Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems

摘要： A ?exible and effective algorithm for complex roots and poles ?nding is presented. A wide class of analytic functions can be analyzed, and any arbitrarily shaped search region can be considered. The method is very simple and intuitive. It is based on sampling a function at the nodes of a regular mesh, and on the analysis of the function phase. As a result, a set of candidate regions is created and then the roots/poles are veri?ed using a discretized Cauchy’s argument principle. The accuracy of the results can be improved by the application of a self-adaptive mesh. The effectiveness of the presented technique is supported by numerical tests involving different types of structures, where electromagnetic waves are guided and radiated. The results are veri?ed, and the computational ef?ciency of the method is examined.