Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals

Photons propagate in photonic crystals in the same way as electrons propagate in solids. The periodical refractive index induces forbidden frequency bands, which nurture a variety of novel integrated devices and several fundamental studies ranging from threshold-less lasers to quantum computing. However, these investigations have to face the unavoidable disorder of real-world structures: if on one hand it largely hampers experiments, on the other hand it opens the possibility to study three-dimensional (3D) photon strong localization. We report on 3D+1 Maxwell-Bloch simulations of light dynamics in inverted opals exhibiting a complete photonic bandgap. We show that the disorder-induced localized states strongly alter the photonic crystals response to femtosecond optical pulses, drastically reducing the diffusion constant and trapping light. We find that an optimal amount of randomness favours the strongest localization; correspondingly, self-starting laser processes are mediated by Anderson states that prevail over spatially extended Bloch modes.