Comparison of Anisotropy Reduction Strategies for Transformation Optics Designs

In this paper, we present new strategies to reduce anisotropy in transformation optics designs and compare them to other techniques. Perturbation functions are used to modify the original transformation to achieve a quasi-conformal map, resulting in a medium with isotropic properties. All strategies investigated have no effect on the original boundary conditions of the transformation, such that neither the initial design is affected nor are reflections at the boundaries introduced. The results show that there exists a clear compromise between the residual anisotropy and the required refractive index contrast in the optimized transformation, but the former can be made as small as desired when the degree of freedom provided by perturbation functions is increased, although it is never exactly zero.