Exact analytic formulas for calculating the effective permittivity, permeability, and crossed magnetoelectric tensors for photonic crystals in the long-wavelength limit are presented. The formulas are valid for arbitrary Bravais lattice and form of inclusions, which can be dielectric, magnetic, or chiral. We have applied them to study the optical anisotropy of homogenized magnetodielectric three-dimensional photonic crystals, which can be induced by the type of Bravais lattice or the form of the inclusion even in the case when the photonic crystal is composed of isotropic materials. It is established that the electromagnetic modes, propagating in such anisotropic magnetodielectric metamaterials, are extraordinary, unlike the modes in homogenized nonmagnetic dielectric composites, where at least one mode is ordinary.

Abstract-We have derived simple analytical expressions for the frequency-dependent effective permittivity tensor of a one-dimensional metal-dielectric photonic crystal in the long wavelength limit. Our results describe the transition between the regime, described by Rytov's formulas for sufficiently long waves, and that predicted by Xu et al. [6], where the effective plasma frequency is independent of the metallic-layer parameters. The derived expressions can be useful for determining the frequency intervals where such an anisotropic system can exhibit metamaterial behavior.

The influence of the surface-potential shape on exciton optical spectra for thin semiconductor films is investigated theoretically. Using a realistic model with both intrinsic and extrinsic contributions, we calculate the polarization vector and the electric field in the case of s-polarized incident light at one of the thin-film surfaces. Our analytic results are employed to study the relation between the surface potential parameters and the spectra of reflectivity and transmissivity. The generation of near-surface localized excitons and their optical manifestation are also analyzed.

On the basis of the formalism of the Boltzmann kinetic equation for the distribution function of the conduction electrons, the photonic band structure of binary dielectric-metal superlattice is theoretically studied. Using the constitutive nonlocal relation between the electrical current density and the electric field inside the metallic layer, the dispersion equation for photonic eigenmodes in the periodic stack is analytically expressed in terms of the surface impedances at the interfaces of the metal and dielectric layers. In the case of very thin metallic layers, the optic spectrum for the superlattice exhibits narrow pass bands as a result of the strong contrast between the impedances of the dielectric and the metal. The narrow pass bands are attributed to Fabry-Perot resonances in the relatively-thick dielectric layer. The metal nonlocality is well pronounced in the infrared and, therefore, the nonlocal effect upon the photonic band structure of the superlattice can be strong when the Fabry-Perot resonance bands are in that frequency range. Our results for the photonic spectrum have been compared with those obtained within the local Drude-Lorentz model. Noticeably differences not only in the the magnitude, but also in the sign of the real part of the Bloch wave number in the Fabry-Perot resonance bands, have been found.

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