An effective description is developed for a metalodielectric photonic bandgap (PBG) material far beyond the quasi-static limit of traditional effective-medium theories. An analytic approach, recently presented by the authors, is further advanced to provide the complete effective permittivity and permeability functions. Reflection and transmission coefficients are presented for both TM and TE oblique plane-wave incidence, based on the determination 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 anisotropic effective refractive index, effective permittivity, and effective permeability, thus completing the macroscopic description of the interaction of electromagnetic waves with the medium. Among the novel aspects of the analysis is the equivalence of our PBG system with a physically dispersive system at ultraviolet frequencies and the derivation and explanation of the development of high dispersive magnetization (permeability) for these media, independently of the microscopic magnetic properties of the metallic implants.
© 1999 Optical Society of America
(160.1190) Materials : Anisotropic optical materials
(260.1180) Physical optics : Crystal optics
(260.2030) Physical optics : Dispersion
(350.2450) Other areas of optics : Filters, absorption
(350.4010) Other areas of optics : Microwaves
Harry F. Contopanagos, Chryssoula A. Kyriazidou, William M. Merrill, and Nicólaos G. Alexópoulos, "Effective response functions for photonic bandgap materials," J. Opt. Soc. Am. A 16, 1682-1699 (1999)