Effective impedance model for analysis of reflection at the interfaces of photonic crystals.

We present an alternative definition of impedance to describe the reflection at the interfaces of photonic crystals. We show that this effective impedance can be defined only by the properties of the photonic crystal modes and is independent of the properties of the incident region. This approximate model successfully explains the main features in the reflection spectrum and of various interface terminations of photonic crystals. In particular, we show an impedance matching condition at which reflectionless transmission of power to a low-group-velocity photonic crystal mode is possible, a property that is attractive for various dispersion-based applications of photonic crystals.