Photonic band structures of a two-dimensional ionic dielectric medium

The photonic band structures of the two-dimensional square lattice of air cylinders embedded in an ionic crystal are calculated using the plane-wave method. The dielectric function of the ionic crystal is taken as {ε}({ω})={ε}({∞})(ωLO²-ω²)/(ωTO²-ω²), with {ε}({∞}), ωTOi, and ωLO denoting the high-frequency dielectric constant and transverse- and longitudinal-optical-phonon frequencies, respectively. The frequencies of the electromagnetic modes are determined from the zeros of the determinants of the matrix equation. Both E and H polarizations are considered. Our calculation shows that the low-frequency photonic bands resemble the bands of a frequency-independent dielectric medium, while the bands near the transverse-optical-phonon frequency ωTO are strongly flattened. Our study also suggests that while the plane-wave method gives reliable photonic bands for the frequency below ωTO, a better method has to be used for the photonic bands very near or above ωTO. {} 1996 The American Physical Society.