Extreme non-linear elasticity and transformation optics

Allan Roulund Gersborg, Ole Sigmund

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Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics. © 2010 Optical Society of America.
Original languageEnglish
JournalOptics Express
Issue number18
Pages (from-to)19020-19031
Publication statusPublished - 2010

Bibliographical note

This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-18-19020. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.


  • Optical design of instruments
  • Waveguides
  • Physical optics
  • Optical properties
  • Optical devices
  • Integrated optics
  • Waves
  • Metamaterials


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