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Axisymmetric parametric radiation—A weak interaction model

In this paper the difference‐frequency field of a a parametric acoustic radiator is approximated via a weak finite‐amplitude solution of the second‐order nonlinear paraxial wave equation (i.e., the nonlinear optical analog established by E. A. Zabolotskaya and R. V. Khokhlov [Sov. Phys.–Acoust. 15, 35–40 (1969)]) obtained by expressing the primary waves of an axisymmetrically excited bifrequency piston projector in terms of a weighted sum of Gauss–Laguerre eigenmodes. By relating the fundamental (i.e., Gaussian) mode in the farfield of the projector to those of equivalent ’’Bessel beams’’ a closed‐form expression for the difference‐frequency field is thus obtained as a function of range. Following a review of the solution’s phenomenological properties comparisons are made of predicted results and experimental data reported in the literature.