Numerical Methods for Metamaterial Design

ISBN-13: 9789400766631 / Angielski / Twarda / 2013 / 213 str.

Kenneth Diest

Opis

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.

Spis treści

1 Introduction; Kenneth Diest. 1.1 Introduction. 1.2 Ancient Metamaterials. 1.3 Modern Metamaterials. 1.4 Design. References.

2 An Overview of Mathematical Methods for Numerical Optimization; Daniel E. Marthaler. 2.1 Introduction. 2.2 Mathematical Optimization.  2.3 Finding Solutions. 2.4 Algorithms Utilizing Gradient Information. 2.5 Gradient Free Algorithms. 2.6 Summary. References.

3 Optimization with Surrogate Models; Tom Schaul. 3.1 Introduction. 3.2 Background. 3.3 Artificial Curiosity. 3.4 Exploration/Exploitation Trade-off. 3.5 Curiosity-driven Optimization. 3.6 Minimal Asymptotic Requirements. 3.7 Discussion. References.

4 Metamaterial Design by Mesh Adaptive Direct Search; Charles Audet, Kenneth Diest, Sébastien Le Digabel, Luke A. Sweatlock, and Daniel E. Marthaler. 4.1 Introduction. 4.2 The mesh adaptive direct search class of algorithms. 4.3 NOMAD: A C++ implementation of the MADS algorithm. 4.4 Metamaterial Design Using NOMAD. References.

5 Nature Inspired Optimization Techniques for Metamaterial Design; Douglas H. Werner, Jeremy A. Bossard, Zikri Bayraktar, Zhi Hao Jiang, Micah D. Gregory, and Pingjuan L. Werner. 5.1 Introduction. 5.2 Nature Inspired Optimization Methods. 5.3 Metamaterial Surface Optimization Examples. 5.4 Homogenized Metamaterial Optimization Examples. References.

6 Objective-First Nanophotonic Design; Jesse Lu and Jelena Vuckovic. 6.1 Introduction. 6.2 The Electromagnetic Wave Equation. 6.3 The Objective-first Design Problem. 6.4 Waveguide Coupler Design. 6.5 Optical Cloak Design. 6.6 Optical Mimic Design. 6.7 Extending the Method. 6.8 Conclusions. References.

7 Gradient Based Optimization Methods for Metamaterial Design; Weitao Chen, Kenneth Diest, Chiu-Yen Kao, Daniel E. Marthaler, Luke A. Sweatlock, and Stanley Osher. 7.1 Introduction. 7.2 Level Sets and Dynamic Implicit Surfaces. 7.3 Eigenfunction Optimization. References.

Appendix: The Interface Between Optimization and Simulation.

O autorze

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.

Blurb

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.