Optical forces on electric dipoles are usually expressed in terms of the incident electric field components. Gradient forces are then expressed in terms of the electric intensity gradient, while standard and nonstandard scattering forces are found to be physically coupled to contributions associated with both the Poynting vector and an additional term attached to the spin angular momentum of the incident light (spin-curl forces). In this work, we establish a rigorous and formal identification of the Rayleigh limit of the generalized Lorenz-Mie theory with the transverse forces in the Rayleigh limit of the dipole theory, thus complementing a previous work on longitudinal forces and evidencing the origin of spin-curl forces in terms of couplings between beam shape coefficients of distinct order and their relationship with what has recently been called nonstandard scattering forces.

电偶极子上的光学力通常用入射电场分量表示。然后用电强度梯度表示梯度力，而发现标准和非标准散射力在物理上耦合到与Poynting矢量和附加到入射光的自旋角动量的附加项相关的贡献（自旋卷曲力）。在这项工作中，我们用偶极子理论的瑞利极限中的横向力建立了对广义Lorenz-Mie理论的瑞利极限的严格和形式上的确定，