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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Partial-wave series expansions in spherical coordinates for the acoustic field of vortex beams generated from a finite circular aperture
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Partial-wave series expansions in spherical coordinates for the acoustic field of vortex beams generated from a finite circular aperture

机译：有限圆孔径产生的旋涡束声场在球坐标系中的分波级数展开

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摘要

Stemming from the Rayleigh-Sommerfeld surface integral, the addition theorems for the spherical wave and Legendre functions, and a weighting function describing the behavior of the radial component vp1 of the normal velocity at the surface of a finite circular radiating source, partial-wave series expansions are derived for the incident field of acoustic spiraling (vortex) beams in a spherical coordinate system centered on the axis of wave propagation. Examples for vortex beams, comprising ρ-vortex, zeroth-order and higher order Bessel-Gauss and Bessel, truncated Neumann-Gauss and Hankel- Gauss, Laguerre-Gauss, and other Gaussian-type vortex beams are considered. The mathematical expressions are exact solutions of the Helmholtz equation. The results presented here are particularly useful to accurately evaluate analytically and compute numerically the acoustic scattering and other mechanical effects of finite vortex beams, such as the axial and 3-D acoustic radiation force and torque components on a sphere of any (isotropic, anisotropic, etc.) material (fluid, elastic, viscoelastic, etc.), either centered on the beam's axis of wave propagation, or placed off-axially. Numerical predictions allow optimal design of parameters in applications including but not limited to acoustical tweezers, acousto-fluidics, beamforming design, and imaging, to name a few.
机译：根据Rayleigh-Sommerfeld表面积分，球面波加法定理和Legendre函数以及描述有限圆辐射源表面上法向速度径向分量vp1行为的权重函数（分波序列）在以波传播轴为中心的球面坐标系中，得出声螺旋（涡旋）光束的入射场的扩展。考虑了包括ρ-涡旋，零阶和高阶贝塞尔-高斯和贝塞尔，截断的诺伊曼-高斯和汉克尔-高斯，拉盖尔-高斯以及其他高斯型涡旋束的涡旋束的示例。数学表达式是亥姆霍兹方程的精确解。此处显示的结果对于精确分析和数值计算有限涡旋光束的声散射和其他机械效应（例如，任意（各向同性，各向异性，等）材料（流体，弹性，粘弹性等），或者以光束的波传播轴为中心，或者离轴放置。数值预测允许在应用中优化设计参数，这些应用包括但不限于声学镊子，声流体，波束成形设计和成像等。

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