Optical design of reflectionless complex media by finite embedded coordinate transformations

Transformation optics offers an unconventional approach to the control of electromagnetic fields. The transformation optical structures proposed to date, such as electromagnetic invisibility cloaks and concentrators, are inherently reflectionless and leave the transmitted wave undisturbed. Here, we expand the class of transformation optical structures by introducing finite, embedded coordinate transformations, which allow the electromagnetic waves to be steered or focused. We apply the method to the design of several devices, including a parallel beam shifter and a beam splitter, both of which are reflectionless and exhibit unusual electromagnetic behavior as confirmed by 2D full-wave simulations.