Notes on the Gaussian beam expansion

A powerful Gaussian-beam expansion technique [J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752–1756 (1988)] is widely used in calculating the Fresnel field integral. A basic ideal of this treatment is to expand the source distribution function into the superposition of a series of Gaussian functions. The evaluation of the radiation field is then greatly simplified. As a supplement, this paper presents a simple approach to determine the expansion coefficients for the sound source. The results for the ultrasonic field radiated by piston transducers are typically given, in a fairly good agreement with those calculated by numerical integration and Breazeale’s. The limits of the present method are also discussed.