Affine nonmagnetic transformation optics and its application to a practical bending adapter design

One of the bottlenecks that limit the transition of transformation-optics devices from concepts to practical use is the non-unit magnetic permeability generally required from a mathematical transformation. Simple renormalization of permeability, as used in many previous designs and experiments, introduces impedance mismatch and thus degrades the functional photonic performance. Here we propose an area-preserving affine coordinate transformation as a general method to solve this problem. Ideal transformation-optics functions can be preserved while nonmagnetism is achieved. As a specific example, we illustrate how to apply this affine method into the design of a two-dimensional electromagnetic beam bending adapter. Concerns related to fabrication, such as anisotropy degree and bending angles, are fully discussed. Our study is a significant step toward practical use of ideal transformation optics devices that can be implemented directly with existing dielectric materials.