Light propagation in two-dimensional photonic crystals based on uniaxial polar materials: results on polaritonic spectrum

Abstract

The dispersion relations of two-dimensional photonic crystals made of uniaxial polaritonic cylinders arranged in triangular lattice are calculated. The particular case of the transverse magnetic polarization is taken into account. Three different uniaxial materials showing transverse phonon-polariton excitations are considered: aluminum nitride, gallium nitride, and indium nitride. The study is carried out by means of the finite-difference time-domain technique for the solution of Maxwell equations, together with the method of the auxiliary differential equation. It is shown that changing the filling fraction can result in the modification of both the photonic and polaritonic bandgaps in the optical dispersion relations. Wider gaps appear for smaller filling fraction values, whereas a larger number of photonic bandgaps will occur within the frequency range considered when a larger filling fraction is used. The effect of including the distinct wurtzite III–V nitride semiconductors as core materials in the cylinders embedded in the air on the photonic properties is discussed as well, highlighting the effect of the dielectric anisotropy on the properties of the polaritonic part of the photonic spectrum.