Computation of the Acoustic Radiation Force on a Rigid Cylinder in Off-Axial Gaussian Beam Using the Translational Addition Theorem

The interaction of a Gaussian beam with a particle that is located off-axially is a fundamental problem encountered across many scientific fields. This paper provides a viable theoretical framework to efficiently compute the expansion coefficients of an acoustical Gaussian beam. The expansion coefficient. of an on-axial Gaussian beam is firstly deduced and then the translational addition theorem for Bessel functions is employed to obtain a general description for an off-axial Gaussian beam. The expansion coefficient for the off-axial Gaussian beam is expressed in an analytical form in terms of an infinite series over the underlying translation coefficient. Numerical simulations valid the proposed methods for on-axial and off-axial acoustical Gaussian beam. The simulation results of the waveform for the Gaussian beam which expressed by finite series expansion equations, are in agreement with those obtained for the Gaussian expression using the exact equation. The method is used to calculate the off-axial acoustic radiation force on a rigid cylinder in Gaussian acoustic field. The results are in agreement with those calculated by numerical quadrature. The numerical analytical approach presented in this paper may provide a theoretical basis for particle acoustic scattering and acoustic radiation force computation for off-axial acoustic beam.