Nonlinear Scaling Laws for Parametric Receiving Arrays. Part I. Theoretical Analysis

Abstract

Abstract : Following a review of the literature on Parametric Receiving Arrays, the problem of defining their performance characteristics under saturated and unsaturated conditions is considered. Basically, the problem is resolved by establishing equations for the axial field of a spatially symmetric pump wave in the spectral domain via Kuznetsov's nonlinear paraxial wave equation. As a biproduct of this analysis, a simplification of terms involving the phase of pump wave in these equations results, upon transformation to the time domain, in a new form of Burgers' equation for a plane piston projector. Unlike previous forms of Burgers' equation, the latter combines the effect of wave interactions in the near and far field regions of the source. Numerical comparisons of the more complete spectral equations and the spectral form of the new Burgers' equation are shown to be in good agreement with experimental results previously reported in the literature. Approximate solutions of these equations are also derived. The three methods thus established for representing the pump field are then used to derive scaling laws for parametric receiving arrays, which clearly showh the limiting effect of pump wave saturation upon the conversion efficiency of the up-conversion process as the pump amplitude is increased indefinitely.