Axial radiation force exerted by general non-diffracting beams

Abstract

The axial radiation force exerted by a general non-diffracting beam on an object of arbitrary shape in lossless medium is analyzed. The object may be on or off the beam’s axis. The analysis is based on the plane-wave representation of the beam using an azimuthal function and conical angle. The analytical expression relates the force to axial projections of the extracted and scattered momentum. Using an extended optical theorem, the extinction is related to the scattering at the forward direction of the beam’s plane wave components. The axial force is expressed using the scattering amplitude and known angular functions.

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

“…where the factors, cos β and cos θ s , correspond to the axial projections of extracted momentum and scattered momentum [10,11,14], respectively, and…”

“…By the axial projection of momentum, the axial radiation force exerted by the general nondiffracting beam (4) on an object of arbitrary shape and location was given in [14] as…”

“…an extended optical theorem for the extinction cross section, denoted by σ ext , was derived in the context of acoustics by [14] as an azimuthal angle integration…”

“…The optical theorem for an incident plane wave is known as one of the central theorems in scattering theory [28][29][30]; the theorem relates the extinction section to the complex scattering amplitude at the forward direction. An extended theorem for a non-diffracting beam was given recently in the context of acoustics [14]. 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.…”

“…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].…”