Effective properties and band structures of lamellar subwavelength crystals: Plane-wave method revisited

The plane-wave method used to compute the band structure of photonic crystals is revisited in light of recent mathematical results about the Fourier factorization of products of discontinuous functions. Highly accurate numerical predictions for the effective index and for the band structure are obtained for two- and three-dimensional dielectric lamellar crystals with high dielectric contrasts. At the same time, we clarify some aspects related to the effective properties of multidimensional crystals by establishing clear Links between their band structures and their effective indices. [S0163-1829(98)07239-7].