New approach to plot polarization singularity lines of electromagnetic fields in nonparaxial optics

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.