In this work, we suggest a new algorithm for plotting the singularity lines of an electromagnetic field, which uses its derivatives in a certain area of space and the position of a single point belonging to an unknown singularity line. This algorithm is based on the common properties of rationally parameterizable curves. The implementation of this method is capable of plotting these lines significantly faster and with higher precision, as compared with ordinary methods. The advantages of the suggested method are illustrated by comparing the results of its application in problems of light–matter interaction, in which singularity lines are plotted using both the suggested algorithm, and ordinary algorithms.

中文翻译：

---

非旁轴光学中绘制电磁场极化奇异线的新方法

在这项工作中，我们提出了一种用于绘制电磁场奇异线的新算法，该算法在空间的特定区域中使用其导数，并使用属于未知奇异线的单个点的位置。该算法基于合理可参数化曲线的共同属性。与普通方法相比，该方法的实现能够更快，更精确地绘制这些线。通过比较其在光-物质相互作用问题中的应用结果，说明了所建议方法的优势，在该问题中，使用所建议算法和普通算法绘制了奇异线。