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In this paper, a simple and computationally low-cost modification of the standard finite-difference time-domain (FDTD) algorithm is presented to reduce numerical dispersion in the algorithm. Both two-and three-dimensional cases are considered. It is shown that the maximum error in phase velocity can be reduced by a factor of 2-7, depending on the shape of the FDTD cell. Although the reduction procedure is optimal for only single frequency, numerical examples show that the proposed method can also improve the accuracy significantly in wide-band inhomogeneous problems.

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A bianisotropic matrix technique is presented for the development of a homogenized surface susceptibility model of metasurfaces with arbitrary uniaxially mono-anisotropic scatterers, illuminated by obliquely incident TE waves. Based on the sole assumption that the scatterers can be described by pointdipoles, the proposed formulation establishes a simple relation between the homogenized metasurface susceptibility matrix and the scatterer polarizability matrix. For this purpose, the exact interaction coefficients, associating the metasurface local field vectors with the dipole moment vectors, are extracted in terms of rapidly convergent series. The resulting analytical expressions for the interaction coefficients are applicable to both near-field and far-field problems. Moreover, the derived formula for the surface susceptibility matrix reveals the existence of off-diagonal terms, corresponding to a magnetoelectric coupling effect at the lattice level. The accuracy of the method is verified via comparisons with full-wave-simulation results for several metasurfaces of planar resonators and magnetodielectric spheres. It is observed that the efficiency of the model is contingent upon the electrical size of the scatterers rather than the lattice periodicity, since the former determines the validity of the point-dipole approximation, which is the only assumption throughout the analysis.

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The dispersive characteristics of a photonic crystal fiber enhanced with a liquid crystal core are studied using a planewave expansion method. Numerical results demonstrate that by appropriate design such fibers can function in a single-mode/single-polarization operation, exhibit high- or low- birefringence behavior, or switch between an on-state and an off-state (no guided modes supported). All of the above can be controlled by the application of an external electric field, the specific liquid crystal anchoring conditions and the fiber structural parameters.

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Abstract-The tuning properties of two-dimensional dielectric and metallic photonic crystals, which contain nematic liquid crystal materials as defect elements or layers, are thoroughly analyzed using appropriate formulations of the finite difference time domain (FDTD) method. Our methodology correctly incorporates the anisotropy introduced by the liquid crystal materials together with the dispersive properties of the metallic elements; it is used for calculating both the dispersion diagrams of the defect-free photonic crystal as well as the device response in the presence of the defect elements. Numerical simulations reveal that defect states originating from the liquid crystal impurities can be effectively tuned by the application of a local static electric field. Indeed, tuning ranges up to almost 100 nm can be achieved requiring operating voltages lower than 4 V. It is also concluded that the placement of a defect mode relative to the bandgap edges greatly influences both its linewidth as well as its tuning range.