An analytic extension to the nonparaxial regime of the full-Poincar (FP) beams is presented. Instead of the stereographic mapping used in the paraxial case, these FP fields are defined in terms of a mapping from the polarization Poincar sphere onto the sphere of plane-wave directions. It is shown that multipolar fields with complex arguments can be used to implement this mapping and provide closed-form expressions. The three-dimensional polarization singularities of the resulting fields are studied with the help of auxiliary fields presenting vortices at points where the polarization is circular or linear. Finally, the Mie scattering and trapping properties of the FP fields are studied, both of which are greatly simplified by the choice of fields.

提出了对全庞加莱 (FP) 梁的非旁轴区域的解析扩展。代替在近轴情况下使用的立体映射，这些 FP 场是根据从偏振庞加莱球到平面波方向球的映射来定义的。结果表明，具有复杂参数的多极场可用于实现此映射并提供封闭形式的表达式。借助于在极化为圆形或线性的点处呈现涡旋的辅助场，研究所得场的三维极化奇点。最后，研究了 FP 场的 Mie 散射和俘获特性，这两者都通过场的选择得到了极大的简化。