Pseudo-Gaussian cylindrical acoustical beam – Axial scattering and radiation force on an elastic cylinder

Abstract

a b s t r a c tMaking use of the addition theorem for the cylindrical wave functions and the complexsource-point method in cylindrical coordinates, an exact solution to the Helmholtz equation is derived, which corresponds to a tightly focused (or collimated) cylindrical quasi-Gaussian beam with arbitrary waist. The solution is termed "quasi-Gaussian" to make a distinction from the standard Gaussian beam solution obtained in the paraxial approximation. The advantage of introducing this new solution is the efficient and fast computational modeling of tightly focused or quasi-collimated cylindrical wave-fronts depending on the dimensionless waist parameter kw 0 , where k is the wavenumber of the acoustical radiation. Moreover, a closed-form partial-wave series expansion is obtained for the incident field, which has the property that the axial scattering (i.e. along the direction of wave propagation) and the axial acoustic radiation force (which is a time-averaged quantity) on a cylinder, can be calculated without any approximations in the limit of linear acoustical waves in a nonviscous fluid. Examples are found where the extinction in the radiation force function plot is found to be correlated with conditions giving reduction of the backscattering from an elastic cylinder. Those results are useful in beam-forming design, particle manipulation in acoustic tweezers operating with focused cylindrical beams, and the prediction of the scattering and radiation forces on a cylindrical particle or liquid bridges.

Resonance scattering and radiation force calculations for an elastic cylinder using the translational addition theorem for cylindrical wave functions

“…Panels the cylinder, which was also confirmed in Ref. 41. Consequently an axial trapping cannot be accomplished with the zeroth-order cylindrical quasi-Gaussian beam.…”

Generalization of the optical theorem for monochromatic electromagnetic beams of arbitrary wavefront in cylindrical coordinates

“…Assuming that the beam is propagating perpendicularly with respect to the dielectric cylinder of circular cross-section of radius a so that k z = 0 and k r = k, the axial component of the incident electric field polarized along the z-direction (i.e. transverse magnetic TM polarization) is expressed as [46],…”

“…is the modified cylindrical Bessel function of the first kind of order zero, ρ -is a complex distance, and x R is the Rayleigh range [46], which is related to the non-dimensional beam waist kw 0 such that…”

Acoustic radiation torque on an off-axis elliptical cylinder in Gauss beams

“…2017年, Mitri [25] 分析了一对黏性柱体的声辐射力 矩并考虑了柱体间多次散射对结果的影响, 而后 Wang等 [26] 考虑了Airy波入射下的同样问题. 为 了 更 精 确 地 模 拟 实 际 边 界 附 近 的 声 操 控 问 题 , Mitri [27] 坐 标 为 (x 0 , y 0 ). 为 了 后 面 数 学 讨 论 的 方 便 , 以 O为原点再建立一柱坐标系(r, q, z), 两坐标系之 间满足关系: .…”