Interband transitions in photonic crystals

We present a formalism to describe transitions between photon modes in a ph otonic crystal with a temporally and spatially varying dielectric constant, in analogy to optical transitions between electronic states in metals and semiconductors. Resonant transitions between different photonic bands are d iscussed, and predictions of the theory are compared to electromagnetic sim ulations. We contrast the cases of electronic and photonic transitions, and explore how the photonic band structure allows opportunities for phase mat ching and stationary-wave generation in nonlinear optical frequency-convers ion processes. [S0163-1829(99)11503-0].