Photonic band structures of a two-dimensional ionic dielectric medium

Abstract

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 \ensuremath{\epsilon}(\ensuremath{\omega})=\ensuremath{\epsilon}(\ensuremath{\infty})(${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}^{2}$-${\mathrm{\ensuremath{\omega}}}^{2}$)/(${\mathrm{\ensuremath{\omega}}}_{\mathrm{TO}}^{2}$-${\mathrm{\ensuremath{\omega}}}^{2}$), with \ensuremath{\epsilon}(\ensuremath{\infty}), ${\mathrm{\ensuremath{\omega}}}_{\mathrm{TO}\mathrm{i}}$, and ${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}$ 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 ${\mathrm{\ensuremath{\omega}}}_{\mathrm{TO}}$ are strongly flattened. Our study also suggests that while the plane-wave method gives reliable photonic bands for the frequency below ${\mathrm{\ensuremath{\omega}}}_{\mathrm{TO}}$, a better method has to be used for the photonic bands very near or above ${\mathrm{\ensuremath{\omega}}}_{\mathrm{TO}}$. \textcopyright{} 1996 The American Physical Society.