A new spin on Ashkin's laser trapping forces in the ray optics regime

Abstract

We repeat the derivation of the forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime as first reported by Ashkin; in this case, however, we investigate the impact of partial absorption of light by the sphere on these trapping forces. Our model indicates that the effect of absorption is to reduce the axial and transverse trapping forces as a function of absorption, as well as changing the axial trap position. The trap stiffness is predicted to remain relatively unchanged even for high levels of absorption. The model also predicts that a rotational force is imparted on the sphere as a consequence of absorption. The torque associated with a single ray is first derived, which is shown to increase as a function of both absorption, radius, and the angle of incidence. This enables a derivation of the torque acting on a trapped sphere as it is laterally displaced from the trapping position, which is found to increase linearly with respect to the transverse displacement of the sphere. The torque is derived to be zero for the case of no absorption, and also for the case of axial displacement of the sphere, regardless of absorption. The model reduces exactly to Ashkin's model for the case of zero absorption.