Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres

Abstract

Various researchers have predicted situations where the acoustical or optical radiation force on a sphere centered on a Bessel beam is opposite the direction of beam propagation. We develop the analogy between acoustical and optical radiation forces of arbitrary-order helicoidal and ordinary Bessel beams to gain insight into negative radiation forces. The radiation force is expressed in terms of the asymmetry of the scattered field, the scattered power, the absorbed power, and the conic angle of the Bessel beam and is related to the partial-wave coefficients for the scattering. Negative forces only occur when the scattering into the backward hemisphere is suppressed relative to the scattering into the forward hemisphere. Absorbed power degrades negative radiation forces.

Material-Independent and Size-Independent Tractor Beams for Dipole Objects

“…Such behavior corresponds to parameters and satisfying equation 1 þ 2 ¼ 3 2 2 , where is the ratio of the drop and surrounding fluid sound speeds (see Refs. [8,20]). Therefore, the density ratio provides FIG.…”

Optical theorem for acoustic non-diffracting beams and application to radiation force and torque

“…Situations giving pulling forces for spheres in non-diffracting Bessel beams have been computed in acoustics [6][7][8][9][10] and in optics [11][12][13]. It was noticed early [6][7][8] that acoustical situations predicting to give negative forces corresponded to a significant reduction of the far-field scattering into the backward hemisphere relative to the forward hemisphere.…”

“…For a sphere of radius a centered on the axis of the beam (8), the far-field scattering was given in [10] in terms of a partial wave expansion as…”

“…It was noticed early [6][7][8] that acoustical situations predicting to give negative forces corresponded to a significant reduction of the far-field scattering into the backward hemisphere relative to the forward hemisphere. An analysis of momentum projection and conservation associated with optical far-field scattering [11] motivated an analogous analysis in the acoustical case [10,14] which shows the relationship between the asymmetry in the scattering and the direction of the radiation force. There have been related theoretical discussions of momentum projection in optics [15] followed by a demonstration of negative optical forces in a beam closely resembling intersecting plane waves [16].…”

“…Here we use this extended optical theorem to examine the extinction cross section on a sphere centered on the axis of a non-diffracting beam, in particular, to examine the extinction for a sphere centered on a Bessel beam as an example. The results, together with a prior result of an asymmetry factor of scattering, are then applied to recover the axial radiation force and torque given in [10,24].…”