Anomalous reflections at photonic crystal surfaces

Abstract

We explore the reflection phenomena when a light beam propagating in a photonic crystal is incident upon the interfaces between the crystal and a uniform dielectric. We prove that a generalized wave-vector conservation relation still applies even when the interface is not aligned with special crystal directions. Using this conservation relation, we show that neither the phase velocity nor the group velocity directions of the reflected beam satisfies Snell's law. Rather, the system exhibits remarkable and unusual reflection effects. In particular, total internal reflection is absent except at discrete angular values. The direction of the reflected beam can also be pinned along special crystal directions, independent of the orientation of the interface. And finally, at glancing incidences, strong backward reflections may occur. These effects may be important for creating integrated photonic circuits, and for on-chip image transfer.