Photonic crystal heterostructures and the envelope approximation

An envelope approximation method to explain and compute the frequency-dependent behavior of photonic crystal heterostructures was developed. The method begins by distilling each photonic crystal region to its dispersion relation and electric field Bloch mode shapes, for which purpose efficient bulk photonic crystal mode solvers were widely available. Thus, it was shown that photonic crystal heterostructures form devices with useful transmittance characteristics and that the envelope approximation described above provides an efficient and direct route towards the computation of the response of such structures.