 Waveguide cutoff frequency

For a transverse electric mode of a rectangular waveguide, the dispersion relation is ${\omega }^2=c^2(k^2+{\kappa }_{mn}^2)$, with ${\kappa }_{mn}^2=(m\pi /a{)}^2+(n\pi /b{)}^2$. Below ${\omega }_{mn}=c{\kappa }_{mn}$, the longitudinal wave number is imaginary and the mode is evanescent. If $a\ge b$, the lowest propagating cutoff is ${\omega }_{10}=\pi c/a$, or ordinary frequency $c/(2a)$.