Preserving omnidirectionality in optimized asymmetric transformation optics designs

Optimization techniques are efficient methods to simplify the design of transformation optics devices. Asymmetric devices obtained through these methods typically lose omnidirectionality and perform well only when illuminated from a finite set of directions. We present here an optimization approach that results in simplified, omnidirectional designs of fairly large bandwidths. The method leverages a class of coordinate transformations that result in transformation media whose material parameters follow identical isocontours. We show that discretizing these media in a finite number of layers that follow the common isocontours and optimizing the material parameters inside each layer is an effective way to significantly simplify the design complexity while preserving most of the original performance including omnidirectionality.