Effective refractive index and group velocity determination of three-dimensional photonic crystals by means of white light interferometry

Abstract

White-light interferometry measurements over a wide spectral range in the optical region have been performed on three-dimensional 3D opal-based photonic crystals that have permitted extracting the optical phase delay introduced by samples with an increasing number of layers. The absolute phase that corresponds to the wave vector inside the samples has been obtained by a proper normalization procedure. From the absolute phase and the transmittance, we have determined the complex effective refractive index of the 3D photonic crystals, whose real part shows normal dispersion outside the pseudogap and anomalous negative dispersion across the pseudogap. By a numerical derivative of the measured phase, the group velocity is directly obtained, which displays slowing down at the band edge and superluminal behavior inside the photonic gap. The evolution of the measured quantities with sample thickness and their convergence toward the infinite crystal behavior are successfully compared to theoretical calculations of the optical properties for the finite system as well as of the energy bands. The role of structural disorder on the measured quantities is also discussed.