Theoretical investigations on cutoff wave number of quad-polar waveguide

The hollow waveguides with angular deformation are widely used in high power millimeter wave system. In this manuscript, the cutoff wave number of the quad-polar waveguide with a boundary of is theoretically analyzed based on the perturbation analysis. Using the boundary condition and the orthogonal properties of the trigonometric functions, a determinant is obtained and then the exact closed-form expression of cutoff wave number is deduced from the determinant. Based on the cutoff wave number, the eigen field is calculated by nonlinear programming method. The values of the cutoff wavenumbers, eigen fields and surface currents for the first few modes are calculated and compared with the results obtained from simulation software. The high correspondence of the calculated values with the simulated results proves that the proposed method is an appropriate option for fast and precise analyzing quad-polar waveguides.