Theory of photonic crystal heterostructures

We develop an envelope function formalism to describe the behavior of light inside a structure assembled out of dissimilar photonic band-gap materials. These photonic heterostructures are the optical analogs of quantum electronic heterostructures that make up resonant tunneling diodes and superlattices. We show that the behavior of these media is readily quantified and explained by reducing each constituent photonic band-gap material to a set of parameters related to the photonic crystals' dispersion relation, which are then used as inputs to an envelope equation. We also prove the validity of the approximation by comparison to full numerical simulations.