Analysis of the waveguide with loss or gain by the finite‐element method

In the past the finite-element method with a variational formulation has been used for numerical analyses of the propagation characteristics of electromagnetic waveguides. However, this method based on the variational representation is not applicable to waveguides with losses or gains. This paper derives a generalized Galerkin equation which is established for waveguides with losses or gains. The finite-element method is proposed based on this Galerkin equation. As examples of numerical calculations, a waveguide loaded with a lossy dielectric, a helical waveguide and a microstrip line were analyzed.