A new analytical solution for the difference‐frequency field of an unsaturated parametric acoustic radiator via the “quasi‐optical” analogy

Abstract

In this paper a weak finite‐amplitude solution for the difference‐frequency field of a parametric acoustic array is derived via the second‐order nonlinear paraxial wave equation [i.e., the nonlinear optical analog established by E. A. Zabolotskaya and R. V. Khokhlov, Soy. Phys. Acoust. 15, 35–40 (1969)] by expressing the primary waves of an axisymmetrically excited bifrequency piston projector as a weighted sum of Gauss‐Laguerre modes. By relating the fundamental (i.e., Gaussian) modes in the farfield of the projector to those of equivalent “Bessel beams” a new closed‐form expression for the difference‐frequency field is thus obtained as a function of range. A review of the solution's phenomenological properties will then be presented, followed by a brief comparison of predicted results and experimental data reported in the literature.