Stationary energy-transport velocity of light scattered dynamically from a bunched solid-state plasma

A theoretical investigation of the stationary energy transport velocity (${\overrightarrow{\mathrm{v}}}_E$) of light diffracted dynamically by a bunched solid-state plasma is made. The treatment is based on a quasistatic two-wave interference approximation, the solid is represented by a collection of bound and free classical, harmonic oscillators, the different volume elements of the material interact via the macroscopic radiation field only, and the opaque crystal is assumed to be semi-infinite. Analytical expressions are derived for the spatially nonoscillating and oscillating (pendulum) components of ${\overrightarrow{\mathrm{v}}}_E$. The limiting cases where the plasma, with respect to its optical properties, is collision dominated and collisionless are examined. A minor part of the paper is devoted to a study of ${\overrightarrow{\mathrm{v}}}_E$ in the one-wave approximation, and the results are applied to a $n$-InSb plasma. The main emphasis of this work is given an analysis of ${\overrightarrow{\mathrm{v}}}_E$ in a $n$-InSb plasma where a sinusoidal free-carrier density wave is created by means of the linear piezoelectric interaction of the conduction electrons with a single acoustic mode. Numerical calculations showing the variations of ${\overrightarrow{\mathrm{v}}}_E$ with the sound intensity, with the acoustic and optical frequencies, and as a function of the depth below the crystal surface are presented. The general results, obtained by means of a Boltzmann-equation calculation of the free-carrier density modulation which takes into account nonlocal transport effects, are compared with those obtained on basis of the collision-dominated Hutson-White model of the acoustoelectric interaction, and under the assumption that the conduction-electron bunching is so small that the splitting of the plasma dispersion relation is almost or even completely negligible. In the Appendix the influence of spatial dispersion effects on ${\overrightarrow{\mathrm{v}}}_E$ in the one-wave model is studied.