Gersborg Allan R, Sigmund Ole
Technical University of Denmark, Department of Mechanical Engineering, Solid Mechanics, Nils Koppels Allé, Bld. 404, DK-2800 Kgs. Lyngby, Denmark.
Opt Express. 2010 Aug 30;18(18):19020-31. doi: 10.1364/OE.18.019020.
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 (Ez) 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.
变换光学是设计新型光学元件（如高透射率波导和隐身装置）的有力概念。特定变换的选择是一个不唯一的问题。在此我们揭示，对于机械泊松比ν的极值，允许所有介电和宽带光学实现的变换对应于弹性能量势的极小值。对于TE（Hz）偏振光，不可压缩变换ν = 1/2是理想的，而对于TM（Ez）偏振光，应使用具有负泊松比ν = -1的可压缩变换。对于TM偏振，力学类比对应于变换光学文献中已知的修正廖泛函。最后，理想变换与固体力学材料模型之间的类比使变换光学的概念自动化并得到拓展。
