Modern CAD tools for waveguide networks use full wave analysis in electromagnetic field computations. Coaxial waveguides naturally serve as feeding lines and interconnecting elements. Since the modal field expansion in such waveguides is determined by their eigenvalue spectrum, it is necessary to possess algorithms capable of computing any desired number of eigenvalues in a fast way and with high numerical precision. Two algorithms for computing the TM and TE eigenvalues of a coaxial waveguide are introduced in this paper. They are based on interlacing properties of the zeros of Bessel function cross-products. The computation of the eigenvalues is directly performed by searching the zeros of these functions avoiding an indirection over a linear matrix eigenvalue problem and the related complications of unavoidable degradation of accuracy and the extraction of complete subsets.
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