Expansion of linear focused sound fields using Bessel beams

Abstract

Previous work on scattering by Bessel beams shows that expansion of incident sound fields in term of these beams has application to scattering [P. L. Marston, J. Acoust. Soc. Am. 122, 247–252 (2007)]. In this work, we expand a focused cylindrically symmetric sound field in terms of Bessel beam components. In particular, the authors are interested in a focused beam radiated from a spherical cap source. A physical optics model is applied to sound propagation close to the source to facilitate the calculation of the Bessel beam expansion coefficients. This type of model is useful for focused scattering [P. L. Marston and D. S. Langley, J. Acoust. Soc. Am. 73, 1464–1475 (1983)]. Once the expansion coefficients are found the sound field can be evaluated by the appropriate superposition. The model gives results in agreement with O’Neil [H. T. O’Neil, J. Acoust. Soc. Am. 21, 516–526 (1949)] and Chen [X. Chen, K. Q. Schwarz and K. J. Parker, J. Acoust. Soc. Am. 94, 2979–2991 (1993)]. Comparison is also made with direct integration of a Kirchhoff integral for both on and off axis pressures with good agreement. [Work supported by ONR.]