Global Complex Roots and Poles Finding Algorithm in C × R Domain

An algorithm to find the roots and poles of a complex function depending on two arguments (one one real) is proposed. Such problems are common in many fields science for instance electromagnetism, acoustics, stability analyses, spectroscopy, optics, elementary particle physics. The proposed technique belongs class global algorithms, gives full picture solutions fixed region Ω ⊂ C × R can be very useful preliminary analysis problem. represented as curves this domain. It an efficient alternative not only plane zero search algorithms (which require multiple calls different values additional real parameter) but also tracking algorithms. developed based generalized Cauchy Argument Principle Delaunay triangulation three-dimensional space. usefulness effectiveness method demonstrated several examples concerning guides (Anti-Resonant Reflecting Acoustic Waveguide, coaxially loaded cylindrical waveguide, graphene transmission line) resonant structure (Fabry-Pérot open resonator).