A finite element analysis of TE modes in twisted waveguides

The scalar Helmholtz equation is solved by the use of finite element methods to analyze the TE mode in the twisted waveguide. For this purpose, on the basis of the weighted residual method, a two-dimensional integral equation described in the twisted coordinates is introduced by reducing that in the general curvilinear coordinates. After the finite-element formulation, it is shown that the numerical solution monotonously converges with an increase in the number of nodes. Moreover, the cut-off constant and the dispersion relation calculated by the present scheme are shown to be in good agreement with those calculated by the perturbation method. Some comments are offered on the TE mode distributions in a twisted rectangular waveguide and on the influence of the shift of the waveguide on those distributions.