“…In [11,12], the eigenvalues of a circular waveguide embedded in lossy surroundings were determined from the initial guess given by the high-frequency asymptotic analysis of the problem. The root-finding strategy employed in [57,80] starts out from the lossless eigenvalues of the structure. These eigenvalues lie on the coordinate axis and can be calculated with relatively little numerical effort [57] by using a root search along real (for propagating modes) and the imaginary axis (for evanescent modes).…”