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

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.