Polarization ellipses in a nonparaxial field form twisted strips when traced along closed contours around a circular polarization singularity line. We found an analytical expression for the twist number of the strip when the contour is coplanar with the polarization ellipse in its center. Necessary and sufficient conditions for strips having one or three half-twists are found. A set of five parameters of electromagnetic field at the polarization singularity point is found which definitely determines the value of the twist number of the strip.

中文翻译：

---

确定非平面结构电磁场中光学莫比乌斯带的三重半扭转

当沿着圆偏振奇点线周围的闭合轮廓追踪时，非近轴场中的偏振椭圆会形成扭曲的条带。我们找到了当轮廓与其中心的偏振椭圆共面时条带扭曲数的解析表达式。找到了带材具有一圈或三圈半捻的充分必要条件。找到了极化奇点处电磁场的一组五个参数，这些参数明确地决定了带材的扭转数的值。