Scaling two-dimensional photonic crystals for transformation optics

We propose a method to manipulate Bloch waves in curved photonic crystals for achieving transformation optical devices in two dimensions. Instead of starting from an effectively homogeneous medium, we transform a regular photonic crystal into a curved one in the physical space. A scaling law is established to construct the curved photonic crystal with similar unit cells and different scales, which is made of dielectrics only. A wave compressor and a bending waveguide are designed using dielectrics with indices only from 1 to 4. The approach will be useful in constructing low-loss transformation media requiring small indices, or large anisotropy which is particularly difficult for E-polarization using the conventional effective medium approach.