An Auxiliary-Current Vector Norm Method for Computing the Cutoff Wavenumbers of Anisotropic Waveguides

In this work, the auxiliary-current vector norm (ACVN)-based method of auxiliary sources (MAS) is extended and employed for the computation of the cutoff wavenumbers (or eigenvalues) of arbitrarily shaped, perfectly electric conducting (PEC) waveguides, having anisotropic permittivity and permeability infills. To solve the problem, the cross-sectional domain of the anisotropic waveguide is excited by a line-source current. Then, the eigenvalues are extracted as the wavenumbers for which the ACVNs are maximized. We prove analytically that, in the special case of the circular problem with gyrotropic anisotropy, the poles of the auxiliary sources (ASs) amplitudes are given by the roots of the exact characteristic equations derived by the separation of variables method (SVM). We compare and validate the MAS-ACVN, for TE/TM and hybrid HE/EH modes, for uniaxial and gyroelectric infills, with the SVM and with a coupled-field volume integral equation (CFVIE) formulation for circular waveguides, as well as with the high-frequency structure simulator (HFSS) commercial software for noncircular cross sections featuring concentric/eccentric inhomogeneous profiles. The computational performance of the method is also discussed. Finally, we demonstrate the applicability of the MAS-ACVN on the cutoff frequency determination of dispersive ferrite-loaded waveguides.