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

Likun Zhang,Philip L Marston

doi:10.1364/boe.4.001610

Abstract

Acoustical and optical non-diffracting beams are potentially useful for manipulating particles and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the context of acoustics. The theorem relates the extinction by an object to the scattering at the forward direction of the beam's plane wave components. Here we use this theorem to examine the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting Bessel beam as an example. The results are applied to recover the axial radiation force and torque on the sphere by the Bessel beam.

Highlights

An idealized non-diffracting beam is a beam whose transverse intensity pattern has the feature of propagation-invariance [1,2,3,4,5]
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]
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

Summary

Introduction

An idealized non-diffracting (optical or acoustic) beam is a beam whose transverse intensity pattern has the feature of propagation-invariance [1,2,3,4,5]. 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]. Acoustic [23, 24] and optical [25] beams with an extra azimuthal phase dependence exp(imφ ), called vortex beams, have a helicoidal wavefront and carry orbital angular momentum This feature of angular momentum transport allows the beam to exert a torque to rotate an object. In this paper we illustrate the application of an extended optical theorem on acoustic radiation forces and torques associated with a non-diffracting beam. The results, together with a prior result of an asymmetry factor of scattering, are applied to recover the axial radiation force and torque given in [10, 24]

Optical theorem of a non-diffracting beam

Application to extinction by a sphere

Application to the axial radiation force on a sphere

Application to the radiation torque on a sphere

Conclusions and discussion