Polarition Intensities in α-Quartz

Abstract

The initial studies of light scattering from polaritons emphasized kinematic aspects [1–4]. Polariton dispersion was detailed experimentally for several materials, and the effect of birefringence, damping, and index of refraction variation near the laser frequency were examined. However, interest in polariton cross-sections was dormant until Faust and Henry [5] discovered a zero in the nonlinear electric susceptibility of GaP and showed how Poulet’s [6] two-component phenomenological model could be used to explain their optical mixing data. Poulet’s model has been elaborated upon by Loudon [7] and by Kleinman [8] and has recently been used by Kaminow and Johnston [9] and by Ushioda et al. [10] to analyze the influence of displacive and electro-optic contributions upon the Raman susceptibility. Extensions of the earlier work have most recently been made by Henry and Garrett [11] and by Burstein et al. [12] In the present analysis of quartz the Burstein formalism [12] will be used, because it is already cast into a form suited to computer solution of the many-mode case. In quartz we shall consider eight modes of E symmetry and obtain numerical solutions of the equations developed by Burstein et al. The formalism of Henry and Garrett can be shown to be equivalent, if damping constants are handled carefully, however their calculations are developed only for crystals having a single optical mode and contain approximations at various stages which are not suitable for quartz. Their conclusion that resonant absorption exactly cancels resonant gain near IR- and Raman-active phonon frequencies [11] is not true for quartz, nor for other crystals where two or more IR- and Raman-active modes are present, one of which has large Raman gain and very small IR oscillator strength.