Nonlinear mixing of surface acoustic waves propagating in opposite directions

Abstract

The parametric mixing of two modulated surface acoustic waves propagating in opposite directions is studied with reference to nonlinear signal processing applications by the coupled mode theory of nonlinear surface waves. In the case of propagation in opposite directions the combination frequency waves generated out of the nonlinear interaction of the two primary waves and their harmonics with one another do not satisfy the phase-matching condition. Hence there exists no mode coupling between the primary waves. At the same time the amplitude of each combination frequency wave is proportional to the product of a harmonic amplitude of one of the interacting waves with a harmonic amplitude of the other wave. The variation of these harmonic amplitudes as functions of the slow scale variables are governed by two sets of coupled amplitude equations, each set pertaining to one primary wave and its harmonics. It is further shown that, in addition to surface wave modes, there also exist bulk wave modes in a certain range of values of the primary wave frequency ratio. The paper concludes with indicating the relevance of the present study to the acoustical implementation of nonlinear signal processing operations like convolution, correlation, etc.