© 2013

Numerical Methods for Metamaterial Design

  • Kenneth Diest
  • A thorough treatment of the underlying mathematics of each optimization method, as well as detailed references that further expand on each method

  • Numerous examples that describe how each method is implemented and used to optimize specific design problems

  • Links to implementations of the optimization routines discussed throughout the book that are available online

  • An appendix that lists step-by-step instructions on how to integrate optimization routines with current electromagnetic simulation software


Part of the Topics in Applied Physics book series (TAP, volume 127)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Kenneth Diest
    Pages 1-29
  3. Tom Schaul
    Pages 55-70
  4. Charles Audet, Kenneth Diest, Sébastien Le Digabel, Luke A. Sweatlock, Daniel E. Marthaler
    Pages 71-96
  5. Douglas H. Werner, Jeremy A. Bossard, Zikri Bayraktar, Zhi Hao Jiang, Micah D. Gregory, Pingjuan L. Werner
    Pages 97-146
  6. Jesse Lu, Jelena Vuckovic
    Pages 147-173
  7. Weitao Chen, Kenneth Diest, Chiu-Yen Kao, Daniel E. Marthaler, Luke A. Sweatlock, Stanley Osher
    Pages 175-204
  8. Back Matter
    Pages 205-213

About this book


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.


Genetic algorithms Gradient descent Hybrid design techniques Inverse Metamaterial Design Metamaterial design book Metamaterial design overview Nanophotonic Design Numerical optimization methods design of metamaterials

Editors and affiliations

  • Kenneth Diest
    • 1
  1. 1.MIT Lincoln Labs in LexingtonLexingtonUSA

About the editors

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.

Bibliographic information

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