Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals

Abstract

An analysis of the diffracted beams emerging from three-dimensional photonic crystals is herein presented. The wave vectors of nonspecular beams are calculated for a triangular two-dimensional lattice and the change in their directions as a function of the wavelength is confirmed experimentally for the case of face-centered-cubic colloidal crystals illuminated under normal incidence. A fluctuating behavior of beam intensity as a function of the wavelength of the incident light is predicted for perfectly ordered lattices. As it is the case for specularly reflected and ballistically transmitted beams, this modulation arises from multipole resonances of the sphere ensemble that are smoothed out via the diffuse light scattering produced by imperfections in the crystalline structure. When optical extinction is introduced in order to model the effect of imperfections, it is possible to accurately reproduce experimental observations.