Temperature dependent complex photonic band structures in two-dimensional photonic crystals composed of high-temperature superconductors

Complex photonic band structures in two-dimensional photonic crystals composed of high-temperature superconductors (HTSCs) for the case of E-polarization are calculated as a function of temperature below T-c, where T-c is the critical temperature of the HTSC. The calculations are based on a temperature dependent complex dielectric function, which includes contributions of both superconducting electrons (SCEs) and normal conducting electrons (NCEs), and a frequency dependent plane wave expansion method. Both temperature independent and temperature dependent damping term in the dielectric function are considered to calculate dispersion relations and the lifetime of the eigenmodes. The results are compared with those obtained by existing calculation methods, which neglect the contribution of NCEs. Our results correspond quite well with those obtained by the existing method in the low-temperature range 0 < T/T-c <= 0.3; however, results obtained with the two methods are quite different in the temperature range 0.3 < T/T-c <= 1. We demonstrate that the contribution of NCEs is non-negligible with increasing temperature.