High-Order Pseudo-Gaussian Scalar Acoustical Beams

作者：Mitri Farid G^*

来源：IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2014, 61(1): 191-196.

DOI：10.1109/TUFFC.2014.2890

Exact solutions of the scalar Helmholtz equation describing tightly spherically-focused beams are introduced without any approximations using the complex source point method in spherical coordinates. The generalized solutions, valid for any integer degree n and order m, describe high-order pseudo-Gaussian vortex, intermediate (vortex), hollow (non-vortex), and trigonometric (non-vortex) beams having an arbitrary beam waist w(0). A very useful property of these beams is the efficient and fast computational modeling of tightly focused or quasi-collimated wave-fronts depending on the dimensionless waist parameter kw(0), where k is the wave number of the acoustical radiation. Examples that illustrate hollow vortex and non-vortex beams are provided, and numerical simulations for the magnitude, isosurface, and phase plots of the pressure wave field of higher-order quasi-Gaussian beams are evaluated with particular emphasis on kw(0) for strongly (kw(0) = 3) to weakly focused (i.e., quasi-collimated) beams (kw(0) = 7). Potential applications are in beam-forming design, imaging, particle sizing and manipulation in acoustical tweezers, and phenomena related to scattering, radiation force, and torque.

• 出版日期2014-1