A new triangular element is proposed in the vector finite‐element solution of a dielectric waveguide. In the conventional finite‐element expression based on the three magnetic field components, each component is treated independently by continuous elements. The elements used in this paper are subject to the condition that the longitudinal field components are continuous between adjacent elements and the transverse components have tangential components continuous at the element boundary. In this method, as many zero eigenvalues as the number of unknowns of the longitudinal components are generated. However, all the remaining nonzero eigenvalues correspond to the physical modes and no spurious solutions typical in the conventional vector finite‐element solutions are generated. The present elements are suited for representation of the forced boundary conditions, and the analysis region can easily be applied to an arbitrary waveguide. To investigate the validity and effectiveness of the present method, it was applied to a hollow cylindrical waveguide, a dielectric loaded rectangular waveguide, an anisotropic refractive index dielectric waveguide, and a ferrite loaded square waveguide.
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Mitsuo Hano (1988) studied this question.