Effective response functions for photonic bandgap materials

An effective description is developed for a metalodielectric photonic bandg ap (PBG) material far beyond the quasi-static limit of traditional effectiv e-medium theories. An analytic approach, recently presented by the authors, is further advanced to provide the complete effective permittivity and per meability functions. Reflection and transmission coefficients are presented for both TM and TE oblique plane-wave incidence, based on the determinatio n of the equivalent impedance for each lattice plane in the crystal and the transfer-matrix method for reconstructing the effect of successive lattice planes. An analysis of the semi-infinite and slab observables yields the a nisotropic effective refractive index, effective permittivity, and effectiv e permeability, thus completing the macroscopic description of the interact ion of electromagnetic waves with the medium. Among the novel aspects of th e analysis is the equivalence of our PEG system with a physically dispersiv e system at ultraviolet frequencies and the derivation and explanation of t he development of high dispersive magnetization(permeability) for these med ia, independently of the microscopic magnetic properties of the metallic im plants. (C) 1999 Optical Society of America [S0740-3232(99)02207-3].