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Two-dimensional superconductor-dielectric photonic crystal

2D hexagonal lattice photonic crystal made of superconducting rods embedded in dielectric matrix and dielectric rods embedded in superconducting matrix are studied. We used two-fluid mode to describe the electromagnetic response of the superconductor phase. The superconductor-dielectric photonic band structures are computed using the plane wave expansion method. We found an extremely large low frequency gap as due to the electric field expulsion in the superconductor. Qualitative explanations for the dependency low frequency gap size on dielectric constant, penetration depth and filling fraction are given. A smaller gap has been found at much higher lattice constant/wavelength ratio. We also found a fundamental mode with extremely localized electric field in the dielectric phase, similar to the localized mode in defective photonic crystal. This photonic crystal could be useful for superhigh-Q periodic resonant cavities.