Theory of photonic band structures: a vector-wave k·p approach

Abstract

The k· p band-structure formalism, originally developed for electrons in semiconductors is shown to be a powerful method for describing photonic dispersion relations in periodic dielectric structures. An expression analogous to the f-sum rule in electronic problems is derived for the effective refractive index of the composite. Band structures obtained analytically using the method are in excellent agreement with the results of computationally intensive plane-wave calculations.