Interaction of a nondiffracting high- order bessel (vortex) beam of fractional type α and integer order m with a rigid sphere: linear acoustic scattering and net instantaneous axial force

Closed-form analytical solutions for the acoustic scattering and net axial force of a new class of Bessel beams, termed nondiffracting Bessel vortex beams of fractional type α, are derived. This new class of Bessel beams preserves the same nondiffracting feature of conventional high-order Bessel beams of integer order. The far-field acoustic scattering field by a rigid sphere centered on the beam axis is expressed as a partial wave series involving the real number α, the scattering angle relative to the beam axis θ, and the half-conical angle β of the wave number components of the beam. Unlike the acoustic scattering properties of conventional high-order Bessel beams, the acoustic forward scattering (θ = 0°) and backscattering (θ = 180°)of Bessel vortex beams of fractional type α by a rigid sphere do not vanish unless α becomes an integer number. Furthermore, an expression for the net instantaneous axial force is derived for the case of progressive, stationary, and quasi-stationary waves. These results provide new insights into the acoustic scattering theory in the context of nondiffracting beams. The properties of nondiffracting Bessel vortex beams of fractional type α may lead to the development of an "acoustic blender" with possible applications in particle rotation, mixing, and manipulation. Imaging and other related applications may also benefit from this new type of acoustic beams.