Rough 1D photonic crystals: A transfer matrix approach

Interfacial roughness is prevalent in 1D photonic crystals and other layered structures, but is not generally accounted for in their design nor the analysis of their optical properties due to a lack of simple theoretical approaches. We present a transfer matrix formalism to incorporate the effects of interfacial roughness in the optical properties of stratified systems such as 1D photonic crystals and apply it to calculate the optical response of some nanoporous anodic alumina and porous silicon structures. We have validated our formalism by comparing our results to some experiments.