Algorithm for locating complex zeros and poles with the use of border tracking on complex plane, and its application in dispersion characteristics calculation

This paper proposes a new algorithm, very efficient numerically, used for locating zeroes and poles of complex function. The algorithm starts from the regions on the complex plane, where the function evaluates values with different signs
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for either or both real and imaginary part. The algorithm runs through the path created by triangles, at whose vertices the function is evaluated. When analysing the signs of the function, the tracking directions are chosen along the border of two complex regions, where zeros/poles are further expected. Calculations of complex propagation coefficient for partially loaded cylindrical waveguide are given to show one of the possible applications of the proposed algorithm.