Analytical calculation for cutoff wavenumbers of metallic waveguides with elliptical-circular and circular-elliptical cross section

The cutoff wavenumbers of the elliptical-circular and circular-elliptical metallic waveguides are calculated accurately through closed-form expressions. These analytical expressions give accurate results for the cutoff wavenumbers when the eccentricity of the elliptical boundary is specialized to small values. The resulted formulas are free of Mathieu functions, including only algebraic expressions with Bessel functions. The expressions are valid for every different value of the indices n and m, corresponding to every higher-order TM or TE mode. Numerical results are given for various higher-order modes, as well as a comparison with the exact solution.