Photonic crystal heterostructures and the envelope approximation

Summary form only given. Photonic crystal heterostructures are concatenations of photonic crystals having different bandstructures. Examples include controlled defects, type-I and type-II heterostructures, and superlattices. These novel and prospectively powerful functional devices rely on computationally intensive analysis in a conventional fully numerical treatment. We have developed an envelope approximation method to explain and compute the frequency-dependent behaviour of photonic crystal heterostructures. The method begins by distilling each photonic crystal region to its dispersion relation and electric field Bloch mode shapes. We then combine the effects of adjacent dispersion relations to compute the effect of the entire heterostructure on the propagation of light.