Raman instability in n-type piezoelectric semiconducting plasmas

Abstract

The paper aims at the detailed analytical investigation of Raman instability in a magnetoactive n-type cubic piezoelectric semiconducting crystal belonging to class 4̄3m under a geometrical configuration which can also be employed in analyzing the phenomenon under either Voigt or Faraday orientation. The electric vector E0 of the spatially uniform pump electromagnetic wave (applied along the y axis) is normal to the magnetostatic field B0 (along the z axis) as well as to the plane of propagation (x-z plane) of the scattered waves (Ω,k) and (Ω1,k1). The propagation vectors k, k1 (antiparallel to each other) are in the x-z plane making an angle θ with the x axis. The dispersion relation has been obtained by using a hydrodynamic model of the homogeneous, piezoelectric, one-component (electron) semiconducting plasma; and the threshold value of the pump electric field (necessary to achieve physically reasonable growth of the unstable mode) and the growth rate of the unstable Raman mode well above the threshold field have been obtained for isotropic (B0=0) and magnetoactive (B0≠0) plasmas. We have applied our analysis to a specific semiconductor, n-InSb at 77 K, duly irradiated by a pulsed 10.6-μm CO2 laser for numerical estimation. The phase velocity of the growing unstable mode is found to be constant over the whole range of system parameters and equal to the electromagnetic wave velocity in the crystal. The magnitude of threshold electric field decreases with increasing magnetostatic field and decreasing wave vector. The growth rate increases and attains a maximum value at a certain value of the pump intensity, magnetostatic field, and θ; and if these are raised further, growth rate starts decreasing. When the analysis is extended to Voigt and Faraday configurations, the results are not very encouraging.