Backward-wave parametric interaction between longitudinal and transverse elastic waves

The parametric interaction between a continuous, forward-traveling longitudinal elastic wave pump and continuous, forward- and backward-traveling transverse elastic waves is considered. The coupling between the waves is provided by third-order terms in the elastic energy density. Using "typical" values for loss and nonlinearity and omitting all reflected waves in the analysis, the threshold value of longitudinal wave pump at 3 GHz needed to generate the two transverse waves from the thermal background is calculated. Also, amplification coefficients, for either forward- or backward-traveling transverse signal waves are calculated for a 3-GHz pump and for various pump amplitudes and interaction distances. It appears that amplification is only practical for a continous wave pump strain amplitude of at least 10_-6 which with current experimental practice is probably too high to realize. If, however, continuous wave strain amplitudes this large could be realized, and if a reflectionless experimental situation could be achieved, the analysis will show that a high-gain, parametric transverse elastic wave amplifier could be constructed. The highgain region could be achieved by operating the device very near to the conditions where it becomes a "backward-wave-oscillator" (BWO).