Nonlinear interactions in degenerate surface acoustic wave elastic convolvers

Abstract

The degenerate surface acoustic wave elastic convolver is analyzed by solving the nonlinear piezoelectric equations of motion subject to appropriate boundary conditions. The nonlinear equations are treated by a perturbation theory by assuming that the nonlinear stress and nonlinear electric displacement are small compared to the respective linear quantities. We obtain expressions for the open‐circuit voltage (V₀) and short‐circuit current (I₀) in terms of power (P⁽ⁱ⁾) in the incident waves and linear and nonlinear constants of the material. We also calculate the figure of merit M=V^rms₀(P⁽¹⁾P⁽²⁾/W²)^−1/2 (W is the width of the incident acoustic beam) and the internal impedance Z₀=V₀/I₀. We obtain numerical values of M and V₀ from an estimate of the nonlinear constants available in the existing literature and compare them with experiments.