White-light interferometry measurements over a wide spectral range in the optical region have been performed on three-dimensional ͑3D͒ 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 ͑negative͒ 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.

Phase measurements on self-assembled three-dimensional photonic crystals show that the group velocity of light can flip from small positive (slow) to negative (superluminal) values in samples of a few mum size. This phenomenon takes place in a narrow spectral range around the second-order stop band and follows from coupling to weakly dispersive photonic bands associated with multiple Bragg diffraction. The observations are well accounted for by theoretical calculations of the phase delay and of photonic states in the finite-sized systems.

Optical properties of fcc opals oriented along the [111] direction are calculated by means of a scattering-matrix approach based on approximating each sphere with cylindrical slices. The use of a plane-wave basis in each layer allows distinguishing zero-order reflection and transmission from higher-order (diffraction) spectra. Optical spectra at large values of the angle of incidence indicate the presence of diffraction effects and of polarization mixing along the LW orientation. Reflectance and transmittance in the high-energy region show a rich spectral dependence and compare reasonably well with recent experimental observations on polystyrene opals. Diffraction spectra as a function of the number of layers display an oscillatory behavior, pointing to the existence of a Pendellösung phenomenon, related to the exchange of energy between two propagating modes in the investigated three-dimensional photonic crystal. This phenomenon could be observed in transmittance experiments on high-quality opals with controlled thickness.

Opal photonic crystals viewed along the ͓111͔ direction of the fcc structure have a threefold symmetry axis; however this microscopic symmetry is difficult to observe in optical measurements performed on macroscopic areas containing microdomains with different orientations. In this work polarized transmittance measurements on ͓111͔-stacked silica opals with single oriented microdomains, identified by field-emission scanning electron microscopy and laser-scanning confocal microscopy, demonstrate different optical response of twin structures with the two possible vertical stacking sequences. A detailed comparison with theory shows that microtransmittance experiments probe the photonic band structure along the ⌫-L-K and ⌫-L-U orientations of the Brillouin zone, respectively, thus giving conclusive evidence for macroscopic optical response related to the presence of a threefold ͑instead of a sixfold͒ symmetry axis in the photonic microstructure.