Reflectivity of 1D photonic crystals : a comparison of computational schemes with experimental results

Abstract

We report the reflectivity of one-dimensional finite and semi-infinite photonic crystals, computed through the coupling to Bloch modes (BM) and through a transfer matrix method (TMM), and their comparison to the experimental spectral line shapes of porous silicon (PS) multilayer structures. Both methods reproduce a forbidden photonic bandgap (PBG), but slowly-converging oscillations are observed in the TMM as the number of layers increases to infinity, while a smooth converged behavior is presented with BM. The experimental reflectivity spectra is in good agreement with the TMM results for multilayer structures with a small number of periods. However, for structures with large amount of periods, the measured spectral line shapes exhibit better agreement with the smooth behavior predicted by BM.