Journal article
Quasi-Gaussian Bessel-beam superposition: application to the scattering of focused waves by spheres
The Journal of the Acoustical Society of America, Vol.129(4), pp.1773-1782
04/2011
Handle:
https://hdl.handle.net/2376/117618
PMID: 21476634
Abstract
A superposition of zero-order Bessel beams is examined that closely resembles an idealized paraxial Gaussian beam, provided the superposition is not tightly focused. Plots compare wavefield properties in the focal region and in the far field for different values of kw(0), the product of the wavenumber k, and the focal-spot-radius w(0). The superposition (which is an exact solution of the Helmholtz equation) has the important property that the scattering by an isotropic sphere can be calculated without any approximations for the commonly considered case of linear waves propagating in an inviscid fluid. The nth partial wave amplitude is similar to the case of plane-wave illumination except for a weighting factor that depends on incomplete gamma functions. An approximation for the weighting factor is also discussed based on a generalization of the Van de Hulst localization principle for a sphere of radius a at the focus of a Gaussian beam. Examples display differences between the directionality of the scattering with the plane wave case even though for the cases displayed, ka does not exceed 2 and w(0)∕a is not less than 2. Properties of tightly focused wavefields and the partial wave weighting factors are discussed.
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Details
- Title
- Quasi-Gaussian Bessel-beam superposition: application to the scattering of focused waves by spheres
- Creators
- Philip L Marston - Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA. marston@wsu.edu
- Publication Details
- The Journal of the Acoustical Society of America, Vol.129(4), pp.1773-1782
- Academic Unit
- Physics and Astronomy, Department of
- Publisher
- United States
- Identifiers
- 99900548137001842
- Language
- English
- Resource Type
- Journal article