Second-order nonlinear mixing processes involving a leaky guided acoustic wave

Abstract

Quasi-phasematched mixing processes of acoustic waves via second-order nonlinearity are analyzed with two perfectly guided waves generating a leaky wave. The efficiency of such processes is quantified by an acoustic nonlinearity parameter (ANP), defined as the linear growth rate of the leaky wave’s amplitude in the initial stage of its spatial evolution. Two approximate ways of estimating the ANP of such processes are suggested. The first starts from a stationary solution of the equation of motion and boundary conditions for the displacement field, obtained within perturbation theory. This approach requires the solution of a near-singular linear system of equations. The second is based on the resonant state expansion of the displacement field generated in the mixing process. It allows to express the ANP in the form of an overlap integral, requiring normalization of the displacement field associated with the leaky wave. For leaky output waves with a high degree of localization at the waveguide, both methods yield results in good agreement, as demonstrated for an example system with generalized (2D) plate modes. The first approach has also been applied to finite element calculations of the ANP for nonlinear mixing processes of (1D) edge waves in an elastic plate with rigid faces.