A simplified algorithm for the second-order sound fields

An analytical description for the second-order field of the sum-, differenc e-frequency and second harmonic components is derived. This treatment is ba sed on the fact that an arbitrary axially symmetric beam can be expressed a s the linear superposition of a set of Gaussian beams [J. J. Wen and M. A. Breazeale, J. Acoust. Sec. Am. 83, 1752-1756 (1988)], so that the three-dim ensional integral for the second-order components is typically expressed as a combination of a set of interaction terms of the Gaussian beams. Corresp ondingly, the evaluation of the field distribution is reduced to the summat ion of exponential integral functions. From some examples, the present appr oach provides the results for the second-order field, which are in good agr eement with those obtained directly by numerical integration. (C) 2000 Acou stical Society of America. [S0001-4966(00)00212-5].