Approximate formula of the lowest-order TM mode of a pentagonal waveguide family

Based on two inequalities, the upper and lower bounds of the cutoff wavenumber of the lowest-order TM mode of a pentagonal waveguide family are derived. By means of taking the geometric mean value, an approximate formula to calculate the cutoff wavenumber of the lowest-order TM mode of a pentagonal waveguide family is developed. It is the function of the cross section geometric parameters of the pentagonal waveguide. Comparisons between the results obtained by the approximate formula and the available numerical published data fully validate accuracy of the approximate formula.