Evaluation of the Dispersion Diagram of Inhomogeneous Waveguides by the Variational Meshless Method

This paper presents an extension of the variational meshless method to the calculation of the dispersion diagram of metallic waveguides including inhomogeneous dielectric regions. The method is based on the combination of the variational formulation of a 2-D boundary problem and of the meshless method using radial basis functions. The problem requires a vector representation of the field, and it leads to a well-conditioned, real, and symmetric eigenproblem, where the matrices depend on the propagation constant β. By solving the eigenproblem for several values of β, a spurious-free dispersion diagram of the guiding structure is obtained. Several structures are studied to demonstrate the accuracy and reliability of the proposed technique. The simulation results are compared with the analytical ones, when available, and with those given by a commercial FEM code, always showing a very good agreement with a smaller number of unknowns.