Anomalous Reststrahl Structure from Slight Surface Roughness

Abstract

Extremely small bumps or pits on the surface of an ionic crystal will result in anomalous reststrahl measurements. Structure appears in each reststrahl band that could easily be mistaken for two-phonon structure on top of the primary bands, at frequencies slightly below the longitudinal-optic-mode frequencies of the crystal. This secondary structure is caused by localized resonances of the ionic vibrations in the immediate neighborhood of the bumps or pits. This effect is derived from a strictly local dielectric theory, by solving Maxwell's equations with appropriate boundary conditions. Such anomalies in reflectance occur in any material when the imaginary part of the dielectric constant is small, and when the real part falls in the interval roughly between -4 and -\textonequarter{}. Thus they might also be important in metals near plasma frequencies. The effect is independent of other types of anomalies that may arise from differences between dielectric properties in the bulk of the material and those near the surface.