Acoustoelectric parametric interactions and other non‐linear effects in a piezoelectric semiconductor

The theory describing departures from linear bchaviour of a single acoustic wave in a piezoelectric semiconductor is extended to include the case of many waves. In addition to the self‐interaction of each wave and the excitation of its associated evanescent mode, there appear in lowest order the three‐wave parametric interactions. Only those parametric intcractions which are phase‐matched are considered. It is shown that the latter consist, of a normal part, obeying the Manley‐Rowe relations, and an anomalous part, associated with the carrier drift, which do not. Coupled with the parametric gain is a velocity shift whose phase is in quadrature with respect to that of the gain. It is pointed out that nonlinear velocity shifts destroy perfect phase‐matching. The down conversion rate maximises at the subharmonic, and the subharmonic generation rate rises with the frequency of pump to a maximum at about 2.3 ω m , where ω m is the frequency for maximum linear gain. In the weak‐activity regime and apart from parametric processes the non‐linear gain is current‐controlled and remains maximised at ω m . Observed frequency shifts may be due to the frequency dependence of the lattice loss as well as that for subharmonic generation.