Abstract
Surface polaritons associated with localized modes in crystals are investigated theoretically by considering the case of Ca${\mathrm{F}}_{2}$: ${\mathrm{H}}^{\ensuremath{-}}$. The dielectric constant is calculated using a simple model tht includes damped oscillators for both the tansverse-optical mode of the pure crystal and the localized mode, for two temperatures, 80 and 300\ifmmode^\circ\else\textdegree\fi{}K. We find that the surface polaritons of the impurities are Zenneck modes, while those of the pure crystal are lossy Fano modes. The dispersion relation for real wave vector and complex frequency is given, and the determination of the dispersion relation by the method of attenuated total reflection (ATR) is calculated. We find that the damping in this system is sufficient that one must consider the ratio of $p$- to $s$-polarized reflectivities in the ATR spectra in order to determine the localized-mode surface-polariton dispersion relation.
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