Superstructure and finite-size effects in a Si photonic woodpile crystal

The reflectivity of finite-thickness silicon photonic woodpile structures was measured in the wavelength range from 0.9 to $1.7\mu \mathrm{m}.$ Polarization and surface orientation dependent measurements were performed as function of angle of incidence and the data were compared with rigorous calculations for the finite structure. Due to the finite size, the reflectivity near the stop gap edge is strongly orientation and polarization dependent. Clear stop gaps can be identified and good agreement with calculations is found. Outside the stop gap region, Fabry-Perot type resonances are observed that are related to the finite thickness of the photonic crystal. In the stop gap region clear dips are found that are not reproduced in the calculation for perfect, finite-size crystals. These are due an irregularity in the pitch of the woodpile structure as observed in electron microscopy images. This irregularity can be described in terms of a superstructure that introduces additional bands due to zone folding of the bandstructure. Calculations based on the superstructure successfully reproduce the major features in the experimental data.