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An artificial opal is a compact arrangement of transparent spheres, and is anarchetype of a three-dimensional photonic crystal. Here, we describe the opticsof an opal using a flexible model based upon a stratified medium whose(effective) index is governed by the opal density in a small planar slice ofthe opal. We take into account the effect of the substrate and assume a well-controlled number of layers, as it occurs for an opal fabricated byLangmuir-Blodgett deposition. The calculations are performed with transfermatrices, and an absorptive component in the effective index is introduced toaccount for the light scattering. This one-dimensional formalism allowsquantitative predictions for reflection and transmission, notably as a functionof the ratio between the irradiation wavelength and the sphere diameter, or asa function of the incidence angle or of the polarization. It can be used for anirradiation from the substrate side or from the vacuum side and can account fordefect layers. The interface region between the opal and the substrate (orvacuum) is shown to have a strong influence, regardless of the exact opalstructure. This break in the periodicity at the interface is a general, butoften ignored feature, of any external coupling to a photonic crystal. Ourcalculations provide also the main features of the Bragg peak for reflection,including its width and strength. Comparisons of this versatile model withexperiments show that despite its simplicity, it is powerful enough to explainnumerous observations.

The optical interface of a photonic crystal: Modeling an opal with a stratified effective index