Theory of electromagnetic waves in a crystal with excitons

Abstract

Light waves are considered the frequencies of which are close to or fall in a region of exciton absorption in a crystal. A relationship is obtained between polarization dipole moment of the crystal and electric field intensity; this relationship is not one of direct proportionality, as is usually assumed, but is expressed by a differential equation. For this reason the Maxwell equations are of a higher order and their solutions are more complex than the well-known ones which follow from the simple phenomenological theory. It is shown that a number of waves exists in the crystal all of which have the same frequency, polarization and direction but different refractive indices. This effect is different from double refraction and occurs also in isotropically polarizable (cubic) crystals. Existence of purely longitudinal electric waves in the crystal is proved. Surface exciton states, the analogues of surface electron states, are discussed.