Laser driven acoustic instabilities in materials with strain-dependent dielectric constants S. Ghosh and S. Dixit School of Studies in Physics, Vikram University, Ujjain 456 010, India Received 21 February 1986; revised 18 August 1986 A simple analysis of the laser driven acoustic wave instability in a material with strain-dependent dielectric constants is given. The analysis is based on the hydrodynamic model of a plasma in the collision dominated regime. Using coupled mode theory, the acoustic instability in the medium is investigated and the threshold value of the pump electric field and the conditions for the initial growth rates of unstable acoustic waves are deduced. It is found that large values of growth can be achieved for materials having an anomalously large dielectric constant, which is otherwise not achievable with piezoelectric interaction. Because of the non-availability of the relevant experimental data, we were unable to compare our theoretical case with an experimental one. Keyword: lasers; acoustic instability; dielectric constants In the last two decades there have been several reports, theoretical and experimental, on the phenomena of frequency mixing and the attenuation/amplification of acoustic waves in piezoelectric semiconductors as a result of electron-phonon interactions~-L These phenonema occur due to the bunching of carrie1"s produced by fields associated with the different waves generated in the sample as a result of mixing, or by the piezoelectric field accompanying the fundamental wave itself. The latter explains the linear amplification/attenuation of the waves, while the former is responsible for the acoustic wave mixing of the carders. Therefore, any process which enhances the bunching of the carriers will enhance the magnitude of the linear and non-linear gain coefficients; while any process which decreases the bunching will also decrease linear gain and gain due to non-linear inter- action. Recently, Ghosh 1° discussed the effect of enhanced bunching, produced by the application of a magnetostatic field across the wave propagation direction, on the modulational amplification coefficients of acoustic waves in piezoelectric semiconductors. In piezoelec- trically inactive materials where the electron-phonon interactions are determined by the deformation potential, linear acoustic gain TM and non-linear gain ~e are in general smaller than in piezoelectrically active materials. The above mentioned reports of different acousto- electric effects assumed the dielectric constant to be a constant. However, such an assumption is not justified as the dielectric constant depends upon the deformation of the material; this is true for both piezoelectrically active as well as inactive materials. Taking this effect into account, Pekar ~3and Ogg 14have pointed out that, in the presence of an electrostatic field, ferroelectric semiconductors with high dielectric constants can have anomalously large linear gain constants otherwise not achievable with 0041-624X/87/030175--06 $03.00 © 1987 Butterworth ~ Co (Publishers) Ltd piezoelectric and/or deformation potential interactions. That is, the electron-phonon interactions, as a result of the strain-dependent dielectric constant (SDDC) in such materials, predominate over the piezoelectric and/or deformation potential interactions. Recently, the study of laser driven instability in semiconductors has emerged as one of the most active frontiers in solid-state plasmasS-l"; microwave devices based on this principle are playing an important role as low noise amplifiers and oscillators ",~. Motivated by the work of Pekar ~3 and Ogg ~4 and the intense interest in the field of laser driven instability, the present authors chose to study, in analytical terms, the laser driven instability and consequent amplifications of acoustic waves in an n- type plasma (electrons only) of a homogeneous, non- degenerate solid with SDDC, irradiated by a spatially homogeneous, pulsed laser beam. Using coupled mode theory in the hydrodynamic regime (kl << 1), the laser driven instability in the medium, the threshold value of the pump electric field amplitude and the initial growth rates of the unstable acoustic waves, well above the threshold value, were investigated. Estimates of the acoustic wave increment in the instability region were made for BaTiO3 crystal. The values obtained were compared with those measured in piezoelectric materialsg; larger acoustic wave gains were found in SDDC materials. Theoretical formulations We used a hydrodynamic model of a homogeneous, one component (electrons only) material of infinite extent, in which the only coupling between conduction electrons and acoustic waves is due to the SDDC. It should be noted that piezoelectric and deformation potential effects were neglected. Thus, the dielectric constant is given by Ultrasonics 1987 Vol 25 May 175