Numerical and experimental investigations of surface roughness in 1D photonic crystals

We present numerical simulations as well as experimental investigations of 1D photonic crystals (PhC) with intentionally introduced surface roughness. An 'experimental simulation' of the roughness was created by gluing alumina powder to both sides of each alumina plate in an alumina-air structure. Transmission experiments were performed on this 1D PhC at microwave frequencies. A 'red-shift' of the band edges observed in experiment and simulation is explained by an increase of the effective thickness of the alumina layers as the surface roughness becomes stronger. The influence of the features of the roughness becomes visible in the simulations only at wavelengths short enough to be of the order of the dimensions of these features. Then, the band edges are smeared and the residual transmission in the band gaps is increased. We show that the main effect responsible for the smearing of the band edges is the scattering of the wave on roughness features. Even for very strong roughness (40% of the plate thickness) the band gaps are not destroyed completely.