath after one layer is nished. In the adaptive layer process, ve high resolution layers can be printed continuously(green). Then the stage moves up and down to let the resin ow in and one low resolution layer is printed to ll the interior. In our testing, the adaptive layer process can on average print 5x the volume than the xed layer process in similar amount of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.13 Comparison of surface nish of x layer process and adaptive layer process. a) Fixed layer process used a 100 m layer thickness. b) Adaptive layer process has 20 m small layer thickness and 100 m large layer thickness. It shows the dierence in print quality when the two methods have similar throughput. . . . . . . . . . . . 28 3.14 Comparison between the multiscale stereolithography with several existing tech- nologies in terms of resolution and overall printable part size. The multiscale process has highest part size-to-resolution ratio meaning that it has high resolution while doesn't sacrice throughput. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.1 Example of functional surfaces in nature. a) Photo and 3D model of hierarchical microstructures on a lotus leaf. [22] b) Photo of a shark and SEM image of denticles on shark skin. [21] c) SEM images of microstructures on the dorsal, head and ventral regions of the gecko. [44] d) A cross-section view of the sapwood (or xylem) in a hardwood tree, illustrating the repeating microstructure of vessels surrounded by bers. [45] e) Images of micro-scales on lepidoptera. [43] . . . . . . . . . . . . . . . 31 xi 4.2 Mechanism of riblet texture in uid drag reduction. [49] a) Flow patterns of laminar ow and turbulent ow. b) Vortex pattern on a at surface in a turbulent ow. c) Vortex pattern on a riblet covered surface in a turbulent ow. The riblets pushed vortices away from the majority of the surface area. High speed ow in the vortices was only in touch with the tip of the riblet. Therefore, the riblet surface has less uid drag due to less contact area with high speed ow. . . . . . . . . . . . . . . . 32 4.3 Schematic of pipe ow setup used to test SLA printed shark skin. . . . . . . . . . 34 4.4 Comparison of the overall size of a printed pipe with a quarter dollar coin. . . . . 36 4.5 Cross-section view of four pipes with dierent interior texture. Scale bar: 200 m 37 4.6 Real and printed shark skin denticles. a) denticles on the skin of lemon shark. [60] b) 3D model of denticles. c) dimensions of the denticles. d) the cross-section of a sample which shows the suspended area. . . . . . . . . . . . . . . . . . . . . . . . 38 4.7 Adaptive layer thickness in multiscale printing of denticles. Dierent color denotes dierent layer during printing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.8 Cross-section view of a layer showing beam switch within a adaptive layer. For the denticle features in the inner surface, the small laser beam was used for high resolution. For the pipe wall, the large laser beam was used for high throughput. . 40 4.9 Printing time of xed voxel process and variable voxel multiscale process at dierent object size scale. The objects printed were pipes with 300 m pitch riblet on the interior surface. At scale 1, the pipe is 20 cm long, with 12 mm diameter, 1.5 mm wall thickness and 142 m riblet height. At other scales, the dimensions for the riblet were kept the same but object size grew in all three dimensions. The purpose is to demonstrate that the multiscale process has more throughput advantage when larger objects are needed to be built and high resolution features need to stay in the same size to maintain the surface function. . . . . . . . . . . . . . . . . . . . . 41 xii 4.10 Measured friction factors for the smooth pipe, the pipe with 142 m riblets and the pipe with denticle covered interior. . . . . . . . . . . . . . . . . . . . . . . . . 42 4.11 Comparison of friction factors of the pipes with dierent riblet height. . . . . . . . 44 4.12 Diagram of vortex pattern on top of riblet with dierent height. On very short, the vortices can still touch the valley area. The total contact area, in this case, is larger than a smooth surface which resulted in more drag. On medium height riblet, vortices are pushed away and total drag decreases. On very tall riblets, smaller vortices started to form in between the riblet which also increased drag. . . 45 5.1 A drop of water on the surface of, a) a lotus leaf in nature, [48] b) an articial lotus leaf printed by the multiscale stereolithography process. The pitch between the micropillars is 300 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.2 Summary of multiscale SLA project. a) invented multiscale lithography process which solved the trade-o between resolution and throughput. b) demonstrated drag reduction eect on articial shark skin structure. c) provided a platform for future studies on multiscale structures. . . . . . . . . . . . . . . . . . . . . . . . . . 48 6.1 First Generation Kinect for Xbox 360 . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.2 Face ID feature on iphone X [64] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 6.3 Apple's Animoji [65] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.4 The principle of one type ToF depth camera: The distance is calculated based on the phase delay between light source and received re ection light. [67] . . . . . . . 54 6.5 Sampling of a modulated signal [66] . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.6 A illustration of a fringe pattern projection structured light system. a) arrangement of the camera, projector and object. b) spacial relationship between projection pattern, image on the object and the image captured by the camera. [68] . . . . . 55 xiii 6.7 A example of depth retrieval. A and C represents projector and camera respectively. A pattern is projected at three dierent scenes and the pixelp A intersects with the scenes at three locations, P 1 ;P 2 ;P 3 . The image of these three locations shows up on the camera image at p c1 ;p c2 ;p c3 . Using the disparity between the three point on the camera image, the distances of P 1 ;P 2 ;P 3 can be calculated. [69] . . . . . . . 56 7.1 Illustration of key components in a general usage case of DOEs in this work . . . . 59 7.2 Illustration of design parameters of a DOE device . . . . . . . . . . . . . . . . . . . 61 7.3 Design ow of DOE using mathematical optimization . . . . . . . . . . . . . . . . 62 7.4 Design ow of DOE using inverse design method . . . . . . . . . . . . . . . . . . . 64 8.1 A example of diractive lenses with two, four, eight levels and smooth prole. [72] 67 8.2 A example showing the importance of phase information in image reconstruction. [73] 67 8.3 Using multiple photolithography process to generate binary optic with 2 N levels. [72] 68 8.4 Scenario for a general scalar diraction problem [67] . . . . . . . . . . . . . . . . . 71 9.1 A comparison between gradient descent and Newton's method. Red path: Newton's method. Green path: gradient descent. [77] . . . . . . . . . . . . . . . . . . . . . . 78 9.2 a - d) Visualization of a particle swarm optimization [79] . . . . . . . . . . . . . . . 81 10.1 Encoded pattern with 630 dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 10.2 Phase distribution on the projection pattern during optimization . . . . . . . . . . 83 10.3 Examples of the amplitude modulation from two candidate DOE design. a) A design with larger variation. b) a design with smaller variation . . . . . . . . . . . 85 10.4 Surface prole of DOE designed to generate projection pattern in Figure 10.1. Scale bar unit: m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 11.1 Periodic dot array pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 11.2 DOE surface prole which generates dot array projection pattern . . . . . . . . . . 88 11.3 3D visualization of DOE surface prole which generates dot array projection pattern 89 xiv 12.1 Characterization of encoded dot pattern generation DOE. a,b) DOE surface optical microscope image. c) Projection image . . . . . . . . . . . . . . . . . . . . . . . . . 91 12.2 Characterization of periodic dot pattern generation DOE. a,b) DOE surface optical microscope image. c) Projection image . . . . . . . . . . . . . . . . . . . . . . . . . 92 13.1 Evolution of radio communication and optical communication. Courtesy: Richard Schatz, KTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 13.2 Diagram of a typical superheterodyne receiver. . . . . . . . . . . . . . . . . . . . . 99 14.1 Factors aect optical nonlinearity. a) material nonlinearity that originates from molecular structures. [84] b) local eld enhancement (optical resonance). [85] c) non-symmetrical structures. [85] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 14.2 Design of optical metamaterial. a) top view. b) cross-section view. . . . . . . . . . 102 14.3 FDTD simulation of the chevron structures. a) re ection(R), transmission(T) and absorption(A) spectrums of the optical metamaterial. b) electric eld prole in the SiO 2 layer. c) magnetic eld prole in the SiO 2 layer. . . . . . . . . . . . . . . . . 103 14.4 Fabrication process of the optical metamaterial. A mold with chevron pattern was fabricated by EBL and etching. Then the pattern was transferred to resist using nanoimprint lithography. The As=SiO 2 =Ag metal layers were created by electron beam evaporation and lift-o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 14.5 Second harmonics generation using optical metamaterial. Fundamental beam is 800 nm, 200 W, 20 m diameter. Four spectrums correspond to dierent light polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 15.1 The experimental setup to measure nonlinear optical coecient. L1 and L2 are lenses; F, secondary harmonics wavelength lter. A, an absorbing pool for catching fundamental re ection beam. [87] . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 xv 15.2 Several examples of split ring resonator geometries. [89,93] a) Single ring with single cut. b) Multi-ring with multi-cut. c) complementary split-ring resonator. d) Spiral resonator. e) Two-layer spiral resonator. f) Split ring resonators with nonlinear inserts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 15.3 Schematic diagrams of two metamaterial architectures for multiple frequency ranges: (A) parallel mixing of large and small structures, (b) hierachical arrangement of large and small structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 15.4 Two methods of characterizing metamaterial that works at both optical and RF wavelength. a) Metamaterial couples to both couple to both optical and RF sources through free space. b) Metamaterial couples to optical source through free space and RF source through a transmission line. . . . . . . . . . . . . . . . . . . . . . . 109 15.5 Method of characterizing nonlinear metamaterial in both near infrared and far- infrared range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 xvi Dissertation Overview This dissertation summarizes the three topics in my Ph.D. study. The main focus is on nanopho- tonics and its applications in 3D printing, 3D sensing, and nonlinear optics. The rst part covers the multiscale stereolithography that we invented. This technology addressed a challenge in traditional additive manufacturing technologies which is the trade-o between resolution and throughput. First, the laser spot size can be dynamically changed by switching wavelength which is enabled by a subwavelength grating lter. Second, dierent layer thicknesses are assigned to dierent parts of the 3D model which is enabled by adaptive layer thickness slicing. Using these two methods, the multiscale stereolithography can treat the high resolution and low resolution parts of the 3D model dierently and improve overall eciency. Chapter 1 provides a brief introduction to popular additive manufacturing technologies. Details regarding laser beam switching and adaptive layer slicing are covered in chapter 3. As a demon- stration, large area articial shark skin samples were printed and tested for uid drag reduction eect which is covered in chapter 4. The result from printed articial lotus leaf is included in chapter 5. The second part covers the inverse design method for diractive optical elements(DOE). DOEs have been a popular choice in applications such as beam splitting and shaping. In recent years, DOE has caught more attention as a compact solution for structured light pattern generation due to the increasing demand in 3D sensing market. DOE design and simulation is challenging because of its large parameter space and limitations in fabrication technologies. In this work, I propose an inverse design method that calculates optimal DOE design in a more ecient way and reduces xvii the discrepancy between simulations and fabricated devices. The details dening the problem is described in chapter 7. Chapter 6 gives a brief introduction of popular 3D sensing techniques. Free space scalar diraction theory used for DOE simulation is introduced in chapter 8. Chapter 9 covers the common numerical optimization methods. As demonstrations, two DOEs for generating dierent structured light patterns were designed, fabricated and characterized which is included in chapter 10, 11 and 12. The third part summarizes my work in metamaterials with nonlinearity at multiple wavelength ranges. Optical superheterodyne on Si platform is a key component that is needed before optical communication systems can use advanced modulation schemes that are being used in radio com- munications now and be built on Si photonics chips. The key challenge is that there is no material in the current Si platform with high nonlinearity. In this work, we propose to demonstrate meta- materials with high non-linearity at both optical and microwave wavelengths simultaneously. In chapter 13, background regarding the evolution of radio communication systems and superhetero- dyne receiver is covered. Chapter 14 include the theoretical and experimental study of the optical metamaterial in this work. In chapter 15, future plans regarding the design and characterization of nonlinear metamaterial at both optical and RF wavelength range are discussed which will pave the way to the realization of optical superheterodyne receivers. xviii Topic 1: Multiscale Stereolithography 1 Abstract Additive manufacturing has many advantages in creating highly complex customized structures. However, existing additive manufacturing technologies have a trade-o between throughput and resolution. In this work, Multiscale Stereolithography process is invented to addresses this issue, and it is able to print macroscale objects with microscale surface structures with high throughput at low cost. This process is realized by dynamic switching of laser spot size and adaptively sliced layer thickness. Digital models are separated into high resolution part and low resolution part. These two parts are printed using variable voxel size technique in which a small voxel size is used for high resolution and a big voxel size is used for high throughput. The variable voxel size is achieved in two steps. In the x-y plane, a resonance grating lter can switch the laser beam prole by changing laser wavelength. In the z-axis, hybrid layers with adaptive layer thickness are used where high resolution part has a small layer thickness and low resolution part has a large layer thickness. Many structures in nature possess superb functions due to the multiscale characteristics in them. For proof-of-concept testing, articial shark skins with micro riblet features were designed and 3D printed. In pipe ow experiments, the 3D printed shark skin demonstrated almost 10% average uid drag reduction. Articial lotus leaf surfaces were also 3D printed to demonstrate superhydrophobic property. In terms of throughput, the multiscale SLA process demonstrated 4.4x better than traditional SLA process in the tests. The advantage becomes even more signicant when bigger size objects are printed. It provided the capability to experimentally study various multiscale structures in future research. Being able to provide high 2 resolution and high throughput at the same time with low cost, the multiscale stereolithography process has the potential to serve as a powerful tool that can bring bio-inspired structures into real-life applications. 3 Chapter 1 Introduction of 3D Printing Technologies Additive manufacturing (AM), commonly known as 3D printing, has been a fast-developing area for more than three decades. It is a process that uses information from a computer-aided design le to build a 3-dimensional (3D) physical object. It is also referred to as rapid prototyping, solid free form, computer automated or layered manufacturing. [1] In this section, the advantages of 3D printing and several main categories will be covered, including stereolithography(SLA), fused deposition modeling(FDM), powder bed fusion(PBF). [2] 1.1 Advantages of 3D Printing 3D printing has signicant advantages over traditional manufacturing methods: • Rapid creation of 3D prototypes: 3D printing can turn digital models into real 3D objects in minutes or hours. As a comparison, traditional methods need to purchase injection molds from suppliers or use time-consuming machining techniques. In the prototyping stage where many rounds of improvement are needed, short turnover time is a huge benet. • Cost-eective: Injection molding tools and machining in prototyping are an expensive in- vestment. 3D printed parts and tools are generally at a much lower cost. 4 • High customization: As there is no need for expensive injection molding tools, each part can be built to t the customers requirement with no additional cost. This attribute is highly valuable in medical applications such as scaold and prosthesis as each piece is dierent for dierent patients. • Build complex geometries [3]: Some parts with complicated internal geometries are hard to manufacture by traditional technologies. As a comparison, in the 3D printing process, the complex shape is decomposed into layers and built one by one, which is much easier. • Flexibility in materials: For additive manufacturing processes such as FDM and SLA, the material type can switch during the printing process to t for dierent parts of the product. Many materials have already been used in additive manufacturing such as polymer, metal, and ceramic. [4] 1.2 Stereolithography(SLA) Stereolithography(SLA) is the rst commercially available prototyping machine and one of the most widely used AM processes. [3] It was invented by Chuck Hall in 1984 and granted a patent in 1986. [5] The process starts with a computer-aided design (CAD) model which contains the geometry of the object to be built. As 3D printing process build one layer of material at a time, the CAD le is sliced into layers and converted to a le format that 3D printing machines can read. The most commonly used le type for stereolithography is STL. After an STL le is generated, the physical printing process can begin. The material being used is photo-curable resin, which consists of monomers that can be polymerized into large molecules. In the apparatus (Figure 1.1), a light beam is generated by a laser source (usually in the wavelength range of ultraviolet) and incident on a set of x-y scanner galvo-mirrors which de ect the light beam to the bottom of the translucent resin bath. In the beginning, the build platform almost touches 5 Figure 1.1: Schematics of a typical stereolithography system. [6] the bottom of the resin bath except there is a thin layer of resin (usually between 5-200 m) in between. Next, the galvo-mirrors scan based on the STL le data so that the light spot traces a cross-section of the object. As one layer has been nished, the build platform moves up the distance of the thickness of a layer to allow fresh liquid resin to ow in and ll the gap. Then the printing of next layer shall start. 1.3 Fused Deposition Modeling(FDM) Fused deposition modeling is another popular method of 3D printing due to low cost, simplicity and fast printing speed. A schematic of an FDM setup is shown in Figure 1.2. In the FDM process, the raw material is prepared as lament and fed into an extrusion nozzle. Typical materials are thermal plastics such as ABS, PLA, PS that have relatively low melting temperatures. The nozzle is heated up and the lament is melted into viscous uid form. Then, as 6 Figure 1.2: Schematics of a fused deposition modeling setup [7] the nozzle moves, the material is deposited on a printing bed or a previously deposited layer. One of the advantages of FDM is that it is easy to have multiple printing materials as adding nozzles with dierent lament is easy. Also, printing resolution is well controllable and can be relatively high when small nozzles are used. A common drawback is FDM requires thermal plastics with proper melt viscosity [7]. Therefore, its material selection is limited. 1.4 Powder Bed Fusion(PBF) Powder Bed Fusion(PBF) systems use power form raw materials and have designs similar to Figure 1.3. A roller spreads a layer of powder from the powder delivery system. Then, an energy 7 Figure 1.3: One type of powder bed fusion 3D printing: Selective Laser Melting(SLM) setup [8] source such as a laser or electron beam starts to deliver energy to the selected area to melt the powder particles. In selective laser sintering (SLS), laser source only provides enough heating so that powder particles' outer surfaces are melted and then bind together. On the other hand, in selective laser melting(SLM), the powder is completely melted which results in better mechanical properties. [9] PBF has a wide range of material selection including polymer, metal, alloy metal, etc. SLS and SLM are very popular due to their unique advantage in metal 3D printing which SLA and FDM can't provide. 8 Chapter 2 A Trade-o in Stereolithography: Resolution vs. Throughput Since it was invented, 3D printing has had a signicant improvement in its resolution and part size. Technology such as two-photon absorption process has pushed the resolution down to 200 nm and industrial 3D printers are able to print an actual size car (Figure 2.1). Figure 2.1: Items printed by dierent 3D printing technologies which is vastly dierent in part size and resolution. Left: Item from Nanoscribe which has 200 nm resolution and sub 1 cm part size. [10] Middle: Item from Formlabs which has 100 m resolution and about 10 cm part size. [11] Right: Auto part from Oak Ridge National Laboratory which has above 1mm resolution and meters in part size. [12] An interesting pattern can be observed if we draw the relationship between part size and resolution for dierent 3D printing techniques in a chart (Figure 2.2). All the data points lay 9 Figure 2.2: Relationship between 3D printing resolution and overall part size for several current technologies. Observe that the larger the part size is, the worst the feature resolution will be. This is a tradeo between resolution and throughput. Data sourced from commercial products, Formlab Form 1, Envisiontec Ultra 3SP, Envision Aria and publications. [13{17] below the diagonal line of the chart. The ratio between part size and resolution is typically around 1000.i.e. The larger the part size is, the rougher the printing quality will be. Hence, current 3D printing technologies must sacrice resolution when part size grows. To understand the result, a closer look at the printing process is needed. The basic element in a digitalized 3D object is called a voxel which is the counterpart of a pixel in 3-dimensional space as in Figure 2.3. To have a ne resolution in 3D lithography, not only we need to have a small x-y plane resolution. Smaller layer thickness in the vertical Z direction is required as well. For example, if we improve the resolution to 1/10 th of the original, the number of new voxels needed to ll the same volume of one original voxel is 10 3 . Therefore, if the size of the voxel 10 Figure 2.3: The eect of resolution increase on the total number of voxel required. In this case, printing resolution is improved to 1/10 of the original. To ll the same amount of volume, we need 10 3 smaller voxels. In general, a linear increase of resolution results in a cubic growth of the number of voxel. is shrunk linearly to increase resolution, the total number of the voxel will have a cubic growth which will be dicult to handle. It will have three major negative impacts on throughput. First, the size of the digital model will be signicantly bigger and much more dicult for a computer to handle. For example, a 10MB digital le may increase to roughly 10GB if the resolution only increases 10 times. Second, in the x-y plan, the laser beam needs to trace longer distance to cover the same cross-section area. Third, a smaller Z-direction thickness makes the fresh liquid much slower to ow in after build platform moves up. The resin ow can be modeled as Hele-Shaw ow [18](Figure 2.4). Q = h 3 12 P b L (2.1) 11 Where h is layer thickness, P is resin pressure, is the viscosity of the resin, L is the length of the resin boundary into the paper plane and b is the width of the area the resin needs to ow in. To cover an area with width b, we have Qt = Lbh. Therefore, the time that resin takes to ow in is t = 12 b 2 Ph 2 (2.2) Therefore, the resin ow time has a square growth as layer thickness decreases. As a result, each layer takes a much longer time to nish. The above two reasons combined results in a signicant increase in fabrication time when there is only a small improvement in resolution. For example, a part may cost a few hours to print originally. When the resolution increases 10 times, the time required may increase to a few weeks. The factors mentioned above explains locations of data points for most 3D printers in Figure 2.2 assuming each machine uses the best resolution possible on the condition that part building time is reasonable. Figure 2.4: Resin ow process. Denote the liquid pressure as P , layer thickness as h and width of the area needs to be coated as b. 12 Chapter 3 Multiscale Stereolithography In this work, I present a low cost(built under $2500) multiscale stereolithography technology that can achieve both high resolution and throughput at the same time. Such capability enables us to create multiscale object using 3D printing. Many structures in nature possess superb functions due their multiscale features. A few examples are shown in Figure 3.1. Human lung with a network of micro airways and blood vessels have high eciency in oxygen and CO 2 transport. Human bones have hierarchical structure that contains micro ber, blood vessel, nerves and maintains mechanical strength at the same time. Eiel tower as manmade structure consists of steel beam instead of thick steel pillars. With the help of such structure, the material used is much less while mechanical strength is still extraordinary. Sharks swim in oceans with low uid drag due to their scales covered with micro riblets. Lotus leaf is famous for its superhydrophobic property which is a result of hierarchical micro bers covering its surface. Many micro uid device has small uid channels with diameter down to micros which is much smaller than its overall size. For all the examples above, there are at more than 3 orders of magnitude dierence in size between the overall object sizes and feature size which would be dicult for any traditional 3D printer to make due to the aforementioned trade-o between throughput and resolution. To understand the characteristics of multiscale printing process, we use the example in Figure 3.2. The object is a sculpture with very smooth surface nish. In the printing process, this model 13 Figure 3.1: Structures in nature that has multiscale features. a) Human lung with micro airways and blood vessel. [19] b) Human bone structures. [20] c) Shark skin with micro texture that has uid drag reduction eect. [21] d) Lotus leaf with micro hairs that create super-hydrophobicity. [22] Figure 3.2: Multiscale model slicing of a digital model. a) the sample input 3D sculpture model. The model has very high surface smoothness. The resolution for the surface is at least 3 orders of magnitude smaller than the overall object size. b) the model is sliced into layers. c) Every layer is separated into high resolution part and low resolution part. d) in the vertical direction, the high resolution part has a smaller layer thickness while the low resolution part has a larger layer thickness is sliced into layers and printed layer by layer. By observing an individual layer, we can nd that the boundary needs high resolution to achieve a smooth surface for the object. The interior, which only provides the mechanical support, doesnt require high resolution. However, the interior takes 14 up most of the volume of the object. As the result, the total fabrication time will be determined by the interior. Similar situations exist in many examples in Figure 6 where the overall size of the object is large and only the surface has high resolution features to achieve certain surface functions. To maintain high resolution and high throughput at the same time, this work utilizes variable voxel size to build multiscale object. It consists of two parts, variable laser beam prole and adaptive layer thickness. 3.1 Variable Laser Beam Prole The key component to realizing variable laser spot is an optical lter based on high contrast grating as shown in Figure 3.3. It has dierent transmission behavior for dierent wavelength. Two wavelengths, 405 nm and 445 nm, were used. For the 445 nm light, the lter is almost transparent which gives a larger spot size, while for the other wavelength, 405 nm, the lter works as an aperture and only part of the area is transparent, which gives a much smaller beam spot size. Many studies have been carried out on many methods to change spot size [23{25]. Miller et al. developed an SLS workstation that has two laser spot sizes by pulling an aperture into and out of light path. [24] Sim et al. used lenses with dierent focal length to produce dierent laser spot sizes. [25] Cao et al. reported a stereolithography process that uses a dynamic focusing mirror to change spot size. Several specimens demonstrated more than 25% building time-saving. [23] The advantages of the method in this work over the previous approaches are: • High precision: No mechanical motion is involved in the resolution switching process. Mechanical motions may cause optical path misalignment during the fabrication process. Therefore, if the optical system is well adjusted initially in our system, no precise adjustment is needed afterward, which is important for high resolution printing (<50 m). 15 Figure 3.3: Schematics of beam prole switching process with resonance grating lter. The optical lter has dierent transmission property for dierent wavelength. For 1 = 445 nm the lter is transparent and gives and larger laser spot (300m) on the resin bottom surface. For 2 = 405 nm, only the center area is transparent. The lter works as an aperture and gives a smaller ( 25 m) laser spot on the resin surface. • Fast switching: Doing switching for each layer will have a signicant contribution to much longer total fabrication time. The laser spot size is changed by switching wavelengths which can be done in 50s or less. This saves manufacturing time as resolution switching frequently happens in every layer. As a comparison, moving an optical component can take seconds. 16 • Low cost: The key component, the grating lter, is fabricated by nanoimprint lithography which is a low cost, high throughput method. The rest of the machine shares most of the components with existing stereolithography machines and there is no need for precision motion components. • Versatile in beam shape: Multiple layers of grating lters can be fabricated on the same substrate. Each layer works for a specic wavelength (Figure 3.4). In such a way, a library of beam shapes can be realized in a fashion similar to the shaped-beam electron-beam lithography. [26] Figure 3.4: Staking multiple layers of grating lters can give a library of shapes. As one layer of grating structure is optically thin, after one layer is nished, more layers can be fabricated on top of it. Each layer can shape the beam prole of a specic wavelength. In this way, by using multiple wavelengths and layers, a library of beam shapes can be contained on a single piece of substrate. These shapes are self-aligned when lithography is done. Therefore, no misalignment can be introduced when wavelength changes. 17 3.2 Design and Characterization of Resonance Grating Filter The optical lter in this work has dierent transmission modes for 405 nm and 445 nm light. For the 445 nm light, most light can pass the lter while for the 405 nm light, incident light on the most area of the lter is re ected. Only part of the lter allows transmission of the 405 nm light. Therefore, the lter works as an aperture. The re ection of the 405nm light is achieved by high-contrast gratings that have been used in many applications owing to their properties of high re ectance and broad re ection band [27{38]. In addition, the thickness of the high-contrasts grating is smaller than that of other re ectors such as dielectric re ector. Figure 3.5: SEM image of the grating area The cross-section of an optical lter is shown in Figure 3.6. The lter consists of a bottom quartz layer and a TiO 2 grating layer. Gratings at the center area were etched o(as shown in 18 Figure 3.6: FDTD simulation showing electric eld distribution with 405 nm light incident from the bottom. Very little energy is transmitted. Figure 3.3 to provide an aperture for 405 nm light. The working principle of high-contrast gratings can be described as following: When incident light shines on the gratings, strong resonance is generated and reradiates. When the transmitted waves interfere destructively, transmission disappears and strong re ection occurs. [36, 39, 40]. In the area where gratings were etched o, there is no high refractive index contrast. Therefore, no strong re ection would happen. As a result, light can get through this area. The re ection spectrum can be tuned by adjusting the geometry of the gratings, including pitch, height, and grating width. In this work, TiO 2 was selected because among all materials with low loss at this wavelength range, TiO 2 has the highest refractive index. Since the light sources are polarized, the lter was designed for this specic polarization (TM) and 1-D grating design was used. 19 Figure 3.7: Fabrication process of the resonance grating lter. The lter started with a fused silica substrate with a layer of TiO 2 sputtered on top. Then nanoimprint lithography was used to transfer the grating pattern onto UV resist. After that, a Cr mask was created by metal deposition and lift-o. Then reactive ion etching was conducted to etch TiO 2 to form grating structure. Next, photolithography was done to cover the whole surface while only exposing the center area with a 25 m diameter. Finally, the exposed gratings are etched away by RIE and the photoresist was removed. The fabrication process is summarized in Figure 3.7. The gratings were fabricated by using nanoimprint lithography. [41, 42] First, a Si mother mold was fabricated by interference lithog- raphy. Then a glass mold was duplicated from the Si mother mold by transferring pattern to a layer of UV-curable resist on a glass substrate. The lter substrate was prepared by deposition of a 400nm thick TiO 2 thin lm using direct current (DC) magnetron sputtering on top of a quartz substrate. The grating pattern was transferred from the glass mold to the TiO 2 layer via nanoimprint, lift-o and RIE etching process. In the lift-o process, 10nm thick chrome mask was deposited by electron beam metal evaporation and worked as an etching mask in the following RIE etching. An RIE etching recipe that was developed by Liu et al. [38] with a gas combination of SF 6 , C 4 F 8 and O 2 was used. Figure 3.5 shows a SEM image of nished TiO 2 gratings. After 20 TiO 2 gratings were fabricated, an additional step of photolithography and RIE etching was car- ried out to etch away TiO 2 gratings in a circular area with a diameter of 25 m. This area can virtually be any shape depending on the requirement of applications. Figure 3.8: Simulated and experimental transmission spectrum of the resonance grating. Optical transmission of the grating area was measured and compared with simulation in Figure 3.8. Numerical simulation was performed via nite-dierence time-domain (FDTD) method using Lumerical FDTD solutions software. In the spectrum, the measured center wavelength of re ection matches the simulation result very well at 405nm. Transmission at 405nm is 5% while at 445nm is about 65%, which means 405 nm light will be mostly re ected by the gratings while 445 nm light will pass. The electric eld distribution at 405 nm is shown in Figure 3.6. One big benet of using resonance grating lter is that a library of beam shapes can be built on a single piece of substrate. It works as shown in Figure 3.4. After one layer is fabricated, more 21 layers of gratings can be fabricated on top of it. The working principle of the single layer lter applies to each layer on the multi-layer lter as well. The geometry of gratings on each layer is designed to interact with only one wavelength. Using the top layer in Figure 3.4 as an example. The gratings on this layer are designed to only re ect l 1 . The area without gratings is a dot array. Hence, after passing through the layer, the laser beam prole becomes a dot array. Other wavelengths can transmit through this layer without much change. Another advantage of the grating structures is that they are optically thin. Stacking multi-layers wont introduce signicant optical blur on the surface of the resin. 3.3 Hardware Setup A diagram of the complete multiscale stereolithography setup is shown in Figure 3.9. Multiple wavelength laser source is required in this work. Using a variable laser gives the simplest optical path. In my setup, two laser diodes of 405 nm and 445 nm wavelength are used due to low cost as these wavelengths have been widely used in commercial and industrials applications such as Blu-ray Disk. The laser beams are rst collimated and combined into the same optical path. The optical path goes through the grating lter. Then, the transmitted beams are focused by a lens and re ected by a galvo-mirror module. The module consists of two mirrors that rotate along two axes that are perpendicular to each other. A computer controls the mirrors so that the laser beam traces a cross-section of the object thats being printed. To better explain the beam projection process, a simplied version of the optical path is shown in Figure 3.10. The optical path after the lter works as an imaging system. The transparent part of the lter acts as a light emitting object and the resin surface at the bottom of the resin tank acts as an image plane. Therefore, object distance d o which is from the lter to lens and image distance d i which is from the lens to resin surface follows thin lens equation. 22 Figure 3.9: 3D diagram of the complete multiscale stereolithography setup. Two lasers have wavelength of 405 nm and 445 nm respectively. 1=d o + 1=d i = 1=f where f is the focal length of the lens. In my setup, d o = d i so that there is a magnication of one. 3.4 Adaptive Layer Thickness Another key innovation of multiscale SLA is adaptive layer thickness as shown in Figure 3.11. Given the digital model, our algorithm rst separates the high-resolution part and low-resolution 23 Figure 3.10: Diagram of the simplied optical path in the multiscale stereolithography setup. The part after the lter works as an imaging system. The transparent part on the lter acts as an emitting object. The resin surface at the bottom of the resin tank acts as an image plane. The laser beam prole after passing through the lter is imaged to the resin surface. part with high eciency. The algorithm is developed by Prof. Yong Chens group at USC and details can be found in reference [18]. Next, the high-resolution part is sliced into small layer thickness (20 m) and printed with a small laser beam. The low-resolution part is sliced into large layer thickness (100 m) and printed with a large laser beam. The adaptive layer thickness printing process is illustrated in Figure 3.12 and its compared with the xed layer process used in traditional additive manufacturing. Lets look at the xed layer process rst. After one layer is nished, the build platform moves up to let fresh liquid resin ows in to ll the gap. The resin ow can be modeled as Hele-Shaw ow [18], Q = h 3 12rPL 24 Figure 3.11: Illustration of adaptive layer thickness in multiscale SLA process. Each layer of input digital model is separated into high resolution thickness and low-resolution thickness. High resolution part is printed with a small layer thickness (Green). Low resolution part is printed with a large layer thickness(red). whereQ is ow ux,h is gap height, is the viscosity,P is boundary pressure andL is the length of the vacuum-resin boundary. If resin ows into the gap for a distance of b, the volume it lls is Qt =Lbh. Therefore, the time it takes is t = 12b 2 Ph 2 25 Figure 3.12: A comparison of traditional xed layer process and adaptive layer process. To print one layer in the xed layer process, build platform has to move up and down for a long distance( 1mm) to let the fresh liquid resin ow underneath after one layer is nished. In the adaptive layer process, ve high resolution layers can be printed continuously(green). Then the stage moves up and down to let the resin ow in and one low resolution layer is printed to ll the interior. In our testing, the adaptive layer process can on average print 5x the volume than the xed layer process in similar amount of time. In our experiment, = 0:1 Pa s,P = 1:01e5 Pa for air pressure andh = 0:02 mm. For a layer whose width is w = 100 mm, resin need to ow in for 5 mm on both sides. The time it takes is t = 12 50 2 1:01 10 5 0:02 2 = 75 s This is a signicant time consumption for a 20 m thick layer. Therefore, in practice, the build stage moves up for 1 mm, giving a big gap to let resin quickly ow in and moves down to print next layer as shown in the Figure 3.12. This 'up and down' process takes about 15 seconds which is much faster than 75 seconds but its still longer than the actual exposure time. In the adaptive layer thickness process, 5 high resolution layers are printed continuously before one thick layer is printed. For each thin layer, the stage only moves up a distance of layer thickness, 20 m. The high resolution features are typically less than 500 m wide. The time for the resin to ow in is t = 12b 2 Ph 2 = 12 0:1 0:5 2 1:01 10 5 0:02 2 = 7:4ms 26 which is a very short time. Therefore, the 'up and down motion' of the build platform is removed. Combining the beam size switching and adaptive layer thickness, the following strategy was then used to fabricate the sliced layers: (a) Use the small laser spot (25m using the laser with 405 nm) to fabricate the small features in the current thin layer. (b) Move the Z linear stage up by a layer thickness of 20 m. (c) Repeat step a, b until 5 thin layers are printed (d) Move the Z stage up for 1 mm and down to allow the resin to ow and coat the entire cross-section. (e) Use the big laser spot (300 m using the laser with 445 nm) to fabricate the large features in the current thick layer. (f) Repeat steps a - e until the whole object is fabricated. Compared to stereolithography with xed voxel size, the time savings generated by our printing process can be attributed to two factors. First, the large laser spot size and thick layer thickness make printing the low-resolution area much faster. Second, since the high-resolution features have a small cross-section area, it is easy for the resin to ow in. It means that the recoating operation is not necessary between each thin layer, and can, therefore, be removed. The section above discussed the benet of throughput when using the adaptive layer thickness process instead of the xed layer process. Now let us look at the dierence in print quality when the xed layer process is adjusted to have similar throughput as the adaptive layer process. The results are shown in Figure 3.13. A pyramid-shaped model with 6 mm side length was printed. In Figure 3.13 a), the xed layer process used a layer thickness of 100 m. In Figure 3.13 b), the adaptive layer thickness process has a small layer thickness of 20 m for the surface and a large layer thickness of 100 m for the interior. In our test, they had similar fabrication time. We can 27 Figure 3.13: Comparison of surface nish of x layer process and adaptive layer process. a) Fixed layer process used a 100 m layer thickness. b) Adaptive layer process has 20 m small layer thickness and 100 m large layer thickness. It shows the dierence in print quality when the two methods have similar throughput. 28 observe that sample b) has much better surface quality due to adaptive layer process and variable voxel gives it high throughput at the same time. Figure 3.14: Comparison between the multiscale stereolithography with several existing technolo- gies in terms of resolution and overall printable part size. The multiscale process has highest part size-to-resolution ratio meaning that it has high resolution while doesn't sacrice throughput. To compare with several existing stereolithography technologies, the specs of the multiscale stereolithography is plotted in Figure 3.14. We can observe that the multiscale process has the highest part size-to-resolution ratio meaning that it has high resolution while does not sacrice throughput. 29 Chapter 4 Multiscale Printing of Articial Shark Skin 4.1 Brief Introduction of Functional Surfaces in Nature Nature is an exceptional source of structures that have superb functions. Self-cleaning and super- hydrophobicity property of lotus leaf (Figure 4.1 a) is well known. Other than that, spinules or micro-hairs on Geckos (Figure 4.1 c), insects, spiders keep them water repellent and dry. Fine structures at inner walls of wood (Figure 4.1 d) conduits help water transport in plant. The scales on Lepidoptera(Figure 4.1 e) serves dual purposes. Scales on their wings generate eye- catching eect with structural color and certain scales on some moth creates ultrasonic signals for intraspecic communication. [43] Many structures from nature can be transferred into technologies that have big engineering and economic potential. The skin on fast swimming sharks has been drawing attention for three decades. Shark skin has supercial structures (Figure 4.1 b) known as denticles that are thought to be multi-functional. It has been hypothesized that these surface features prevent biofouling and, more importantly, reduce uid friction drag, which enables more ecient swimming. It has inspired the development of commercially successful products such as the Fastskin swimming suit by Speedo. Shark skin structures could also be applied to ships, underwater vehicles, airplanes, and pipelines to reduce energy waste from friction drag. 30 Figure 4.1: Example of functional surfaces in nature. a) Photo and 3D model of hierarchical microstructures on a lotus leaf. [22] b) Photo of a shark and SEM image of denticles on shark skin. [21] c) SEM images of microstructures on the dorsal, head and ventral regions of the gecko. [44] d) A cross-section view of the sapwood (or xylem) in a hardwood tree, illustrating the repeating microstructure of vessels surrounded by bers. [45] e) Images of micro-scales on lepidoptera. [43] 4.2 Mechanism of Fluid Drag Reduction Eect from Shark Skin Texture Many studies have been conducted over the past few decades to understand the mechanism of drag reduction over shark skin-inspired surfaces. The physical causes responsible for drag reduction are reasonably well understood. [46{48]Most studies focused on the drag reduction eect comes from the riblet structure on top of shark scales. In uid mechanics, ow pattern can be categorized into laminar ow and turbulent ow as shown in Figure 4.2 a). In laminar ow, uid at dierent location follows parallel traces. In turbulent ow, vortices form and the ow distribution is chaotic. Flow speed in vortices is much faster than main ow speed. Typically, in laminar ow, the riblets increases friction drag due to increased surface area(Figure 4.2 b). The drag reduction usually happens in the turbulent ow region. A simplied explanation [49] is that when vortices form, the riblets keep them away from the valleys between the riblets and only the tips of the riblets 31 are in contact with high speed ow in the vortices (Figure 4.2 c). Most of the surface area is in the valleys. There is only low velocity ow in them which only produce very low shear stress. Numerical simulations [50] also shows such velocity distribution on riblets covered surface. Figure 4.2: Mechanism of riblet texture in uid drag reduction. [49] a) Flow patterns of laminar ow and turbulent ow. b) Vortex pattern on a at surface in a turbulent ow. c) Vortex pattern on a riblet covered surface in a turbulent ow. The riblets pushed vortices away from the majority of the surface area. High speed ow in the vortices was only in touch with the tip of the riblet. Therefore, the riblet surface has less uid drag due to less contact area with high speed ow. 32 Saif, M and Koury, E studied drag in pipes lined with riblets lm and observed 5 - 7% drag reduction. [51, 52] Bixler et. al used molding to duplicate from real shark skin sample and the replica got 29% drag reduction with superhydrophobic coating. [53] Bechert et. al fabricated 3D interlocked riblet structure using micro casting and printing and observed 7.3% drag reduction. [54] Lauder and Li et. al did a series of study of drag eect of shark skin denticles under dynamic self-propellant condition which involved a real shark skin membrane, 3D printed solid denticles on a exible membrane as well as a laser cut membrane. [55{57] The membrane made of real shark skin sample achieved 12.3% drag reduction and the 3D printed sample achieved 9.6% drag reduction. 4.3 Previous Studies on Fabricating Articial Shark Skin The low drag property is very promising in many emerging areas such as micro uidic devices, unmanned aerial vehicle(UAV), autonomous underwater vehicles(AUV), etc. Although various methods have been used to reproduce shark skin geometry, a trade-o between throughput and resolution always exists and severely hinders the progress in this eld. Up to now, most of the manufacturing technologies in previous studies are limited to molding and micromachining which is a natural result of the characteristics of shark skin texture. The texture involves riblets that have pitches of a fraction of a millimeter and smallest feature of sub 100 micrometer size. To duplicate the feature, high resolution fabrication technique is required. However, if we want to apply the texture to the aforementioned applications, a few challenges will arise. First, the area to be covered is much larger compared to the minimum feature size of the riblets which prevents some high resolution, low throughput technologies, such as two-photon lithography [58] and electron beam lithography from being used in fabricating shark skin texture. Second, the surface to which the riblets attach is not always at and can be highly customized geometry which the technologies such as molding, laser cutting, and micromachining are hard to accommodate. 33 The exibility of stereolithography makes it very appealing in realizing articial shark skin texture on customized surface shapes. Multiple attempts have been made using SLA. Lauder et al. fabricated a high resolution shark skin denticle using two-photon lithography [57], however, no large area sample could be fabricated for uid mechanics study. DMD based stereolithography machine has been a popular option in fabricating microscale objects [16,59] with the benet that the whole cross-section can be cured with one exposure. The smallest feature they can build is dened by the image of a single pixel on the DMD. To achieve a smaller resolution, the whole exposure area need to be demagnied due to the xed number of pixels available on the device. In other words, the SLA printers in these works have to either print small high-resolution objects or big low-resolution objects. The shark skin texture is a multiscale problem which has both high resolution and big print volume. It can be handled eectively with our multiscale process. 4.4 Multiscale Printing of Articial Shark Skin Texture The way we test our printed shark skin texture is using pipe ow measurement. Several pipes were printed with shark skin texture of dierent parameter covering their interior surface. A schematic of the setup is shown in Figure 4.3. Figure 4.3: Schematic of pipe ow setup used to test SLA printed shark skin. 34 The printed pips are shown in Figure 4.4 and 4.5. Each pipe was jointed with commercially available smooth pipes. There was a port at each end of the test section connected with a dierential pressure transducer. The transducer measured the pressure dierence at the beginning and the end of the test section, therefore, gave the pressure drop when water owing through the pipes. The pressure drop can be translated to a friction coecient using the Darcy-Weisbach law: f D = 4P L 2D <U > 2 where4P is the pressure drop,L is the length of the pipes (187 mm), D is the internal diameter of the pipes, is the density of water and <U > is the average velocity of the water in the pipe cross-section. The signal was collected by a NI-DAQ and sent to a computer. The ow rate was measured by a owmeter at downstream and collected by an Arduino microcontroller and sent to the computer. The water was driven by a commercial water pump in a reservoir. The ow rate was adjusted by a valve at upstream of the test section. Although most of the previous research on articial shark skin focused on the riblet structure, the actual texture on real shark skin is riblets on top of scales, also called denticles in biology (Figure 4.6 a). Up to now, there is no theory on how the denticles interact with water ow to reduce drag. The rst reason is the complication of turbulent ow. Another important reason is that denticle structure that covers a large area is dicult to make using traditional manufacturing processes. Hence, researchers didnt have the capability to study the structure experimentally. As the multiscale SLA gives us the capability to fabricate microstructure over a large area, we decided to fabricate large area denticle structure for the rst time. The design is shown in Figure 4.6 b) The actual printed sample is shown in Figure 4.6 c), d). The images clearly show that a big part of each denticle is suspended which is hard to fabricate using traditional manufacturing techniques but can be easily handled by SLA. 35 Figure 4.4: Comparison of the overall size of a printed pipe with a quarter dollar coin. Figure 4.7 and 4.8 shows details about how the denticles structure was printed by multiscale process. Digital model was rst sliced into layers using the adaptive layer thickness process. The high-resolution features, which are the denticles and a thin layer of the wall that they connected to, were sliced into thin layers of 20 m. The low-resolution feature, which is the pipe wall, was sliced into thick layers of 100 m. The printing sequence is the same as described in section 4.2. Beam diameter was switched during the printing of each adaptive layer. The denticles were printed with the small laser beam of 25 m diameter. The pipe wall was printed with the large 36 Figure 4.5: Cross-section view of four pipes with dierent interior texture. Scale bar: 200 m laser beam of 300 m diameter. The similar process was also used in printing pipes with a riblet covered interior in Figure 4.4. 37 Figure 4.6: Real and printed shark skin denticles. a) denticles on the skin of lemon shark. [60] b) 3D model of denticles. c) dimensions of the denticles. d) the cross-section of a sample which shows the suspended area. To demonstrate the advantage in throughput of the multiscale printing process. Objects with dierent scales were printed and printing time was recorded or extrapolated. At scale 1, the object is a pipe with 20 cm length, 12 mm diameter, 1.5 mm wall thickness, 300 m riblet pitch and 142 m riblet height which is similar to the samples in Figure 4.4. At other scales, the dimensions for the riblet remained the same while the overall size of the pipe grew in every direction. It is 38 Figure 4.7: Adaptive layer thickness in multiscale printing of denticles. Dierent color denotes dierent layer during printing. to simulate the situation when large objects are needed to be printed while the high resolution features need to maintain the same geometries in order to keep the same surface functions. As we can see in Figure 4.9, at scale 0.5, the multiscale process is about 3.8x faster than the xed voxel process. The ratio becomes 4.4 at scale 1 and 11 at scale 5. The larger the object is, the bigger advantage the multiscale process has. This pattern can be explained by the equations below. 39 Figure 4.8: Cross-section view of a layer showing beam switch within a adaptive layer. For the denticle features in the inner surface, the small laser beam was used for high resolution. For the pipe wall, the large laser beam was used for high throughput. t fixed / L 3 V SmallVoxel t multi / L 3 V BigVoxel +h L 2 V SmallVoxel 40 Figure 4.9: Printing time of xed voxel process and variable voxel multiscale process at dierent object size scale. The objects printed were pipes with 300 m pitch riblet on the interior surface. At scale 1, the pipe is 20 cm long, with 12 mm diameter, 1.5 mm wall thickness and 142 m riblet height. At other scales, the dimensions for the riblet were kept the same but object size grew in all three dimensions. The purpose is to demonstrate that the multiscale process has more throughput advantage when larger objects are needed to be built and high resolution features need to stay in the same size to maintain the surface function. where L is the object size. The printing time for the xed voxel process is proportional to object volume divided by voxel volume. Since the voxel volume is a constant, the printing time grows cubically as the object size increases. The printing time for the multiscale voxel process consists of two terms. The rst term is the object volume divided by the big voxel size which indicates interior structure printing time. The second term is the object surface area divided by small voxel size which indicates surface high resolution printing time. Although the rst term 41 grows cubically as well, a much bigger voxel size is used which largely reduce the growth in the rst term. Then the whole expression mainly becomes square growth which is one order of magnitude smaller than the xed voxel process. 4.5 Pipe Flow Measurement Result and Discussion Figure 4.10: Measured friction factors for the smooth pipe, the pipe with 142 m riblets and the pipe with denticle covered interior. Friction factor estimates for the smooth bore pipe, the pipe with the optimal 142 m riblets and the pipe with denticles are plotted in Figure 4.10 as a function of the Reynolds number, Re = <U>D , where is the dynamic viscosity of water. Note that the Reynolds numbers in the experiment ranged between Re 5000 and Re 12000. Over this entire range of Reynolds number, the pipe with riblets had a smaller friction coecient compared to the smooth bore pipe, 42 indicating drag reduction. The degree of drag reduction varied with the Reynolds number. On average, the friction coecient was 0:046 0:0017 for the smooth pipe and 0:042 0:0016 for the pipe with riblets, which yields an average drag reduction of 9.6%. In the test, the denticle structure produced more drag than other samples. This may due to the fact that the pipe ow measurement method generates dierent ow pattern than the tank ow method in the previous study. [56] To study how riblet geometry aects drag, both taller and shorter riblets were also tested. The measured friction factors are shown in Figure 4.11. The measurements demonstrate that, for the conditions tested, the 142 m riblets yielded the best performance. Both increasing and reducing the riblet height worsened performance. A explanation is illustrated in Figure 4.12. The way riblets reduce drag is to push high-velocity vortices away from the surface. When the riblets were too low (88 m case), the vortices can still touch the valley area. The total contact area, in this case, is larger than a smooth surface which resulted in more drag. When the riblets were too tall (222 m case), smaller vortices started to form in between the riblet which also increased drag. The observations described above are in broad agreement with previous results, which demon- strate that riblets can generate as much as 10% drag reduction. [46, 61] Further, previous ex- perimental and numerical studies [46, 47, 61] also demonstrate a clear optimum in riblet size for given ow conditions. However, the exact numbers obtained here must be treated with some caution. This is because the average friction factor observed for the present smooth bore pipe, f D = 0:0463 is higher than that observed in previous smooth pipe experiments. Specically, the friction factor typically ranges between 0.04 and 0.03 over the range of Reynolds numbers tested. [62] We attribute this to potential roughness eects since the 3D-printing process with a minimum layer thickness of 20 m yields a rougher surface than that in nely polished or honed pipes. Nevertheless, the current measurements provide a nice demonstration of potential applications. 43 Figure 4.11: Comparison of friction factors of the pipes with dierent riblet height. 44 Figure 4.12: Diagram of vortex pattern on top of riblet with dierent height. On very short, the vortices can still touch the valley area. The total contact area, in this case, is larger than a smooth surface which resulted in more drag. On medium height riblet, vortices are pushed away and total drag decreases. On very tall riblets, smaller vortices started to form in between the riblet which also increased drag. 45 Chapter 5 Multiscale Printing of Articial Lotus Leaf With the help of multiscale stereolithography process, many other biomimetic structures may be fabricated and studied experimentally. As an example, Figure 5.1b) shows an articial lotus leaf with micropillars which have water repellent function, printed using the same process. A contact angle of 139 was measured on the articial lotus leaf with 300 m pillar pitch using a water droplet of 10L volume. Although the angle is smaller than that on a lotus leaf in nature(Figure 5.1a) which can be larger than 150, [63] it is a preliminary result showing that similar structure can be easily fabricated with the process. Structure optimization and detailed characterization can be included in future works. Figure 5.1: A drop of water on the surface of, a) a lotus leaf in nature, [48] b) an articial lotus leaf printed by the multiscale stereolithography process. The pitch between the micropillars is 300 m. 46 Summary In this work, a multiscale stereolithography (SLA) process is developed to address one of the central limitations associated with existing additive manufacturing technologies: the trade-o be- tween throughput and resolution. The multiscale stereolithography process consists of two parts. In the X-Y plane, a resonance grating lter is used to switch the laser beam prole for dierent laser wavelengths. In the Z-axis, an object is built by using an adaptive layer thickness for large and small features. The multiscale SLA machine is low cost, miniaturized, and precise. Arti- cial shark skin samples with riblets and denticles were printed. The riblet with optimum height demonstrated almost 10% average drag reduction. The multiscale SLA process showed 4.3x higher throughput compared to traditional SLA processes. Moreover, this advantage becomes even larger when bigger objects need to be printed. Large area samples are also fabricated with denticles that have resolution similar to natural shark skin. These preliminary tests conrm that the present technique yields novel fabrication capabilities that can enable the study and development of mul- tifunctional biomimetic surfaces. Given its ability to simultaneously provide high resolution and throughput using relatively low-cost hardware systems, the multiscale stereolithography process described in this paper has the potential to open up many application areas out of reach of current 3D printing technology. 47 Figure 5.2: Summary of multiscale SLA project. a) invented multiscale lithography process which solved the trade-o between resolution and throughput. b) demonstrated drag reduction eect on articial shark skin structure. c) provided a platform for future studies on multiscale structures. 48 Topic 2: Inverse Design of Diractive Optical Elements for Structured Light 49 Abstract 3D sensing has been an increasingly popular area due to the development of face recognition on mobile devices as well as autonomous driving cars. Diractive optical element(DOE) is a low cost, compact solution for generating structured light for 3D sensing applications. However, the parameter space of DOEs is if often signicantly larger than traditional geometric optical elements such as lenses and periodic diractive optical elements such as gratings. The reason is that the height of each pixel on a DOE is an independent variable and there is no inherent symmetry to reduce the number of variables. Therefore, the parameter sweeping approach is not practical for designing DOEs. Using iterative numerical optimization is an eective way to reduce the number of iterations required to nd the optimal design. In this work, I propose an inverse DOE design method with particle swarm optimization which takes DOE radiation pattern as input and manufacturability of DOE as the gure of merit. This inverse method has the benet of reducing the number of variables in optimization and minimizing the loss of performance due in fabrication. As a demonstration, two DOEs that project periodic dot array pattern and encoded binary pattern were fabricated. Optical characterization showed the radiation patterns matched the designs which validates the inverse design method. 50 Chapter 6 Introduction to 3D Sensing Techniques In the past decade, due to the progress in depth sensor technology and computation power. Much more information representing the 3D spatial information has been mapped into digital format. As a result, signicant market demand has emerged in areas such as autonomous driving vehicles, virtual reality(VR), augmented reality(AR), 3D face recognition, etc. The rst example of capturing depth information in the consumer electronics market is in the gaming industry with the introduction of Microsoft Kinect TM (Figure 6.1) in 2010 which is an accessory for Xbox 360. It uses a structured light depth camera to capture players' gesture and enable people to play games and control the interface without using a game controller. Although its capability was limited, people in both consumer market and research began to realize the potential of 3D sensing and changes it might bring to the ways people interact with digital content. Figure 6.1: First Generation Kinect for Xbox 360 51 In 2017, the face ID feature was introduced on Apples iphone X(Figure 6.2). The purpose of this feature was primarily for biometric authentication with which owner can unlock the phone, make a nancial transaction, etc. Besides, it was also applied to Animoji(Figure 6.3) where it captures users facial expression and generates the corresponding expression on an emoji with animation. Since then, the presence of 3D sensors on mobile devices increased signicantly as consumers started to anticipate that one of the most important electronic devices in daily life should be to capture 3D information instead of 2D. Figure 6.2: Face ID feature on iphone X [64] In this section, two of the most common 3D sensing technologies, time of ight(ToF) camera and structured light camera, are brie y introduced. 6.1 Time of Flight Camera Time of ight cameras detects distances by measuring the round trip time of a light beam traveling between the light source and the measured object. The most direct method uses a mechanical scanner to sweep through the surface of an object. The distance between the camera and measured 52 Figure 6.3: Apple's Animoji [65] location is calculated as d = t=(2c) where t is time of travel and c is the speed of light. Then the results are aggregated and form a depths map of the whole scene. [66]However, this type of system is generally bulky and costly. Another popular method is to illuminate the entire scene with rf modulated light source and use a sensor array to detect signal from the entire scene at once. At each image location, distances are calculated by measuring the phase delay of modulation caused by light travel distance. A illustration is shown in Figure 6.4. In this case, signals from 4 neighboring pixels are used to calculate the distance of one location in the scene. The measurement time of the 4 pixels has 90 degrees delay between each other. Denoting the signal asa 0 ;a 1 ;a 1 and a 3 (Figure 6.5). The phase can be calculated as ' = arctan a 0 a 2 a 1 a 3 Based on the phase delay above, the corresponding depth or distance is D = c 2 ' 2f 53 where c is the speed of light and f frequency of the modulation. Note that in this method, the non-ambiguous distance is limited by the frequency of modulation. In the example in Figure 6.5 where the modulation frequency is 20 MHz, it allows a non-ambiguous distant up to 7.5 m. Distances further than that will be measured as within 7. 5m. Such a phenomenon is called phase wrapping. Several methods have been developed for phase unwrapping such as amplitude correction, multi-camera methods etc. [67] Figure 6.4: The principle of one type ToF depth camera: The distance is calculated based on the phase delay between light source and received re ection light. [67] Figure 6.5: Sampling of a modulated signal [66] 54 6.2 Structured Light Figure 6.6: A illustration of a fringe pattern projection structured light system. a) arrangement of the camera, projector and object. b) spacial relationship between projection pattern, image on the object and the image captured by the camera. [68] Structured light depth sensing has two key components, a pattern projector and a camera. A typical system is illustrated in Figure 6.6. The projector provides an active illumination with spatially modulated intensity distribution on an object. Common modulation patterns include fringes, grid, dot array, etc. Then the camera takes an image with the object overlayed with the projection pattern. If the object is a planar surface, the captured pattern may be similar to the original. If the object is not a planar surface, the features in the pattern will be distorted and depth information can be retrieved via the distortion using certain depth retrieval algorithms. The traditional way of depth retrieval using structured light is using trigonometry and very similar to stereo vision systems. A simple example is shown in Figure 6.7. A pattern from projector 'A' is projected into three dierent scenes. A pixel, p A , in the image captured by camera 'C' is used an example for calculation. The radiation from p A intersects the scenes at location P 1 ;P 2 ;P 3 , respectively. Due to dierent distances, the image of P 1 ;P 2 ;P 3 will show up at dierent places,p c1 ;p c2 ;p c3 , on the camera sensor. Assuming the distance ofP 2 is known from calibration, the distances of the other two point, P 1 ;P 3 can be calculated. [69] 55 z i = 1 1 z2 + d REL i bf z 2 (6.1) z i = z 2 + z i ;i = 1; 3 (6.2) where z i is the distance(depth) between point P i and the camera. d RELi is the relative disparity between p ci and the referent point p c2 . b is the baseline of the camera-projector system and f is the focal length of the camera and the projector. Figure 6.7: A example of depth retrieval. A and C represents projector and camera respectively. A pattern is projected at three dierent scenes and the pixel p A intersects with the scenes at three locations, P 1 ;P 2 ;P 3 . The image of these three locations shows up on the camera image at p c1 ;p c2 ;p c3 . Using the disparity between the three point on the camera image, the distances of P 1 ;P 2 ;P 3 can be calculated. [69] As a comparison, a stereo vision system uses two cameras instead of one camera and one projector which is more similar to how human eyes work. The stereo vision system also relies on a similar trigonometry principle. However, identifying the conjugate point on the images from 56 the two cameras often relies on the texture of the object which is subject to the ambient lighting condition. A low texture scene will also dicult for the stereo vision system to detect even in good lighting condition. Structured light systems have an advantage in these situations as it uses the texture from a projected pattern which is actively provided by the system itself. 57 Chapter 7 Inverse Diractive Optical Elements Design and Simulation 7.1 Statement of the Problem This section describes the key components in the design process in this work. The basic scenario is illustrated in Figure 7.1. The main goal is to design diractive optical elements that can project user-dened structured light pattern when illuminated by a coherent light source. The light source is assumed to be a collimated coherent light source such as a laser diode or VCSEL with collimation optics. Therefore the output of the light source can be treated as a plane wave before arriving the DOE. At the plane immediately before the DOE, the complex amplitude of the incident light is denoted as U in (;). At the plane immediately after the DOE, the complex amplitude of the incident light is denoted as U out (;). The complex transmittance function of the DOE is then dene using U in and U out as t(;) = U out U in (7.1) t represents the modulation in both amplitude and phase from the DOE to the light transmitted through it. Hence, the transmittance function can be expressed as 58 t(;) =A(;)e j'(;) (7.2) where A and ' are scalars representing amplitude and phase modulation, respectively. After the DOE, the light starts free space propagation. In the scope of this work, the propa- gation can be described using scalar diraction theory. Details on diraction theories in dierent regime are covered in section 8.2. The general propagation direction is +z, and the location of DOE is set to be z = 0. The imaging plane is located at z > 0. Ideally, the light intensity distributionjU(x;y;z)j 2 at the imaging plane is the desired structured light pattern. Figure 7.1: Illustration of key components in a general usage case of DOEs in this work 7.2 Design consideration A few parameters are determined by 3D lithography and optical characterization tool available in this work: 59 • Only phase modulation DOE can be fabricated which means the amplitude modulation factor A(;) = 1 everywhere on the DOE. • 8 or 16 dierent levels are available from fabrication at each pixel on DOE. Meaning that the phase modulation factor '(;) can be one of the 8 or 16 discrete numbers between 0 and 2. • The laser as the light source has a wavelength of 940 nm. 7.3 Methods of Design and Simulation This section covers the description of the DOE parameter space, common optical design and optimization methods and the inverse design method used in this work. The parameter space for designing a DOE can be easily understood using Figure 7.2. The DOE surface is pixelized into m rows and n columns. Overall DOE dimensions are generally determined by its application. For example, the size of a DOE in mobile phone for facial recognition is limited by the space available for it. As more pixel gives higher image quality since more information is encoded, the values of m and n are determined by DOE size divided by the highest possible lithography resolution. At each pixel, amplitude modulationA(;) and phase modulation'(;) are two independent parameters. Assuming each has L discrete values available to choose, the parameter space size of this DOE is (LL) mn (7.3) One of the most common methods of designing optical devices is sweeping the parameter space and select the one design with the best performance. This method is useful when the parameter 60 space is relatively small so that the time for running simulation is acceptable. It applies to cases such as periodic gratings [38], lens system with a small number of surfaces etc. Figure 7.2: Illustration of design parameters of a DOE device In the case of DOE, the parameter space is generally too big for sweeping. As a example, assuming we are designing a DOE that is m = 1000 by n = 1000 pixels. A(;) and '(;) each has L = 10 discrete values available. A(;) ranges from 0 to 1 and '(;) ranges from 0 to 2. The size of the parameter space, according to equation 7.3, is (10 10) 10001000 61 Figure 7.3: Design ow of DOE using mathematical optimization which is an astronomical number of dierent DOE designs to be simulated before the best design can be found. Obviously, the brute force sweeping method is not practical for DOEs. 62 In the case of large parameter space, using iteration based mathematical optimization can be a practical path to reduce the computational load. A typical design ow is shown in Figure 7.3. At the beginning, a random DOE design is generated as a starting point in the parameters space. In each iteration, an image is calculated using the diraction theories covered in section 8.2. The mathematical optimizer has a gure of merit(FOM) or object function which is a gauge of how good is the result of this iteration. In this case, the FOM is the quality of the image or how close is the generated projection image to the ideal pattern. If the FOM is considered optimum, the current design is accepted and iteration stops. If not, iterations continue and the next DOE design will be generated and evaluated. The pros and cons of this method are: • Pro: The image quality is set as FOM. It aligns with the need of applications which is to generate desired structured light patterns. • Con: DOE parameters are allowed to vary freely which includes both amplitude and phase modulations. However, most lithography technologies can only manufacture DOEs that only have one type of modulation. Thus the optimum DOE design form the optimization may not be manufacturable. In this work, only phase modulation DOEs can be fabricated. If the amplitude modulation is forced to be 1, the resulting image will be far worst than optimum. We'll call this method forward method for the ease of reading. In this work, an inverse design method is utilized in optimizing DOEs. The inverse design ow is illustrated in Figure 7.4. The key dierence of the inverse method to the forward method is that the gure of merit is set to be the ease of manufacture. The projection patterns in this work are binary images such as periodic dot array or arbitrary dot array. The intensity on the image plane jU(x;y)j 2 63 Figure 7.4: Design ow of DOE using inverse design method is independent of the phase of the incident light. Therefore, the phase at each pixel on the image plane can change freely and the image pattern remains the same. Therefore, the parameter space of the inverse method is set to be phases of the complex amplitudes on the image plane. Iterations are conducted with the following steps: 1. At the beginning, an image with the ideal scalar amplitude but a random phase is generated to initiate the iterations. 2. The generated complex amplitude is used to inversely calculate what DOE design is required to produce such a pattern. In a general case, no analytical solution has been found to precisely retrieve the information on DOE. However, many studies have proposed methods that generate reasonable results. [70,71]. In this work, the propagation distance is restricted and Fresnel or Fraunhofer diraction conditions always apply. In the Fresnel and Fraunhofer diraction regime, the complex amplitude of image,U(x;y), and DOE design,t(;) are the 64 Fourier transform of each other. Therefore, a DOE design can always be retrieved precisely within each iteration. 3. A FOM is calculated based on the ease of fabrication. As in this work, only phase modulation DOE can be fabricated which means the amplitude modulation part of the transmittance function has to be 1. In other words, a DOE design candidate with t = A(;)e j'(;) = 1e j'(;) is considered the easiest to fabrication and have the best FOM. 4. If the FOM is considered optimum, the design is accepted. If not, a new phase distribution on the image is generated by the mathematical optimizer and iterations continue until an exit condition of the optimizer is met. After a optimum DOE design, t optm =A optm (;)e j'optm(;) , is generated, the phase modu- lation ' optm (;) is converted to corresponding pixel height: h(;) ='(;) 2(n 1) (7.4) where n is the refractive index of the DOE material. Besides, in this work, the lithography technology can only provide 8 or 16 discrete surface levels. Hence, the surface height from equation 7.4 is rounded to the nearest available level. The inverse method has several advantages. First, as it produces DOE designs that are tailored to manufacturability, the fabricated sample will be close to the design. As a result, the image will close to our estimation as well. Second, only the phases at the bright spot pixel locations on the image are variables during iterations. The number of variables is normally less compared to forward method where all DOE pixels are considered variables. 65 Chapter 8 Introduction to Diractive Optical Element and Free Space Propagation 8.1 Diractive Optical Elements Diractive optical element(DOE) is a category of devices that use a surface relief to control the wavefront of light. It has been widely used for applications of beam shaping, beam splitting, pattern generation, and holographic projection, etc. DOEs has many advantages over classic optical elements. A primary one is the high degree of freedom on phase front manipulation. Besides, DOEs are lightweight and compact which is favorable for integration into electronics with a small form factor. A example of diractive lenses is shown in Figure 8.1. In terms of the type of modulation, DOEs can be classied into two categories, amplitude modulation and phase modulation. One example of amplitude modulation DOE is the Fresnel zone plate. However, a signicant portion of power is lost in amplitude modulation which will result in low diraction eciency. In comparison, the phase modulation DOEs are more ecient. Also in cases such as pattern generation and image reconstruction, phase information is often more important than amplitude information as shown by the example in Figure 8.2. DOEs can also be categorized into binarized optic and kinoform. [72] On kinoform, the phase modulating surface features very smoothly. On binarized optic, the surface feature has limited 66 Figure 8.1: A example of diractive lenses with two, four, eight levels and smooth prole. [72] Figure 8.2: A example showing the importance of phase information in image reconstruction. [73] numbers of discrete height level. If the DOE is made with only one lithographic mask and etching process, it only has two surface levels which represent modulations of 0 and . More lithography steps can be used to increase the number of levels(Figure 8.3) which will in general increase diraction eciency. The DOEs in this work can be fabricated with 8 or 16 levels and fall into the binary optic category. 67 Figure 8.3: Using multiple photolithography process to generate binary optic with 2 N levels. [72] 8.2 Free Space Propagation Theory 8.2.1 From Vector Diraction to Scalar Diraction In classical electromagnetic theory, electromagnetic waves are described as vector eld. In Carte- sian coordinates, they can be written as: ~ E(x;y;x;t) = 2 6 6 6 6 6 6 4 E x (x;y;z;t) E y (x;y;z;t) E z (x;y;z;t) 3 7 7 7 7 7 7 5 ~ H(x;y;x;t) = 2 6 6 6 6 6 6 4 H x (x;y;z;t) H y (x;y;z;t) H z (x;y;z;t) 3 7 7 7 7 7 7 5 The propagation of EM waves are governed by Maxwell's equation: 68 r ~ E = @ ~ H @t r ~ H = @ ~ E @t r ~ E = r ~ H = 0 From Maxwell's equations, on the condition that the medium of propagation is linear, homo- geneous, isotropic and non-dispersive, Helmholtz equation can be derived as: [74] r 2 ~ E n 2 c 2 @ 2 ~ E @t 2 = 0 where n = 0 is the refractive index of the propagation medium, c = 1 p 00 is the speed of light in vacuum. A similar equation applies to the magnetic eld as well: r 2 ~ H n 2 c 2 @ 2 ~ H @t 2 = 0 In the two equations above, all components of ~ E and ~ H satisfy the same equation and can be treated separately using a scalar wave equation: r 2 U(x;y;z;t) n 2 c 2 @ 2 U(x;y;z;t) @t 2 = 0 Therefore, we can use scalar theory instead of vector theory to describe the propagation of light. In practice, various boundary conditions are introduced when dealing with optical devices. A few extra conditions are required before using the scalar diraction theory. • wavelength dimension of interest such as structure geometries, apertures, etc. • distance of propagation Z 69 Comparison between dierent realms of optics theory: ! 0 =) no diraction; geometricaloptics dimensions of interest =) Scalar diraction theory dimensions of interest =) Vector diraction theory 8.2.2 Rayleigh-Sommerfeld Diraction Formula A general scalar diraction scenario is shown in Figure 8.4. At the input plan z = 0 where the scalar eld is given as U =U(;;) The goal of a scalar diraction theory is the calculate the scalar eld distribution,U = U(x;y;z;) at any z> 0 plane. The Rayleigh-Sommerfeld(R-S) diraction formula is dened as: [74] U(x;y;z;) = k 2j |{z} 1 ○ ZZ +1 1 U(;;) | {z } 2 ○ e jkr 0 r 0 | {z } 3 ○ cos(~ n;~ r 0 ) | {z } 4 ○ dd (8.1) where k = 2 v is the wave number, ~ r 0 = p (x) 2 + (y) 2 +z 2 is the distance between a virtual point source to a location on the output plane. The R-S formula treats the complex amplitude at the input plane as individual virtual point sources. The point sources send out spherical waves and propagate to the output plane. The complex amplitude at the output plane is the interference from all the virtual point sources. The physical meaning of every term in the R-S formula is explained below: 1. Constant factor that is independent of x,y,z 2. Complex amplitude of virtual point source on the input plane 70 Figure 8.4: Scenario for a general scalar diraction problem [67] 3. Amplitude attenuation and phase of an expanding spherical wave from a virtual point source at (;; 0) 4. Oblique factor that contributes to amplitude loss at an oblique propagation direction The R-S is valid as long as U satises the Sommerfeld radiation condition [74]: lim R!1 @U @n jK U R = 0 (8.2) This condition is satised if U vanishes at least as fast as a set of diverging spherical waves with increasing R. 71 8.2.3 Paraxial Approximation to Rayleigh-Sommerfeld Diraction Despite the R-S diraction formula is the exact model for scalar propagation, the evaluation of the integral in formula 8.1 is computationally expensive. Besides, every location on the output plane requires the evaluation once. When designing a diractive optical element, the process generally involves iteration of candidate designs and update the designs using mathematical op- timizers. Therefore, approximations to the R-S are often utilized to simplify the physical model and computation load. In the paraxial approximation, the following assumptions are made: • z the maximum dimension of non-zero region of U or region of interest on the output (;)plane • z the maximum dimension of the region of interest on the input (x;y) plane Now if we apply the paraxial approximation to the R-S formula 8.1, two parts can be simplied: • cos(~ n;~ r 0 ) 1 • in the denominator of the sperical expanding factor,~ r 0 z Therefore, under paraxial approximation, the R-S formula becomes: U(x;y;z;) = k j2z ZZ +1 1 U(;;)e jkr 0 dd (8.3) Valid for: z 2 ( 2 + 2 ) max , and z 2 (x 2 +y 2 ) max 8.2.4 Fresnel Diraction The Fresnel Diraction is based on the Taylor expansion of the r 0 in the exponential phase term in equation 8.3. 72 r 0 = z 2 + (x) 2 + (y) 2 1=2 =z " 1 + x z 2 + y z 2 # 1=2 (8.4) Use Taylor series: [1 +b] 1=2 = 1 + 1 2 b 1 8 b 2 +:::; jbj< 1 Then, r 0 z " 1 + 1 2 x z 2 + 1 2 y z 2 # (8.5) on the condition that 1 8 k z " x z 2 + y z 2 # < 1 The R-S formula nally becomes: U(x;y;z;) = k e jkz j2z ZZ +1 1 U(;;)e jk 2z [(x) 2 +(y) 2 ] dd (8.6) which is called Fresnel diraction integral. Comparing it with the original R-S formula, we observe that the propagation phase becomes quadratic phase term which implied that this method uses quadratic shape wave fronts to approximate the spherical wave fronts in the R-S formula. Note that Equation 8.6 is in the form of convolution. Therefore it can be written as: U(x;y;z;) =U(;;) N h(x;y;z;) (8.7) h = k j2z e k 2z (x 2 +y 2 ) (8.8) where h is the convolution kernel representing the point spread function with quadratic wave front. 73 If we expand the exponent, equation 8.6 becomes U(x;y;z;) = k e jkz j2z e jk 2z (x 2 +y 2 ) ZZ +1 1 fU(;;)e jk 2z ( 2 + 2 ) ge jk z (x+y) dd (8.9) Note that the equation is in the form of Fourier transformation. Here we dene the 2D Fourier transform of a complex function g as: G(x;y) = F x;y fg(x;y)g (8.10) = ZZ +1 1 e j2(fxx+fyy) dxdy (8.11) where f x ;f y = spacial frequency coordinates Based on the denition 8.10, equation 8.9 can be written as : U(x;y;z;) = k e jkz j2z e jk 2z (x 2 +y 2 ) F ; fU(;;)e jk 2z ( 2 + 2 ) g fx= k 2z x;fy= k 2z y (8.12) 8.2.5 Fraunhofer Diraction In the Fresnel diraction, the r0 in the exponential phase factor is approximated by the zero and rst order of it's Taylor expansion. In Fraunhofer diraction, a more restricted condition is applied so that the diraction formula can be largely simplied. Let's start from equation 8.5 and expand the quadratic terms. Then, the quadratic term regarding and are dropped. r 0 z " 1 + 1 2 x z 2 + 1 2 y z 2 # (8.13) = z 1 z (x +y) + x 2 +y 2 2z | {z } keep + 2 + 2 2z | {z } drop (8.14) 74 The condition required for this operation is Fraunhofer condition: k 2z 2 + 2 max < 1 (8.15) This condition implies that the exponential phase term in the equation 8.9 is close to one and therefore can be ignored. The region that satises condition 8.15 is called Fraunhofer diraction region or far eld. The Fraunhofer diraction integral can be written as: U(x;y;z;) = k e jkz j2z e jk 2z (x 2 +y 2 ) ZZ +1 1 fU(;;)ge jk z (x+y) dd (8.16) = k e jkz j2z e jk 2z (x 2 +y 2 ) F ; fU(;;)g fx= k 2z x;fy= k 2z y (8.17) Except for the coecients in the front, the result is simply a Fourier transformation of the complex amplitude a the input plane. 75 Chapter 9 Introduction to Numerical Optimization Optimization is a category of methods that people use to seek the optimum solution to certain problems and is widely used in many area such as engineering, economics, sociology etc. To use optimization tools, a objective function f(~ x) need to be determine rst. The objective function f is a quantitative measure, or a 'score', of a candidate solution. The input, ~ x = (x 1 ;x 2 ;:::;x n ), are called variables. The optimal solution ~ x is called global optimizer and is dened as: [75] f(~ x )f(~ x) for all~ x This section covers three of the most common computational optimization algorithms, which are gradient descent, Newton's method and particle swarm which is used in this work. 9.1 Gradient Descent and Newton's method The gradient descent method is the most widely used computational optimization method due to it's simplicity. The optimizer start from either a random or a user dened location ~ x (1) and move a small step in the negative gradient direction at each iteration: [76] ~ x (t+1) ~ x (t) rf(~ x (t) ) 76 wheret is step number or iteration index and > 0 is called step size. This method relies on the rst order Taylor expansion of the objective function: f(~ x)f(~ x (t) ) +rf(~ x (t) )(~ x~ x t ) (9.1) The gradient descent ensures that f(~ x (t+1) )f(~ x (t) )jjrf(~ x (t) )jj 2 2 f(~ x (t) ) (9.2) Therefore, it will converge at a local minimum if is properly selected. The minimum will also be the global minimum if the problem is convex. Newton's method is another commonly used optimization method. Comparing with gradient descent which uses the rst order derivative of the objective function, Newton's method uses the second order derivative. The algorithm can be described simply as [76] ~ x (t+1) ~ x (t) H 1 t rf(~ x (t) ) where H t =r 2 f(~ x (t) ) is the Hessian of f and dened as H t;ij = @f(~ x) @x i @x j j ~ x=~ x (t) As the gradient descent and Newton's method is based on the rst order and second order Taylor expansion, they require that the objective function f is rst order and second order dier- entiable, respectively. These requirements may not be met for complex problems where derivatives are not given explicitly. Figure 9.1 shown a comparison between the gradient descent method and Newton's method on the contour plot of a function. Since Newton's method uses second derivative information, 77 Figure 9.1: A comparison between gradient descent and Newton's method. Red path: Newton's method. Green path: gradient descent. [77] the objective function is approximated by a quadratic function at each step. In comparison, the objective function is approximated by a linear function at each step in the gradient descent method. As a result, Newton's method takes a more direct route to the minimum therefore usually converges faster than the gradient descent method. 78 9.2 Particle Swarm Optimization The Particle swarm optimization(PSO) used in this work is a mathematical optimization method inspired by biology study simulating the behavior and organization of animal groups such as bird ocks. The goal is to locate the global optimum point for a given objective function using a ' ock' of candidates swarming in the domain of denition of the objective function iteratively. Each candidate is called a particle as it appears to be a dot in the search space when being plotted. Each particle has several attributes attached [78]: • a position inside the search space • a velocity, which will be used to calculate next position • value of the object function at the current location • the best location found so far by this particle • best function value found by all particles The object function f : R n ! R. Therefore the search space has n dimensions. Generally, PSO optimizers are designed to search the global minimum in the search space. In case a global maximum is preferred, a function g =f can be used as the objective function instead. We denoteN as the total number of particles(population), i as the index for each particle,~ x i as the position of the i th particle,~ v i as the velocity for the i th particle, ~ p i as the best position so far for the i th particle and g as the best position so far the the swarm. A general particle swarm process can be described as follow: 79 input : Object function f output: Global optimum location~ g, optimum function value f(~ g) Initialize swarm: for particle i = 1 to N do Randomly initialize the velocity~ v i and position~ x i Set the particle's current best location to be the initial position: ~ p i ~ x i end Running swarm: while Stop criteria are not met do for particle i = 1 to N do Generate two ramdom numbers~ r p and~ r g . Update particle's volocity: ~ v i ~ ~ v i + ~ ~ r p (~ p i ~ x i ) +~ ~ r g (~ g~ x i ) Update particle's position: ~ x i ~ x i ~ v i if current best value is better than previous best value: f(~ x i )<f(~ p i ) then Update the particles best value position: ~ p i ~ x i if Current best value is better than previous best value of the swarm:f(~ p i )<f(~ g) then Update swarm's best position: ~ g ~ p i end end end end where the parameters ;; are dened by the user for tunning the swarm behavior which is a balance between particle's previous velocity, particle's own previous best position and swarm's previous best position. A visualization of the swarming process is shown in Figure 9.2. In the beginning, particles were located around the search space with an arrow indicating each particle's velocity. After 80 iterations, most of the particles aggregated at the global minimum location while a few particles stopped at other local minimums. Figure 9.2: a - d) Visualization of a particle swarm optimization [79] Stop criteria of PSO generally includes the following: • Iterations reach a user-dened maximum number • Change of the swarm's best function value is smaller than a certain tolerance. • Optimization time reaches a user-dened maximum. The PSO is metaheuristic as the process completely rely on the observation of the particles and has no requirements on the function being optimized. The advantages are that the number of particles can be small compared to the search space and the objective function doesn't need to be dierentiable. However, the PSO doesn't guarantee that the result is the global minimum. 81 Chapter 10 Design Case No. 1: Encoded Dot Pattern In this section, a design example is explained. The inverse design method is used for designing the required DOE and the intermediate results at each iteration steps are shown. Figure 10.1: Encoded pattern with 630 dots 82 The required projection pattern is shown in Figure 10.1. The pattern consists of 630 bright dots with the arranges specically tailored to a certain 3D depth retrieval algorithm. At each iteration, the phase value at each pixel is updated according to the direction from the particle swarm optimizer. A typical case is shown in Figure 10.2. Figure 10.2: Phase distribution on the projection pattern during optimization From the pattern, a candidate DOE design will be generated with complex amplitude of t =A(;)e ; . The scalar amplitude part, A(;) will be used to calculate a FOM base on the ease of fabrication. As our lithography only produce DOE with no amplitude modulation. In other words, A(;) = 1 everywhere with no variation. The design with a smaller variation in A(;) are considered 'easier' to fabricated and should have better FOM. As the particle swarm 83 optimizer seeks the minimum FOM by default, the FOM is dened as the standard deviation of A of that design. FOM =std(A(;)) = v u u t 1 mn 1 m X i=1 n X j=1 jA( i ; j )j 2 where is the mean of all the elements in A: = 1 mn m X i=1 n X j=1 A( i ; j ) Figure 10.3 shows A(;) of two DOE designs. As amplitude modulation is directly related to optical transparency of the DOE, design a) has more dark pixel than design b). Therefore, design b) has a smaller standard deviation in A(;) and lower FOM which is preferred. In the iterations, designs like b) will be selected over designs similar to a). Once the optimal DOE is design generated, the phase modulation is converted to DOE surface prole. The surface pixel heights are shown in Figure 10.4. 84 Figure 10.3: Examples of the amplitude modulation from two candidate DOE design. a) A design with larger variation. b) a design with smaller variation 85 Figure 10.4: Surface prole of DOE designed to generate projection pattern in Figure 10.1. Scale bar unit: m 86 Chapter 11 Design Case No. 2: Periodic Dot Array Pattern The second design example is a 20 6 dot array pattern shown in Figure 11.1. The design and optimization process is similar to the rst example. Figure 11.1: Periodic dot array pattern The DOE surface prole is shown in Figure 11.2 and Figure 11.3. We can observe that the DOE surface prole is showing periodicity in horizontal direction. In vertical direction, periodicity also 87 Figure 11.2: DOE surface prole which generates dot array projection pattern exists but it's hard to observe on the gure as the pitch is as small as 5 pixels. This observation agrees with our previous knowledge that periodic pattern can be generated by gratings which is a spatially periodic modulation of light. 88 Figure 11.3: 3D visualization of DOE surface prole which generates dot array projection pattern 89 Chapter 12 Optical Characterization The designs from previous optimization process were fabricated and characterized. The 3D lithography was conducted by our project collaborators and the details were not disclosed. For projection pattern characterizations, a collimated laser at 940 nm wavelength was used as the light source and illuminated at the back of the DOE samples. The image screen was placed at 600 mm away from the DOE. The projection image was captured by an industrial camera. A bandpass lter with 30 nm bandwidth and 940 nm center wavelength was mounted on the camera lens. The results for encoded dot pattern projection DOE and periodic dot pattern projection DOE are shown in Figure 12.1 and 12.2, respectively. From the result, we can conclude that the two pattern examples are successfully produced by DOE projection. However, we can also observe two issues on the images which deserve future improvement. First, there is a brighter spot at the center of each projection image. This is from the 0th order diraction which is the component of light that is not diracted. Second, the brightness of the images decreases at the edge. A few factors can contribute to the issues. First, the formulation in the diraction theories section assumes the source consists of an innite number of point sources. 90 Figure 12.1: Characterization of encoded dot pattern generation DOE. a,b) DOE surface optical microscope image. c) Projection image 91 Figure 12.2: Characterization of periodic dot pattern generation DOE. a,b) DOE surface optical microscope image. c) Projection image 92 However, each pixel on the DOEs has a nite size of around 2.8 m and acts as a source with nite size. This will result in an envelop function being applied to the image which is the reason the brightness decreased at the edge. Second, the 3D lithography technique only provides a limited number of pixel height level and the pixel sidewall is sloped rather than vertical which made the actual phase modulation deviate from the optimal value. Therefore the diracted light can't create perfect interference and generate uniform brightness at the center. However, with the improvement of fabrication resolution and quality, the issues mentioned above can both be mitigated. 93 Summary In this work, an inverse method for designing diractive optical elements is proposed. This method uses a target DOE radiation pattern as input to seek an optimal DOE design via numerical optimizations. The gure of merit in the optimizations is based on the device's manufacturability. The inverse method reduced the number of variables in the optimization and the discrepancy between designs and fabricated devices. Two DOEs that were based on the output from the inverse design method were fabricated using 8 or 16 levels 3D lithography. Optical characterization demonstrated the projection patterns matched targets well. The inverse design method has the potential of opening doors for dielectric metasurfaces in the eld of 3D sensing. 94 Topic 3: Nonlinear Metamaterial over Multiple Wavelength Ranges 95 Abstract The evolution of optical communication systems has followed the footsteps of the developments of radio communication. The future optical communication systems will be the same as the RF communication systems today: It will be built on a Si photonics chip with integrated electronics. The information will be coded with advanced modulation schemes and the signal will be detected by an optical superheterodyne receiver. To realize optical superheterodyne, the nonlinear mixer is the key challenge. There is no material in the current Si platform with high nonlinearity. We propose to demonstrate metamaterials with high non-linearity at both optical and microwave wavelengths simultaneously for the rst time. The integrated optical mixer based on the meta- materials will take a signicant leap of Si photonics. There are three stages while the project progresses. In the rst stage, the major focus is on studying the non-linearity at each single fre- quency range, particularly in optical frequency which is more dicult. A nonlinear metamaterial in optical frequency is demonstrated. After that, based on the knowledge gained from the 1st stage, we will focus on studying metamaterials for both optical and microwave frequencies. In the last stage, we will focus on demonstrating simultaneous high non-linearity at both optical and microwave wavelengths. An optical/microwave mixer will be used as the test bed and the demonstration vehicle. 96 Chapter 13 Background and Motivation 13.1 Evolution of Radio Communication and Optical Communication As the demand for transferring information increases, more and more information is carried by light instead of radio frequency (RF) microwaves due to the higher bandwidth. Radio frequency and optical communications are all based on electromagnetic (EM) wave but on very dierent frequencies. Almost a hundred years after the invention of the radio, the evolution of optical communication systems has followed the footsteps of the developments of the radio. On the radio side, the spark gap transmitter was invented in 1887 which is basically a pulsed RF signal source. It made telegraph possible using Morse code. The rst arc transmitter with continuous radio waves was invented in 1903. The rst radio broadcast of voice and music was in 1906. It used amplitude modulation (AM). The rst coherent radio transmitter was in 1914. The rst super- heterodyne radio receiver [80] was demonstrated in 1918. On the optical side, the rst pulsed semiconductor laser, the counterpart of spark gap transmitter, was invented in 1962. The rst CW semiconductor laser, the counterpart of arc transmitter with a continuous wave, was invented in 1970. The st DFB single mode laser, the counterpart of the coherent radio transmitter, was demonstrated in 1975. Over the same period, radio communication systems have moved from 97 discrete elements to integrated radio and electronic chips. Advanced modulation schemes such as phase shift keying (PSK), [81] quadrature phase shift keying (QPSK), [82] quadrature amplitude modulation (QAM) [83] have been adopted. History always repeats itself. The future optical communication system will be the same as the RF communication system today: It will be built on a Si photonics chip with integrated electronics. The information will be coded with advanced modulation schemes and the signal will be detected by an optical superheterodyne receiver. Figure 13.1: Evolution of radio communication and optical communication. Courtesy: Richard Schatz, KTH 13.2 Superheterodyne Receiver A key component in modern RF communication system is superheterodyne receiver. This tech- nology was invented by E.H. Armstrong in 1918 during World War I and its still being widely used in todays communication system such as TV broadcasting, Wi-Fi, cell phone etc. Figure 13.2 shows a diagram of a superheterodyne receiver. The signal with frequency f 0 rst comes into the antenna and then amplied by a preamplier. And then the signal is mixed with another 98 Figure 13.2: Diagram of a typical superheterodyne receiver. signal with f 1 from the tunable local oscillator. The mixing is a nonlinear process in which the quadratic term is being used. [E local sin(2f 0 t) +E signal sin(2f 1 t)] 2 =E 2 local sin 2 (2f 0 t) + 2E local E signal sin(2f 0 t)sin(2f 1 t) +E 2 signal sin 2 (2f 1 t) the second term transforms into sin(2f 0 t) sin(2f 1 t) = 1 2 cos [2(f 1 f 0 )t] 1 2 cos [2(f 1 +f 0 )t] The mixer generates a new frequency ofjf 1 f 0 j. The frequency of the oscillator tracks right along with the signal from the antenna in such a way so thatjf 1 f 0 j is a constant. Therefore, the output of the mixer is a constant frequency signal which is much easier to amplify or modulate then a variable frequency signal would be. Heterodyning is another word for signal mixing in which you combine signals of two frequencies to get a signal of a third frequency. To realize optical superheterodyne, the nonlinear mixer is the key challenge. There is no material in nature with high nonlinearity in the current Si platform. 99 Chapter 14 Non-linear Metamaterial In this work, we propose using nonlinear metamaterial to realize optical superheterodyne. Meta- material has been drawing attention in the last two decades due to its extraordinary properties such as negative refractive index, articial magnetism, nonlinearity, etc. Metamaterial consists of nanoscale building blocks. Each unit block is much smaller than the optical wavelength and therefore it can be viewed as continuous media. The building blocks act as articial molecule and can have unusual behavior that doesnt exist in nature. The freedom to design its structures gives it the advantage of having high nonlinearity. Also, metamaterials are made from metal and dielectric materials and dened by lithography which is easily compatible with the Si platform. 14.1 Origin of Optical Nonlinearity Nonlinear optical eect arise when electron motion in a strong electromagnetic eld cannot be considered harmonic. [85] The response of material to an electric eld E can be described by polarization density P, the second order can be expressed as: [86] ~ p (2) = Z ! L (~ r; 2!) : ! (2) S : h ~ E loc (~ r;!) i 2 d~ r 100 Figure 14.1: Factors aect optical nonlinearity. a) material nonlinearity that originates from molecular structures. [84] b) local eld enhancement (optical resonance). [85] c) non-symmetrical structures. [85] where ! (2) S is the material susceptibility, ! L is the local eld correction factor and ~ E loc is the local electric eld. The integrating is over the entire metal surface in a unit cell. From this equation, we observe that there are a few factors that aect the nonlinearity of metamaterial. First, a stronger electrical eld is always better. Second, the plasmonic resonance from the structure can increase the local eld correction factor ! L . Third, the structure geometry which decides the integration region inside a unit cell can aect the nal result. These factors will be considered in our metamaterial design. 14.2 Optical Metamaterial Design, Fabrication and Characterization Our optical metamaterial design is shown in Figure 14.2. In each unit cell, there is a chevron shaped Ag nanoparticle. Its cross-section is a As=SiO 2 =Ag sandwich structure. Numerical sim- ulation results are shown in Figure 14.3. The resonance peak was designed to be around 1.55 101 Figure 14.2: Design of optical metamaterial. a) top view. b) cross-section view. um wavelength which is commonly used in optical communication. Strong optical resonance was generated between unit cells and between the top and bottom metal layers. The electric eld prole clearly shows that asymmetric charge distribution due to chevron geometry. Magnetic eld shows that there is strong magnetic resonance as well due to the sandwich design. These factors all contribute to stronger nonlinearity in this metamaterial. The optical metamaterial was fabricated via nanoimprint lithography. The process is illus- trated in Figure 14.4. First, a mother mold with chevron patterns was made by electron beam lithography(EBL) and reactive ion etching. Then the pattern was transferred to imprint resist. In the end, the As=SiO 2 =Ag sandwich structure was created by electron beam evaporation and lift-o. The samples were characterized using femtosecond laser and the result is shown in Figure 14.5. The incident fundamental beam was 800 nm. At 400 nm, there is an obvious secondary harmonic generation signal. It is a proof that the metamaterial can provide high nonlinearity. 102 Figure 14.3: FDTD simulation of the chevron structures. a) re ection(R), transmission(T) and absorption(A) spectrums of the optical metamaterial. b) electric eld prole in the SiO 2 layer. c) magnetic eld prole in the SiO 2 layer. 103 Figure 14.4: Fabrication process of the optical metamaterial. A mold with chevron pattern was fabricated by EBL and etching. Then the pattern was transferred to resist using nanoimprint lithography. The As=SiO 2 =Ag metal layers were created by electron beam evaporation and lift- o. 104 Figure 14.5: Second harmonics generation using optical metamaterial. Fundamental beam is 800 nm, 200 W, 20 m diameter. Four spectrums correspond to dierent light polarization. 105 Chapter 15 Future Works The ultimate goal of this project is to demonstrate a signal mixer in an optical superheterodyne receiver. A few tasks in the future can pave the way for us to the ultimate goal. Nonlinear Coecient of Optical Metamaterial Although we have observed obvious second-harmonic generation(SHG) from our optical metama- terial with only 90 nm thickness which is normally only observable with bulk nonlinear crystals, its nonlinear coecient or (2) is still unknown. Knowing it can help us compare its performance with other nonlinear materials directly. More importantly, well be able to know whether its nonlinearity is aected when combined with other structures to build a mixer in the future. A setup for measuring nonlinear coecients is shown in Figure 15.1. A pulsed laser source is used as a fundamental light. The light is polarized and focused into a prism which covers the test sample. A goniometer is used to adjust the incident angle. The re ected fundamental beam is captured by an absorbing pool. At a small angle with respect to the re ected fundamental beam, the SHG light can be observed after passing through a slit and a lter to block the fundamental wave. SHG signal is recorded by a photodiode. After calibration, the power of the measured SHG beam gives the nonlinear coecients. 106 Figure 15.1: The experimental setup to measure nonlinear optical coecient. L1 and L2 are lenses; F, secondary harmonics wavelength lter. A, an absorbing pool for catching fundamental re ection beam. [87] Microwave Metamaterial Our ultimate goal is to build a nonlinear mixer that works with optical signal sources. However, most of the signal sources available today are in the RF frequency range. Hence, the metamaterial for building nonlinear signal mixer needs to have nonlinearity at both optical and RF range. To do this, A metamaterial for the RF range needs to be designed and combine it with the optical metamaterial weve already made. Compared with optical, nonlinear metamaterial in the RF range is much easier to realize. Metamaterial was rst studies in the RF range. Materials in this range are less lossy. Many studies have already been done to generate high Q value resonance and nonlinearity using structures such as split ring resonators (SSRs). [88{92] A few examples are shown in Figure15.2 [89, 93].The 107 existing designs that are proven to work can be directly used and the geometries can be optimized using HSFF simulation at the frequency of the RF source that will be available to use. Figure 15.2: Several examples of split ring resonator geometries. [89,93] a) Single ring with single cut. b) Multi-ring with multi-cut. c) complementary split-ring resonator. d) Spiral resonator. e) Two-layer spiral resonator. f) Split ring resonators with nonlinear inserts. Nonlinear Metamaterial at Both Optical and Microwave Range Figure 15.3: Schematic diagrams of two metamaterial architectures for multiple frequency ranges: (A) parallel mixing of large and small structures, (b) hierachical arrangement of large and small structures. 108 There are several orders of magnitude dierences in optical and microwave wavelength. So are the metamaterial structures for each wavelength. Their structures have to be mixed together to implement metamaterials for both frequencies. Two approaches can be tested: parallel mixing and hieratical mixing. Parallel mixing, as shown in Figure 15.3 a), put small structures for the optical frequency at the gap of the large split ring resonators where the local electric eld is strong. The possible drawback is small structures covers less area then they are alone giving less interaction volume with light. Hierarchical mixing, as shown in Figure 36 b), embeds small structures inside large structures. The small structures cover a larger area than in the parallel mixing approach. However, they are not located at the resonance hot spot of the large structures. These two approaches should be theoretically studied and experimentally fabricated in order to nd the optimal one. Hybrid Metamaterial Characterization Figure 15.4: Two methods of characterizing metamaterial that works at both optical and RF wavelength. a) Metamaterial couples to both couple to both optical and RF sources through free space. b) Metamaterial couples to optical source through free space and RF source through a transmission line. 109 Once the hybrid metamaterial in the last section is fabricated, it will be tested on its nonlin- earity in both optical and RF wavelength. EM waves at both wavelength ranges will be injected into the structure at the same time. A spectrometer will be used to monitor the frequency shift due to nonlinear mixing. A femtosecond pulsed laser will be used as the optical source as it is monochromatic and provide a very strong electric eld. In terms of RF source, two methods of coupling will be considered: free space coupling and transmission line coupling. In free space coupling, as shown in Figure 15.4 a), RF microwaves will emit from an antenna and propagates to the sample surface. The benet of this method is that RF radiation can cover a large area of the sample so that the interaction volume is larger. In transmission line coupling, as shown in Figure 15.4 b), RF power will be feed into the metamaterial by a lithographically dened short trace probe [91] beside it. A transmission line will connect an RF signal source to the probe. The advan- tage of this method is that energy is directed feed into the gap of SRRs. Therefore, the coupling eciency is higher. However, adding a transmission line connector on the substrate and designing transmission line impedance matching add additional complexity to this method. The power of the RF sources available and energy coupling eciency will nally determine which method is better. Then, the hybrid metamaterial fabricated in the last secretion will be characterized. Nonlinear Metamaterial at both Mid IR and Far IR Range As technologies advances, the frequencies of signal sources will go beyond the RF range. The dimensions of the large structure in the hybrid metamaterial will become smaller and smaller. As the dierence in size between the large and small structure decrease, the two types of architectures discussed in section 15 may not be able to apply. For example, the structure for far-infrared is around tens of micros and the width of gaps in it will at micron level. It wont be possible to put a large number of small chevron structures in the gaps. 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IEEE, 2013. 118 Appendix A Conference Presentations Yuanrui Li, Vladan Jankovic, Pan Hu, Mark Knight, Philip Hon, Wei Wu, Non-linear Op- tical Metamaterials over Multiple Wavelength Ranges for Ultrafast and Secure Communication, EIPBN 2018, Puerto Rico, May 2018 Hao Yang, Boxiang Song, Buyun Chen, Yifei Wang, Pan Hu, Yunxiang Wang, Yuanrui Li, Deming Meng, Xiaodong Yan, Yue Pan, Han Wang and Wei Wu, Eects of Crystallinity of Switch- ing Layer Material on Memristive Device, EIPBN 2018, Puerto Rico, May 2018 Yuanrui Li, Huachao Mao, Pan Hu, Haneol Lim, Mark Hermes, Mitual Luhar, Jongseung Yoon, Yong Chen, Wei Wu, Bio-Inspired Multi-Scale Structure for Fluid Drag Reduction Enabled by Variable Voxel Stereolithography, IEEE 2017, Pittsburgh, PA, July, 2017 Yuanrui Li, Huachao Mao, Pan Hu, Mark Hermes, Haneol Lim, Mitual Luhar, Jongseung Yoon, Yong Chen, Wei Wu, Bio-inspired Functional Surfaces Enabled by Multiscale Stereolithog- raphy, EIPBN 2017, Orlando, FL, June, 2017 Yuanrui Li, Huachao Mao, Yuhan Yao, He Liu, Yifei Wang, Boxiang Song, Yong Chen, Wei Wu, Multiscale Porous Structure Enabled by Variable Voxel Stereolithography, EIPBN 2016, Pittsburg, PA, June, 2016 He Liu, Yuanrui Li, Hsiang-Ting Yeh, Yuhan Yao, Dongseok Kang, Jongseung Yoon and Wei Wu, Full Color Re ective Display Based on High Contrast Gratings, invited, EIPBN 2016, Pittsburg, PA, June, 2016 Huachao Mao, Yuanrui Li, Yong Chen, Wei Wu, Multi-scale Stereolithography Fabrication Using Shaped Beams, SFF Symposium, Austin, TX, 2016 Boxiang Song, Yuhan Yao, Yifei Wang, He Liu, Yuanrui Li, Adam Schwartzberg, Stefano Cabrini and Wei Wu, Probing Sub-5 nm Gap Plasmon Using Collapsible Nano-ngers, AVS 63th International Symposium and Exhibition, Nashville, TN, USA, November, 2016 Boxiang Song, Yuhan Yao, He Liu, Yifei Wang, Yuanrui Li, Stefano Cabrini, Adam Schwartzberg, Stephen Cronin and Wei Wu, Probing Sub-5 nm Gap Plasmon Using Collapsible Nano-ngers, EIPBN 2016, Pittsburg, PA, June, 2016 Yuanrui Li, Xuan Song, He Liu, Yuhan Yao, Yifei Wang, Boxiang Song, Yong Chen and Wei Wu, Stereolithography with Variable Resolutions Using Optical Filters with High-contrast 119 Gratings, EIPBN 2015, San Diego, CA May, 2015 Yuhan Yao, He Liu, Yifei Wang, Boxiang Song, YuanruI Li and Wei Wu, Line width tun- ing and smoothing for periodic grating fabrication in nanoimprint lithography, SPIE Advanced Lithography, San Jose, CA, February, 2015 Y Li, A Abbas, Y Yao, Y Wang, W Li, C Zhou and W Wu, Sub-5 nm Patterning and Appli- cations by Nanoimprint Lithography and Helium Ion Beam Lithography, invited, NMDC 2015 B. Song, Y. Wang, Y. Yao, Y. Li, H. Liu, S. Cabrini, A. Schwartzberg and W. Wu, Probing Sub-5 nm Gap Plasmon Using Collapsible Nano-ngers, NNT(Nanoimprint and Nanoprinting Technology), Napa Valley, CA, 2015 120 Appendix B Publications Li Y, Mao H, Hu P, Hermes M, Lim H, Yoon J, Luhar M, Chen Y, Wu W. Bioinspired Functional Surfaces Enabled by Multiscale Stereolithography. Advanced Materials Technologies. 2019:1800638. Li Y, Mao H, Liu H, Yao Y, Wang Y, Song B, Chen Y, Wu W. Stereolithography with vari- able resolutions using optical lter with high-contrast gratings. Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena. 2015 Nov 18;33(6):06F604. Larson C, Li Y, Wu W, Reisler H, Wittig C. Photoinitiated Dynamics in Amorphous Solid Wa- ter via Nanoimprint Lithography. The Journal of Physical Chemistry A. 2017 Jun 21;121(26):4968- 81. Mao H, Leung YS, Li Y, Hu P, Wu W, Chen Y. Multiscale Stereolithography Using Shaped Beams. Journal of Micro and Nano-Manufacturing. 2017 Dec 1;5(4):040905. Liu H, Yang H, Li Y, Song B, Wang Y, Liu Z, Peng L, Lim H, Yoon J, Wu W. Switchable AllDi- electric Metasurfaces for FullColor Re ective Display. Advanced Optical Materials. 2019:1801639. Wu JB, Zhao H, Li Y, Ohlberg D, Shi W, Wu W, Wang H, Tan PH. Monolayer molyb- denum disulde nanoribbons with high optical anisotropy. Advanced Optical Materials. 2016 May;4(5):756-62. Wang Y, Liu H, Li Y, Wu W. Low DC-bias silicon nitride anisotropic etching. Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena. 2015 Nov 10;33(6):06FA01. Yao Y, Liu H, Wang Y, Li Y, Song B, Wang RP, Povinelli ML, Wu W. Nanoimprint-dened, large-area meta-surfaces for unidirectional optical transmission with superior extinction in the visible-to-infrared range. Optics express. 2016 Jul 11;24(14):15362-72. Yao Y, Liu H, Wang Y, Li Y, Song B, Bratkovsk A, Wang SY, Wu W. Nanoimprint lithog- raphy: an enabling technology for nanophotonics. Applied Physics A. 2015 Nov 1;121(2):327-33. Yao Y, Wang Y, Liu H, Li Y, Song B, Wu W. Line width tuning and smoothening for periodi- cal grating fabrication in nanoimprint lithography. Applied Physics A. 2015 Nov 1;121(2):399-403. 121 Song B, Yao Y, Groenewald RE, Wang Y, Liu H, Wang Y, Li Y, Liu F, Cronin SB, Schwartzberg AM, Cabrini S. Probing gap plasmons down to subnanometer scales using collapsible nanongers. ACS nano. 2017 Jun 14;11(6):5836-43. 122 Appendix C DOE optimization script Image import %Read original pattern data and generate scaled pattern data clear all; close all; %user input divergence_v=19.388; %divergence angle in x direction in degree divergence_h=19.388; %divergence angle in y direction in degree DOE_v=5000; %vertical holograpm size in um DOE_h=5000; %horizontal hologram size in um wavelength=0.94; CCD_size=1024; %ccd resolution in pixels CCD_angle=60; %ccd reception angle original_dot=load('pattern.mat'); [original_length_v original_length_h]=size(original_dot); %original pattern matrix size %analyse original pattern global dot_location; global length_new_v; global length_new_h; global dot_bound; global dot_TL_coord; global dot_size_new_h; global dot_size_new_v; D_pixel_v=wavelength / (divergence_v/180*pi) %physical diameter of a pixel on hologram D_pixel_h=wavelength / (divergence_h/180*pi) length_new_h=round(DOE_h/D_pixel_h); %size of DOE in terms of pillar numbers length_new_v=round(DOE_v/D_pixel_v); 123 dot_size_new_h=length_new_h/CCD_size; %dot size in pixel on CCD horizontally dot_size_new_v=length_new_v/CCD_size; %dot size in pixel vetically disp(['original size(pixel) is ' num2str(original_length_v) ' x ' num2str(original_length_h)]); disp(['DOE size(pixel) is ' num2str(length_new_v) ' x ' num2str( length_new_h)]); disp(['pixel size on holograpm is ' num2str(D_pixel_v) ' um x ' num2str(D_pixel_h) ' um']); figure; imagesc(abs(original_dot)); colorbar; title('Original Pattern'); [dot_bound dot_TL_coord]=FcnFindDots(original_dot); figure; scatter(dot_TL_coord(:,2),(1-dot_TL_coord(:,1)),'s'); %rescale the dot size according to requirement dot_pattern_resized = FcnDotResize(dot_TL_coord,length_new_h, length_new_v, 30, 30); %dot_pattern_resized = FcnDotResize(dot_TL_coord,length_new_h, length_new_v, dot_size_new_h, dot_size_new_v); figure; imagesc(abs(dot_pattern_resized)); colorbar; title('Resized Pattern'); dot_location = find(dot_pattern_resized >0.5); % save('dot_pattern_resized.mat','dot_pattern_resized',' dot_location','original_length_h','original_length_v ',... % 'length_new_v','length_new_h','dot_bound','dot_TL_coord'); function [dot_bound, dot_TL_coord]=FcnFindDots(matrix) %This function finds bright area in matrix and output topleft and bottom right coordinats of each area and center coordinates of each area [size_v, size_h]=size(matrix); dot_bound=[]; %stores boundary info of the dots [topleft coordinates, buttom right coordinates, horizontal size, verticle size] dot_center=[]; 124 dot_TL_coord=[]; go_flag=false; for ii = 1:size_v for jj = 1:size_h go_flag=false; if matrix(ii,jj)>0 %if this is a bright point if (ii==1 & jj==1) %at topleft corner go_flag=true; else if (jj==1 & matrix(ii-1,jj)==0) %at first colomn and point above is dark go_flag=true; else if (ii==1 & matrix(ii,jj-1)==0) %at first row and the point to the left is dark go_flag=true; else if ii>1 & jj>1 if (matrix(ii-1,jj)==0 & matrix(ii,jj-1)==0) %not at first row or first column and top of left point are all dark go_flag=true; end end end end end if go_flag TL_coord=[ii jj]; %record topleft coordinats mover_v=ii; mover_h=jj; go_flag = true; while go_flag if mover_h < size_h & matrix(mover_v,mover_h+1)>0 % mover_h=mover_h+1; else if mover_v < size_v & matrix(mover_v+1,mover_h)>0 mover_v=mover_v+1; else go_flag=false; end end end BR_coord=[mover_v mover_h]; dot_bound(end+1,1:6)=[TL_coord BR_coord ... (BR_coord(1)-TL_coord(1)) (BR_coord(2)-TL_coord(2))]; % center = (TL_coord+BR_coord)/2; 125 % center_fract=center./[size_v size_h]; % dot_center(end+1,1:2)=center_fract; dot_TL_coord(end+1,1:2)=TL_coord./[size_v size_h]; end end end end end function [outputMatrix]=FcnDotResize(Dot_location,OutputSize_h, OutputSize_v, DotSize_h, DotSize_v) %This function outputs matrix based on input matrix size and dots location %and dot size OutputSize_h=round(OutputSize_h); OutputSize_v=round(OutputSize_v); DotSize_v=round(DotSize_v); DotSize_h=round(DotSize_h); Pattern_resized = zeros(OutputSize_v,OutputSize_h); num_dot=size(Dot_location); num_dot=num_dot(1); n=1; while n<=num_dot top=round(OutputSize_v*Dot_location(n,1)); if top < 1 top = 1; end bottom=round(OutputSize_v*Dot_location(n,1)) + (DotSize_v-1); if bottom>OutputSize_v bottom = OutputSize_v; end left=round(OutputSize_h*Dot_location(n,2)); if left<1 left=1; end right=round(OutputSize_h*Dot_location(n,2)) + (DotSize_h-1); if right>OutputSize_h right = OutputSize_h; end Pattern_resized(top:bottom, left:right)=1; n=n+1; end outputMatrix = Pattern_resized; 126 end 127 Particle swarm optimization %particle swarm image to holography 3/24/2018 %clear all; %close all; %global dot_location; %global length_new_v; %global length_new_h; nvar=size(dot_location); %use this when phase within dot are different %nvar=size(dot_TL_coord); %use this when phase within dot are the same nvar=nvar(1); %options=optimoptions('particleswarm','Swarmsize',nvar ,' UseParallel',true); %options=optimoptions('particleswarm','UseParallel',true); options=optimoptions(@particleswarm,'MaxTime',1200,'PlotFcn',' pswplotbestf'); [x,fval,exitflag,output] =particleswarm(@PSCalculateHolograph,nvar ,[],[],options); %optimize for phase within dot are different %[x,fval,exitflag,output] = particleswarm(@ PSCalculateHolograph_SamePhaseWithinDots,nvar,[],[],options); %optimize for phase within dot are the same %reconstruct dot pattern for fcn PSCalculateHolograph %reconstruct dot pattern img=zeros(length_new_v, length_new_h); img(dot_location)=1.*exp(i*x); %reconstruct dot pattern for fcn PSCalculateHolograph_SamePhaseWithinDots %{ N_dot=size(dot_TL_coord); N_dot=N_dot(1); dot_size_h=round(dot_size_new_h); dot_size_v=round(dot_size_new_v); img=zeros(length_new_v,length_new_h); for ii=1:N_dot dot_coord=round([dot_TL_coord(ii,1)*length_new_v, dot_TL_coord(ii ,2)*length_new_h]); if (dot_coord(1)+dot_size_v-1)<=length_new_v | (dot_coord(2)+ dot_size_h-1)<=length_new_h 128 img(dot_coord(1):dot_coord(1)+dot_size_v-1,... dot_coord(2):dot_coord(2)+dot_size_h-1)=1*exp(1i*x(ii)); end % clear dot_coord; end %} % calculated FOM of dot after optimization holo=fft2(img); holo_amp=abs(holo); %FOM = max(holo_amp(:))-min(holo_amp(:)); FOM = std2(holo_amp); holo_normalized=zeros(length_new_v,length_new_h); %holo_normalized is holograph with amplitude normalized to its maximum amplitude holo_normalized=max(holo_amp(:)).*exp(i*angle(holo)); img_normalized=ifft2(holo_normalized); %save('Pattern 3.16 8 patterns\5039_40x60_neg\ ParticleSwarmResult_dot_Resized_to_holo.mat','img','holo',' holo_normalized','img_normalized'); %plot dot pattern figure; imagesc(abs(img)); colorbar; title('dot pattern amplitude'); figure; imagesc(angle(img)); colorbar; title('dot pattern phase'); %plot holograph figure; imagesc(abs(holo)); colorbar; title('holograph amplitude'); figure; imagesc(angle(holo)); colorbar; title('holograph phase'); %plot holograph after nornalization figure; imagesc(abs(holo_normalized)); colorbar; title('adjusted holograph amplitude'); figure; 129 imagesc(angle(holo_normalized)); colorbar; title('adjusted holograph phase'); %plot image after normalization figure; imagesc(abs(img_normalized)); colorbar; title('image if holograph normalized'); %plot image intensity after normalization figure; imagesc(abs(img_normalized).^2); colorbar; title('holography generated dot pattern intensity'); % Save data to file % save('ParticleSwarmResult_dot_Resized_to_holo.mat','img','holo',' holo_normalized','img_normalized'); function FOM = PSCalculateHolograph(dot_phases) global dot_location; global length_new_v; global length_new_h; img=zeros(length_new_v,length_new_h); img(dot_location)=1.*exp(i*dot_phases); holo = fft2(img); holo_amp = abs(holo); %FOM = max(holo_amp(:))-min(holo_amp(:)) FOM = std2(holo_amp) end 130 Phase modulation discretization % Ditigize phase and generate surface profile on the holograph %close all; %clear all; N_level = 7; %N_level= needed level-1, step = 2*pi/N_level ; holo_norm_digi=zeros(length_new_v,length_new_h); %digitize phase for ii=1:length_new_v for jj=1:length_new_h phase = round((angle(holo_normalized(ii,jj)) + pi)/step) * step - pi; amp = abs(holo_normalized(ii,jj)); holo_norm_digi(ii,jj)=amp*exp(1i*phase); end end img_norm_digi = ifft2(holo_norm_digi); %plot dot pattern figure; imagesc(abs(img_norm_digi).^2); colorbar; title('dot pattern intensity'); save('Holo_normalized_digitized.mat','holo_norm_digi'); 131 Calculate DOE surface prole in μm %Calculate surface profile(local thickness) for imprint mold, for real %sample, fft shift is involved %clear all; %close all; wavelength=0.94; %wavelength of light in um rf_index=1.5466; %refractive index of the holography material N_decimal=3; %round thickness to 3 digits right of the decimal point holo_norm_digi_shift=fftshift(holo_norm_digi); %shift quadrants to match real optical situation %calculate thickness on holograph holo_thick = zeros(length_new_v,length_new_h); for m=1:length_new_v for n=1:length_new_h holo_thick(m,n) = (angle(holo_norm_digi_shift(m,n)) + pi) * wavelength/(2*pi*(rf_index-1)); end end %convert holograph thickness to mold thickness mold_thick = -holo_thick + max(max(holo_thick)); mold_thick = round(mold_thick, N_decimal); figure; imagesc(holo_thick); colorbar; title('holograph surface'); figure; imagesc(mold_thick); colorbar; title('mold surface'); save('Surface thickness for 0.94 um wavelength.mat','mold_thick'); 132 DOE design surface prole visualization: surface_profile = mold_thick(1:200, 1:200); width=1; color = [0.3 0.3 0.3]; x_limit = [-inf inf]; y_limit = [-inf inf]; z_limit = [0 100]; b = bar3(surface_profile, width); axis([x_limit y_limit z_limit]); axis off; for k = 1:length(b) zdata = b(k).ZData; b(k).CData = zdata; b(k).FaceColor = 'interp'; end set(gcf,'color','w'); 133

Abstract (if available)

Abstract The main focus of this dissertation is on nanophotonics and its applications in 3D printing, 3D sensing, and nonlinear optics. ❧ The first part covers the multiscale stereolithography. Additive manufacturing has many advantages in creating highly complex customized structures. However, existing additive manufacturing technologies have a trade-off between throughput and resolution. In this work, Multiscale Stereolithography process is invented to addresses this issue, and it is able to print macroscale objects with microscale surface structures with high throughput at low cost. This process is realized by dynamic switching of laser spot size and adaptively sliced layer thickness. Digital models are separated into high resolution part and low resolution part. These two parts are printed using variable voxel size technique in which a small voxel size is used for high resolution and a big voxel size is used for high throughput. Many structures in nature possess superb functions due to the multiscale characteristics in them. For proof-of-concept testing, artificial shark skins with micro riblet features were designed and 3D printed. In pipe flow experiments, the 3D printed shark skin demonstrated almost 10% average fluid drag reduction. Artificial lotus leaf surfaces were also 3D printed to demonstrate superhydrophobic property. In terms of throughput, the multiscale SLA process demonstrated 4.4× better than traditional SLA process in the tests. The advantage became even more significant when bigger size objects were printed. It provides the capability to experimentally study various multiscale structures in future research. Being able to provide high resolution and high throughput at the same time with low cost, the multiscale stereolithography process has the potential to serve as a powerful tool that can bring bio-inspired structures into real-life applications. ❧ The second part covers the inverse design method for diffractive optical elements(DOEs). 3D sensing has been an increasingly popular area due to the development of face recognition on mobile devices as well as autonomous driving cars. DOE is a low cost, compact solution for generating structured light for 3D sensing applications. However, the parameter space of DOEs is if often significantly larger than traditional geometric optical elements such as lenses and periodic diffractive optical elements such as gratings. The reason is that the height of each pixel on a DOE is an independent variable and there is no inherent symmetry to reduce the number of variables. Therefore, the parameter sweeping approach is not practical for designing DOEs. Using iterative numerical optimization is an effective way to reduce the number of iterations required to find the optimal design. In this work, an inverse DOE design method with particle swarm optimization is proposed which takes DOE radiation pattern as input and manufacturability of DOE as the figure of merit. This inverse method has the benefit of reducing the number of variables in optimization and minimizing the loss of performance due in fabrication. As a demonstration, two DOEs that project periodic dot array pattern and encoded binary pattern were fabricated. Optical characterization showed the radiation patterns matched the designs which validates the inverse design method. ❧ The third part summarizes my work in metamaterials with nonlinearity at multiple wavelength ranges. The evolution of optical communication systems has followed the footsteps of the developments of radio communication. The future optical communication systems will be the same as the RF communication systems today: It will be built on a Si photonics chip with integrated electronics. The information will be coded with advanced modulation schemes and the signal will be detected by an optical superheterodyne receiver. To realize optical superheterodyne, the nonlinear mixer is the key challenge. There is no material in the current Si platform with high nonlinearity. I propose to demonstrate metamaterials with high non-linearity at both optical and microwave wavelengths simultaneously for the first time.

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Asset Metadata

Creator Li, Yuanrui (author)

Core Title Metasurfaces in 3D applications: multiscale stereolithography and inverse design of diffractive optical elements for structured light

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 07/15/2019

Defense Date 05/06/2019

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

Tag 3D printing,bioinspired,diffractive optical element,metamaterial,metasurface,nonlinear optics,OAI-PMH Harvest,stereolithography,structured light

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wu, Wei (committee chair), Chen, Yong (committee member), Wang, Han (committee member)

Creator Email liyuanrui09@gmail.com,yuanruil@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-183210

Unique identifier UC11660719

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Legacy Identifier etd-LiYuanrui-7553.pdf

Dmrecord 183210

Document Type Dissertation

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Rights Li, Yuanrui

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA