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E-grāmata: Numerical Methods for Metamaterial Design

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  • Formāts: PDF+DRM
  • Sērija : Topics in Applied Physics 127
  • Izdošanas datums: 13-Aug-2013
  • Izdevniecība: Springer
  • Valoda: eng
  • ISBN-13: 9789400766648
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Numerical Methods for Metamaterial DesignPalielināt
  • Formāts: PDF+DRM
  • Sērija : Topics in Applied Physics 127
  • Izdošanas datums: 13-Aug-2013
  • Izdevniecība: Springer
  • Valoda: eng
  • ISBN-13: 9789400766648
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This book describes a relatively new approach for the design of electromagnetic metamaterials. Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths.

After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered. Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies. Additionally, new techniques for representing dielectric distributions in two dimensions, including level sets, are demonstrated as effective methods for gradient-based optimization.

Each chapter begins with a rigorous review of the optimization strategy used, and is followed by numerous examples that combine the strategy with either electromagnetic simulations or analytical solutions of the scattering problem. Throughout the text, we address the strengths and limitations of each method, as well as which numerical methods are best suited for different types of metamaterial designs. This book is intended to provide a detailed enough treatment of the mathematical methods used, along with sufficient examples and additional references, that senior level undergraduates or graduate students who are new to the fields of plasmonics, metamaterials, or optimization methods; have an understanding of which approaches are best-suited for their work and how to implement the methods themselves.



This book describes a new approach for the design of electromagnetic metamaterials which combines numerical optimization routines with electromagnetic simulations. It features examples that describe how each method is used to optimize specific design problems.
1 Introduction 1(30)
Kenneth Diest
1.1 Introduction
1(1)
1.2 Ancient Metamaterials
2(1)
1.3 Modern Metamaterials
3(13)
1.3.1 Publications
4(2)
1.3.2 Fabrication
6(2)
1.3.3 Modeling
8(6)
1.3.4 The Union of Fields
14(2)
1.4 Design
16(9)
1.4.1 Optical Properties of Metals
16(6)
1.4.2 Current Designs
22(2)
1.4.3 Future Designs
24(1)
References
25(6)
2 An Overview of Mathematical Methods for Numerical Optimization 31(24)
Daniel E. Marthaler
2.1 Introduction
31(1)
2.2 Mathematical Optimization
32(2)
2.3 Finding Solutions
34(2)
2.4 Algorithms Utilizing Gradient Information
36(7)
2.4.1 Unconstrained Nonlinear Optimization
36(3)
2.4.2 Constrained Nonlinear Optimization
39(4)
2.5 Gradient-Free Algorithms
43(7)
2.5.1 Direct Methods
43(3)
2.5.2 Surrogate Methods
46(2)
2.5.3 Stochastic Search Algorithms
48(2)
2.6 Summary
50(1)
References
51(4)
3 Optimization with Surrogate Models 55(16)
Tom Schaul
3.1 Introduction
55(2)
3.2 Background
57(1)
3.3 Artificial Curiosity
57(3)
3.3.1 Artificial Curiosity as a Guide for Optimization
58(1)
3.3.2 Formal Framework
59(1)
3.4 Exploration-Exploitation Trade-Off
60(2)
3.4.1 Exploration Objective: Information Gain
60(1)
3.4.2 Exploitation Objective: Expected Cost Improvement
60(1)
3.4.3 Combining the Objectives
60(2)
3.5 Curiosity-driven Optimization
62(3)
3.5.1 Models of Expected Cost and Information Gain
62(1)
3.5.2 A Good Model Choice: Gaussian Processes
62(1)
3.5.3 Derivation of Gaussian Process Information Gain
63(1)
3.5.4 Curiosity-Driven Optimization with Gaussian Processes
64(1)
3.6 Minimal Asymptotic Requirements
65(2)
3.6.1 Reaching Optima at Arbitrary Distance
65(1)
3.6.2 Locating Optima with Arbitrary Precision
66(1)
3.6.3 Guaranteed to Find Global Optimum
66(1)
3.6.4 Proof-of-Concept
67(1)
3.7 Discussion
67(2)
References
69(2)
4 Metamaterial Design by Mesh Adaptive Direct Search 71(26)
Charles Audet
Kenneth Diest
Sebastien Le Digabel
Luke A. Sweatlock
Daniel E. Marthaler
4.1 Introduction
71(2)
4.1.1 Structuring the Optimization Problem
72(1)
4.2 The Mesh Adaptive Direct Search Class of Algorithms
73(9)
4.2.1 General Organization of the MADS Algorithm
73(3)
4.2.2 Handling of Constraints
76(2)
4.2.3 Surrogates and Models
78(3)
4.2.4 Convergence Analysis
81(1)
4.3 NOMAD: A C++ Implementation of the MADS Algorithm
82(4)
4.3.1 Batch and Library Modes
83(1)
4.3.2 Important Algorithmic Parameters
84(1)
4.3.3 Extensions of MADS
85(1)
4.4 Metamaterial Design Using NOMAD
86(8)
4.4.1 Split Ring Resonator Optimization
86(3)
4.4.2 Split Ring Resonator Filters
89(1)
4.4.3 Coupling Quantum Dots to Split-Ring Resonators
90(4)
References
94(3)
5 Nature Inspired Optimization Techniques for Metamaterial Design 97(50)
Douglas H. Werner
Jeremy A. Bossard
Zikri Bayraktar
Zhi Hao Jiang
Micah D. Gregory
Pingjuan L. Werner
5.1 Introduction
97(2)
5.2 Nature Inspired Optimization Methods
99(12)
5.2.1 Genetic Algorithms
100(3)
5.2.2 Particle Swarm Optimization
103(2)
5.2.3 Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) Optimization
105(6)
5.3 Metamaterial Surface Optimization Examples
111(11)
5.3.1 Metallo-Dielectric Metamaterial Absorbers for the Infrared
112(2)
5.3.2 Double-Sided AMC Ground Planes for RF
114(4)
5.3.3 Matched Magneto-Dielectric RF Absorbers
118(4)
5.4 Homogenized Metamaterial Optimization Examples
122(20)
5.4.1 Homogenization Technique for an Isotropic Planar Slab
123(1)
5.4.2 Anisotrdpic Inversion Technique
124(4)
5.4.3 Low-Loss, Multilayer Negative Index Metamaterials for the Infrared and RF
128(6)
5.4.4 Wide-Angle Zero Index Metamaterials for the IR
134(3)
5.4.5 Dispersion Engineering Broadband Negative-Zero-Positive Index Metamaterials
137(5)
References
142(5)
6 Objective-First Nanophotonic Design 147(28)
Jesse Lu
Jelena Vuckovic
6.1 Introduction
147(1)
6.2 The Electromagnetic Wave Equation
148(3)
6.2.1 Physics Formulation
148(1)
6.2.2 Numerical Formulation
149(1)
6.2.3 Solving for H
149(1)
6.2.4 Solving for E-1
150(1)
6.2.5 Bi-linearity of the Wave Equation
150(1)
6.3 The Objective-First Design Problem
151(4)
6.3.1 Design Objectives
151(1)
6.3.2 Convexity
151(1)
6.3.3 Typical Design Formulation
152(1)
6.3.4 Objective-First Design Formulation
152(2)
6.3.5 Field Sub-problem
154(1)
6.3.6 Structure Sub-problem
154(1)
6.3.7 Alternating Directions
154(1)
6.4 Waveguide Coupler Design
155(6)
6.4.1 Choice of Design Objective
156(1)
6.4.2 Application of the Objective-First Strategy
157(1)
6.4.3 Coupling to a Wide, Low-Index Waveguide
157(1)
6.4.4 Mode Converter
158(1)
6.4.5 Coupling to an Air-Core Waveguide Mode
159(1)
6.4.6 Coupling to a Metal-Insulator-Metal and Metal Wire Plasmonic Waveguides
159(2)
6.5 Optical Cloak Design
161(3)
6.5.1 Application of the Objective-First Strategy
161(1)
6.5.2 Anti-reflection Coating
161(1)
6.5.3 Wrap-Around Cloak
162(1)
6.5.4 Open-Channel Cloak
162(2)
6.5.5 Channeling Cloak
164(1)
6.6 Optical Mimic Design
164(6)
6.6.1 Application of the Objective-First Strategy
166(1)
6.6.2 Plasmonic Cylinder Mimic
166(1)
6.6.3 Diffraction-Limited Lens Mimic
167(2)
6.6.4 Sub-diffraction Lens Mimic
169(1)
6.6.5 Sub-diffraction Optical Mask
170(1)
6.7 Extending the Method
170(2)
6.7.1 Three-Dimensional Design
171(1)
6.7.2 Multi-mode
171(1)
6.7.3 Binary Structure
171(1)
6.7.4 Robustness
172(1)
6.8 Conclusions
172(1)
References
172(3)
7 Gradient Based Optimization Methods for Metamaterial Design 175(30)
Weitao Chen
Kenneth Diest
Chiu-Yen Kao
Daniel E. Marthaler
Luke A. Sweatlock
Stanley Osher
7.1 Introduction
175(2)
7.2 Level Sets and Dynamic Implicit Surfaces
177(8)
7.2.1 Finding the Maximal Bandgap in Photonic Crystals
177(2)
7.2.2 Definition of the Level Set Function
179(1)
7.2.3 Shape Derivatives
179(2)
7.2.4 Normal Velocity Formulas in Photonic Crystals
181(1)
7.2.5 The Level Set Optimization Algorithm
181(4)
7.3 Eigenfunction Optimization
185(18)
7.3.1 Finding the Optimal Localization of Eigenfunctions
185(2)
7.3.2 Localization of Single Eigenmodes with Eigenvalue Constraints
187(1)
7.3.3 Localization of Multiple Eigenmodes
188(1)
7.3.4 Weight Functions
188(1)
7.3.5 Numerical Tests
189(1)
7.3.6 One-Dimensional Problems Without Eigenvalue Constraints
190(4)
7.3.7 Two-Dimensional Laplacian Problems Without Eigenvalue Constraints
194(3)
7.3.8 Two-Dimensional Laplacian Problems with Eigenvalue Constraints
197(2)
7.3.9 Two-Dimensional Bi-Laplacian Problems Without Eigenvalue constraints
199(4)
References
203(2)
Appendix The Interface Between Optimization and Simulation 205
Kenneth Diest is currently a Member of Technical Staff at the Massachusetts Institute of Technology Lincoln Laboratory, where he works on the simulation, design, and fabrication of passive and active nanophotonic devices.  Prior to this, he was a research scientist with the Aerospace Research Laboratories at Northrop Grumman and a visiting scientist at the California Institute of Technology.  He holds both a M.S. and Ph.D. in Materials Science from the California Institute of Technology, and received a B.S. in Materials Engineering from Cornell University in 2002.
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