Local photonic modes in periodic or random, dielectric, and lasing media

Numerous nanophotonics applications involve the spatial confinement of the electromagnetic field to a length scale comparable to the optical wavelength, such as in photonic crystal (PhC) cavities or defects or in microlasers. First, we review a recently proposed, novel optimization scheme for the efficient construction of maximally localized photonic Wannier functions to be used as a set of basis functions for the description of localized modes in PhCs. We then analyze bistable lasing and the mode switching dynamics in multimode PhC microlasers and describe a recently developed theory for the confined, spatial intensity correlations (second-order coherence) in homogeneously disordered random lasers. Finally, a systematic diagrammatic expansion for the eigenmode renormalization of microlaser cavities due to the laser nonlinearity is described.