Numerical study of anomalous refraction in photonic crystals

We present a theoretical study of light propagation through photonic crystal PhC structures using an effective medium approximation based on equifrequency surface calculations. The procedure is illustrated by calculating bending, splitting and focusing phenomena in a slab of two-dimensional PhC using a Fourier imaging technique. In the passband above the first stop band, wave propagation was found to depend dramatically on both light frequency and incident direction. This propagation anisotropy leads to very large negative refraction along the 11 crystal direction. Light emitted from a line source outside the PhC slab can be focused, divided into subbeams inside the PhC, bent negatively, and refocused again on the other side the slab. The results agree well with the field calculated using a finite-difference time-domain method and can be straightforwardly applied to more complicated PhC structures, such as three-dimensional PhC structures. The imaging properties of a PhC slab are also discussed.