Influence of interband transitions of reflections from cubic crystals

Abstract

A form for the contribution of the interband transitions to the susceptibility of a crystal of arbitrary shape is suggested. This contribution differs from that of the ``normal'' transitions which lead to the usual phenomenological Maxwell equations. The explicit form of the susceptibility of a semi‐infinite cubic crystal is found, including the contributions of both interband and normal transitions. The reflection coefficients for light incident on the crystal surface from the vacuum are extracted from the general expression for the vector potential. The influence of interband transitions on the reflection coefficients $r_{\perp }$ (perpendicular polarization) and r_∥ (parallel polarization) are ascertained and compared to the effects of normal transitions. $r_{\perp }$ is found to be related to the complex index of refraction by the same expression as given by classical optics. The expression for r_∥, however, is found to differ from that of classical optics. For weak interband transitions it is found that the difference in phase of $r_{\perp }$ and r_∥ has the shape of a dispersion curve while classical optics gives an absorption curve. The differences between the reflection coefficients of classical optics and those in the presence of interband transitions are depicted graphically. Quite generally, interband transitions are predicted to have a definite fingerprint.