Computing Eigenvalues of Dielectric Waveguides by a Method of Auxiliary Sources With Two Excitation Sources

The Method of Auxiliary Sources with an Excitation Source (MAS-ES) has been successfully employed to compute the eigenvalues of arbitrarily-shaped, simply and multiply-connected hollow waveguides with perfectly electric conducting (PEC) walls. The main advantages of this method are its simplicity, and that it is free of spurious eigenvalues, in contrast to the standard MAS approach. In this paper, we demonstrate that the MAS-ES is also effective in computing the propagation constants (eigenvalues) $\beta$ of a cylindrical dielectric waveguide with core of arbitrary cross section. It is emphasized that two excitation sources (an electric and a magnetic current filament lying within the core) are required to excite hybrid modes of the dielectric waveguide; a hollow PEC waveguide requires only one source. The modified method, thus obtained, is named MAS with Two Excitation Sources (MAS-TES). The fact that the propagating modes are localized in the vicinity of the core allows us to determine the eigenvalues by measuring the response of the core to the excitation sources. This is performed by employing a response function $F(\beta)$ which is maximized when a standing wave is formed in the core. Plotting $F(\beta)$ for a dense set of $\beta$ results in a response curve the peaks of which correspond to the waveguide’s eigenvalues. The method is tested for several dielectric waveguides’ geometries, including two multimode cases, and it is shown to be free from discrete and continuous spurious solutions. All the MAS-TES results are compared with those obtained by an FEM-based commercial software and an excellent agreement is exhibited.