Applications of the expanded basis method to study the properties of photonic crystals with frequency-dependent dielectric functions and dielectric losses

Band structures of two-dimensional photonic crystals (PCs) made of polar material with frequency-dependent dielectric constant are calculated by using an expanded basis method. The effect of the polariton gap (PG) of polar material on the photonic band gaps (PBGs) is explored. It is found that the PBGs are significantly modified near the PG, where the abrupt change of the dielectric constant appears. The feature of electromagnetic (EM) field is revealed when the frequency is located in the flat band. We display the equifrequency-surface configuration of the localized field and the spacial distributions of field. We observe the existence of several equi-ω curves for a specified frequency and the localized field distribution exhibiting various different patterns, dependent of the mode index. We also study the influence of the dielectric losses of the polar material on dispersion and find that the change of the real part of the Bloch wave vector is crucially related to the real part of the dielectric constant and the attenuated length is determined by its imaginary part.