Diffusion induced parametric amplification in centro-symmetric semiconductor plasmas

Based on hydrodynamic model of plasmas and using straight forward coupled mode theory an analytical investigation of parametric interaction of high frequency pump with semiconductor plasma and consequent amplification of acoustic wave has been carried out in centro-symmetric semiconductor medium. The phenomenon of parametric amplification is treated as three-wave interaction process, involving second-order non-linearity of the medium. It is found that, diffusion induced non-linear current density is responsible for the generation of second-order optical susceptibility Χ ( 2 ) in a centro-symmetric medium. It has been found that, for crystals with n 0 = 10 2 4 m - 3 , Χ ( 2 ) = 5.01 x 10 - 7 SI and n 0 = 10 2 2 m - 3 , Χ ( 2 ) = 4.13 × 10 - 9 SI, these values are fairly in agreement with the experimentally observed value for III-V compound semiconductors. Steady-state gain constant and threshold pump intensity for the onset of parametric instability, have also been estimated. The analysis has been performed in non-dispersive regime of the acoustic wave, which is one of the preconditions for achieving an appreciable initial steady-state growth of the parametrically generated signal mode. The minimum threshold pump amplitude E O t h at wave number k = 7.4×10 7 m - 1 (say k m ) has been found. This k m is greatly influenced by carrier concentration and diffusion coefficient of the carriers in the medium. It is found that, gain increases rapidly with the increase in pump amplitude ( > E O t h ) and doping concentration of the medium. Hence, the desired value of the gain can be obtained by adjusting pump intensity and doping concentration of the medium concerned.