Application of the homogenization approximation to rough one-dimensional photonic crystals

As previously reported [Opt. Lett. 29, 2791 (2004)], one-dimensional photonic crystals exhibit a decrease in their normal reflectivity if their interfaces are not flat. We show that the homogenization approximation accurately predicts this diminished optical response by comparing results with finite-difference time-domain (FDTD) simulations applied to the same roughened structures. Within the parameter range tested (rms roughness <20% and rms wavelengths <100% of the photonic crystal periodicity), the homogenization approximation accurately reproduces the reflectivities obtained by the FDTD simulations, which are much more computationally expensive. (c) 2005 Optical Society of America.