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We studied a nematic liquid crystal (LC) cylinder under the action of an axial electric field E(0). Elaborate modeling of the free energy leads to the conclusion that the configuration of the molecules is "escaped radial" for low E(0); a phase transition, however, occurs for a critical value E(c), the configuration becoming axial for E(0) >E(c). From these results, the position-dependent dielectric tensor is determined and the photonic band (PB) structure is calculated for a photonic crystal of LC cylinders. It is shown that by varying E(0) a PB gap can be fully tuned from open to closed. Also, switching to a supercritical field can give rise to interesting polarization and directional effects in the propagation of light.

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The effective bianisotropic response of 3D periodic metal-dielectric structures, composed of crosses with asymmetrically-cut wires, is investigated within a general homogenization theory using the Fourier formalism and the form-factor division approach. It is found that the frequency dependence of the effective permittivity for a system of periodically-repeated layers of metal crosses exhibits two strong resonances, whose separation is due to the cross asymmetry. Besides, bianisotropic metamaterials, having a base of four twisted asymmetric crosses, are proposed. The designed metamaterials possess negative refractive index at frequencies determined by the cross asymmetry, the gap between the arms of adjacent crosses lying on the same plane, and the type of Bravais lattice.

The nonlocal effective permittivity tensor for photonic crystals (PCs), having dielectric and metallic inclusions in the unit cell, is calculated and analyzed within the homogenization theory based on the Fourier formalism and the form-factor division approach. A method allowing us to extract the effective bianisotropic metamaterial parameters (permeability and chirality) from the wave vector dependence of the nonlocal effective dielectric response is proposed. Both the original nonlocal dielectric response parameters and the new bianisotropic metamaterial ones reproduce the photonic band structure of the artificial crystal far beyond the long wavelength limit and for a wide class of metal-dielectric structures. To calculate the optical spectra (reflection and transmission) of finite-size PC, the nonlocal homogenization approach is extended with the method of expansion into photonic bulk-modes (Bloch waves). The application of the developed theory is illustrated with well-known forms of metallic inclusions (slabs, thin wires, split-ring resonators) and experimentally confirmed with novel designs based on metallic crosses.