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Quasi-Conformal Approaches for Two and Three-Dimensional Transformation Optical Media

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Abstract

Transformation optical design is generally complicated by the requirement for highly anisotropic and inhomogeneous constituent materials. Quasi-conformal mappings have appeared as an attractive subset of the general transformation optics method because they only require isotropic, dielectric-only materials. In this chapter, we examine the quasi-conformal method as it applies to transformation optics and show that while it does significantly ease the burden of material design and fabrication, it may also create severely aberrant behavior unless caution is taken. We also show how to extend the method to three dimensions, and examine the performance of an optic designed with the quasi-conformal method.

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Notes

  1. 1.

    COMSOL is a multi physics simulation suite based on the finite element method (FEM). In addition to multiple physics models (e.g., electromagnetics), COMSOL allows the user to choose from a number of classical PDE models—including Laplace’s equation. COMSOL also allows the user to generate new physics models or modify existing templates; a feature we exploit in Sect. 1.8.

  2. 2.

    Rigorously, the slipping boundary condition should be applied to all boundaries as specified in the last section. However, there is little practical difference between this and Dirichlet boundary conditions on the boundaries that are removed from the perturbation.

  3. 3.

    We will explore the impact these methods have on lens performance in Sect. 1.7.

  4. 4.

    Unlike in ray-tracing, we found no significant difference between the strictly conformal—and the quasi-conformal mapped—lenses since the RMS spot size of both lenses lies below the diffraction limit in the simulated range of aperture sizes.

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Authors and Affiliations

  1. Center for Metamaterials and Enhanced Plasmonics, Duke University, Durham, NC, 27708, USA

    Nathan Landy, Yaroslav Urzhumov & David R. Smith

Authors
  1. Nathan Landy
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  2. Yaroslav Urzhumov
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  3. David R. Smith
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Corresponding authors

Correspondence to Nathan Landy or David R. Smith .

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Editors and Affiliations

  1. The Pennsylvania State University, Electrical Engineering East 211A, University Park, 16802, USA

    Douglas H. Werner

  2. University of Massachusetts Amherst, Natural Resources Road Marcus 201 100, Amherst, 01003, USA

    Do-Hoon Kwon

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Landy, N., Urzhumov, Y., Smith, D.R. (2014). Quasi-Conformal Approaches for Two and Three-Dimensional Transformation Optical Media. In: Werner, D., Kwon, DH. (eds) Transformation Electromagnetics and Metamaterials. Springer, London. https://doi.org/10.1007/978-1-4471-4996-5_1

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  • DOI: https://doi.org/10.1007/978-1-4471-4996-5_1

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