Study on acoustic radiation force of an elastic sphere in an off-axial Gaussian beam using localized approximation

In this paper, the expansion coefficients of the off-axial Gaussian beam are obtained using the localized approximation and the translational addition theorem for spherical wave function. The three-dimensional acoustic radiation force of a sphere positioned in an off-axial Gaussian beam is derived. The axial acoustic radiation force of a rigid sphere is computed to verify the derived expressions. The effect of the position of a polystyrene sphere in an off-axial Gaussian beam on the transverse and axial acoustic radiation forces is studied to explore the changing law of particle acoustic manipulation using a Gaussian beam. The calculated results show that the axial force repels the polystyrene particle away from the center of the beam. However, for the transverse force, there is a negative acoustic radiation force at some positions, which is related to the position of the polystyrene sphere in the Gaussian beam, and the negative transverse forces usually pull the polystyrene particle toward the beam axis. In addition, the numerical simulations based on the finite element method are presented to validate the analytical theory, and the comparison results are in good agreement with each other. The study may provide a theoretical basis for the development of single-beam acoustic tweezers using a Gaussian beam.