Optical binding with anisotropic particles: resolving the forces and torques

In the phenomenon known as optical binding, optical fields induce significant forces between microparticles of dielectric matter. Most experimental studies have centered on particles of spherical morphology, assumed to be isotropic and able to tumble freely in a fluid. However, when birefringent micro-crystals and anisotropic nanoparticles such as carbon nanotubes are held in an optical trap, it is essential to account for their orientation. These particles are susceptible not only to optical forces but also torques, and there is considerable interest in their response to light that conveys angular momentum - especially optical vortices. Before the full effects of such interactions can be fully understood, however, it is necessary to cultivate a thorough understanding of the rotational effects that operate in optical binding with conventional laser radiation. Here, the orienting effect of the radiation on each individual particle, as well as the orienting influences they exert on each other, need robust theory to account for partial alignment with the throughput radiation. The aim of this paper is to develop, from results based on quantum electrodynamics and perturbation theory, analytical expressions for the observables associated with pair-wise optical binding in anisotropic, non-polar particles. The intricacies of weighted rotational averaging and tensor analysis are tackled, deploying newly devised methods to resolve results into forms amenable to experimental application. Analyzing the resulting equations allows the identification of terms corresponding to specific properties of the considered particles, including terms reflecting the degree of anisotropy. It is then straightforward to recognize criteria for the validity of commonly held approximations.