Interband transitions in photonic crystals

We present a formalism to describe transitions between photon modes in a photonic 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 discussed, and predictions of the theory are compared to electromagnetic simulations. We contrast the cases of electronic and photonic transitions, and explore how the photonic band structure allows opportunities for phase matching and stationary-wave generation in nonlinear optical frequency-conversion processes.