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.

中文翻译：

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双向反向传播高斯光束对单轴各向异性球的辐射力分析。

基于麦克斯韦应力张量和广义的Lorenz-Mie理论，引入了一种理论方法来研究施加在双对向传播（CP）高斯光束照射下的单轴各向异性球体上的辐射力。光束以任意方向传播，并使用SVWF的坐标旋转定理在粒子坐标系中根据球面矢量波函数（SVWF）进行扩展。通过矢量场的叠加可以得出入射场的总扩展系数。利用麦克斯韦应力张量分析，得到了均匀吸收单轴各向异性球体上的辐射力的解析表达式。通过将还原后的各向异性球体的辐射力与各向同性球体的特殊情况进行比较，可以验证该理论的准确性。为了研究平衡状态，详细讨论了光束参数，粒径参数和各向异性参数对辐射力的影响。与各向同性粒子相比，平衡状态对各向异性参数敏感。此外，比较了单个高斯束阱和高斯驻波阱中单轴各向异性球体上的光学力特性。这表明CP高斯束阱可以更容易地捕获或限制各向异性粒子。但是，当光束不沿主光轴传播时，施加在各向异性球体上的辐射力会表现出非常不同的特性。各向异性参数对CP高斯光束的辐射力的影响与单个高斯光束的影响不同。总之，即使对于各向异性粒子，与单个高斯束阱相比，高斯驻波阱也显示出显着的优势。双高斯光束施加在单轴各向异性球体上的辐射力的理论预测提供了有效的方法，可实现对光镊的改进以及对各向异性粒子的捕获，悬浮和高精度传递。