In this paper, a detailed analytical investigation is made to study the acoustical-phonon (AP) and polaron mode-induced optical parametric amplification (OPA) in transversely magnetized III–V semiconductors. Making use of hydrodynamic model of (one component) semiconductor plasma and adopting the coupled mode approach, an explicit expression is obtained for the threshold pump electric field [Formula: see text] and gain coefficients [Formula: see text] of AP and polaron mode-induced OPA. Externally applied magnetostatic field [Formula: see text] and doping concentration [Formula: see text] are incorporated in terms of electron cyclotron frequency [Formula: see text] and plasma frequency [Formula: see text], respectively. The dependence of [Formula: see text] on wave number [Formula: see text], [Formula: see text] and [Formula: see text] and the dependence of [Formula: see text] on [Formula: see text], [Formula: see text] and pump electric field [Formula: see text] are explored. Numerical estimates made for [Formula: see text]-InSb-CO2 system suggest that the material parameters and externally applied magnetostatic field play an important role in reducing [Formula: see text] and enhancing [Formula: see text]. We find [Formula: see text] (when [Formula: see text]); though [Formula: see text] is smaller than [Formula: see text] under identical conditions. The formulation developed in this paper highlights the importance of Frohlich interaction in transversely magnetized III–V semiconductors for OPA and replaces the conventional idea of using high power pulsed lasers. The results obtained in this analysis suggest that by controlling the material parameters and externally applied magnetostatic field, the performance of acoustical and polaron mode-induced optical parametric amplifiers may be improved. It is expected that a cheaper efficient optical parametric amplifier can be fabricated using [Formula: see text]-InSb-CO2 system as the outcome of this research work.