Using the hydrodynamic model of homogeneous plasma, the parametric decay of a laser beam into an acoustic wave and another electromagnetic wave has been studied in heavily dopedn-type piezoelectric semiconductors in the presence of a transverse magnetostatic field. This decay process results in the parametric excitation of the hybrid mode. The threshold electric field necessary for the onset of instability equals to zero. The magnetostatic field couples the acoustic and the electromagnetic waves and in its absence the instability disappears. The growth rate increases with the square of the magnetic field.

The applicability of Kramers-Kronig (K-K) relation under nearly sharp resonant transition regime in narrow-gap semiconductors has been established and consequently, a generalized dispersion relation for nonlinear optical susceptibility of a dielectric is derived. This relation can be employed in the study of nonlinear optical processes in solids as well as in plasmas over a wide frequency spectrum.