The polaritonic spectrum of two-dimensional photonic crystals based on uniaxial polar materials

We investigate the dispersion relations of two-dimensional photonic crystals made of cylindrical rods of uniaxial polar materials that exhibit transverse phonon-polariton excitations. The rods are considered to be embedded in a dielectric background. The photonic properties are obtained with the use of the finite-difference time domain (FDTD) method and the auxiliary differential equation (ADE) technique. The anisotropy of the dielectric function is explicitly considered using an empirical approach that assigns different weights to contributions of the parallel (z) and transversal (t) polaritonic relations. The effective dielectric function is then expressed as a weighted combination of the longitudinal and transversal components: ε(ω)=αzεz(ω)+αtεt(ω). Different sets of values of the coefficients αz and αt have been considered. The frequencies of the allowed electromagnetic modes are determined as the local maxima of the spectral analysis using a fast Fourier transform (FFT). The particular case of a square photonic crystal superlattice geometry is analyzed, and input data corresponding to phonon frequencies of wurtzite nitride semiconductors is used. It is shown that larger values of the quantity |νz,T-νt,T| are desirable if the associated dielectric anisotropy is used as a tool for tuning photonic properties in the system.