Using the classical hydrodynamic model of semiconductor plasmas, the parametric amplification and dispersion characteristics of optical phonon mode in a semiconductor magnetoplasma are investigated analytically. An expression for effective complex second-order optical susceptibility ($\chi^{(2)}_e=(\chi^{(2)}_e)_r+ \chi^{(2)}_e)_i)$ is obtained under off-resonant laser irradiation. The analysis deals with qualitative behaviour of threshold pump amplitude($\xi_{0,\rm{th}}$) for the onset of parametric excitation, anomalous parametric dispersion (via $(\xi^{(2)}_e)_r)$ and parametric gain coefficient ($g_{\rm{para}}$ via ($(\xi^{(2)}_e)_i)$ with respect to externally applied magnetostatic field ($B_0$) for different values of doping concentration ($n_0$). Numerical estimates are made for n-InSb–CO$_2$ laser system at 77 K. The analysis offers three achievable resonance conditions at which $\xi_{0,\rm{th}}$ reduces whereas $g_{\rm{para}}$ enhances by two orders of magnitude. The lowering in $\xi_{0,\rm{th}}$ and enhancement in $g_{\rm{para}}$, under proper selection of $B_0$ and $n_0$, confirms the chosen nonlinear medium as a potential candidate material for the fabrication of efficient optical parametric amplifiers. The negative and positive enhanced parametric dispersion may be of potential use in the study of squeezed state generation as well as in group velocity dispersion in semiconductor magnetoplasmas.

Assuming the origination of stimulated Raman scattering (SRS) in Raman susceptibility, we obtain expressions for Raman gain coefficients (under steady-state and transient regimes) of semiconductor magnetoplasmas under various geometrical configurations. The threshold value of excitation intensity and most favourable value of pulse duration (above which transient Raman gain vanishes) are estimated. For numerical calculations, we consider n-InSb crystal at 77K temperature as a Raman-active medium exposed to a frequencydoubled pulsed CO$_2$ laser. The variation of Raman gain coefficients on doping concentration, magnetostatic field and its inclination, scattering angle and pump pulse duration have been explored in detail with an aim to determinesuitable values of these controllable parameters to enhance Raman gain coefficients at lower threshold intensities and to establish the suitability of semiconductor magnetoplasmas as hosts for compression of scattered pulses and fabrication of efficient Raman amplifiers and oscillators based on Raman nonlinearities.

Using a quantum hydrodynamic model, quantum effects (via Bohm potential) on modulational amplification in ion-implanted semiconductor magnetoplasmas are investigated. Expressions are obtained for the threshold pump amplitude and the growth rate of modulated beam for both the electrons and implanted colloids.Numerical analysis is performed for n-InSb/CO$_2$ laser system. The dependence of the threshold pump amplitude and the growth rate of modulated beam for electrons on wave number, applied magnetic field (via electron cyclotronfrequency) and electron concentration (via electron-plasma frequency) and the dependence of the threshold pump amplitude and the growth rate of modulated beam for implanted colloids on wave number and colloid concentration(via colloid-plasma frequency) are explored. The lowering in threshold pump amplitude and enhancement of the growth rate of modulated beam for both the electrons and implanted colloids are observed by incorporating the quantum effects. The analysis provides detailed information of quantum effects on modulational amplification in ion-implanted semiconductor magnetoplasmas composed of electrons and negatively charged implanted colloids and establishes the technological potentiality of chosen samples as the hosts for the fabrication of efficient optical modulators.