Off-axial acoustic radiation force of repulsor and tractor bessel beams on a sphere

Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both repulsor and tractor behaviors. The repulsor and the tractor forces are oriented along the beam´s direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam´s axis (off-axial configuration) is unknown. Using the 3-D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone- oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam´s axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the sphere´s size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam´s axis are found, depending on ka values. These results are particularly important for the design of acoustical tractor beam devices operating with Bessel beams.