Analysis of radiation force on a uniaxial anisotropic sphere by dual counter-propagating Gaussian beams

Based on Maxwell's stress tensor and the generalized Lorenz-Mie theory, a theoretical approach is introduced to study the radiation force exerted on a uniaxial anisotropic sphere illuminated by dual counter-propagating (CP) Gaussian beams. The beams propagate with arbitrary direction and are expanded in terms of the spherical vector wave functions (SVWFs) in a particle coordinate system using the coordinate rotation theorem of the SVWFs. The total expansion coefficients of the incident fields are derived by superposition of the vector fields. Using Maxwell stress tensor analysis, the analytical expressions of the radiation force on a homogeneous absorbing uniaxial anisotropic sphere are obtained. The accuracy of the theory is verified by comparing the radiation forces of the anisotropic sphere reduced to the special cases of an isotropic sphere. In order to study the equilibrium state, the effects of beam parameters, particle size parameters, and anisotropy parameters on the radiation force are discussed in detail. Compared with the isotropic particle, the equilibrium status is sensitive to the anisotropic parameters. Moreover, the properties of optical force on a uniaxial anisotropic sphere in a single Gaussian beam trap and Gaussian standing wave trap are compared. It indicates that the CP Gaussian beam trap may more easily capture or confine the anisotropic particle. However, the radiation force exerted on an anisotropic sphere exhibits very different properties when the beams do not propagate along the primary optical axis. The influence of the anisotropic parameter on the radiation force by CP Gaussian beams is different from that of a single Gaussian beam. In summary, even for anisotropic particles, the Gaussian standing wave trap also exhibits significant advantages when compared with the single Gaussian beam trap. The theoretical predictions of radiation forces exerted on a uniaxial anisotropic sphere by dual Gaussian beams provide effective ways to achieve the improvement of optical tweezers as well as the capture, suspension, and high-precision delivery of anisotropic particles.