Waveguide cutoff frequency
= Waveguide cutoff frequency
{title2=$\omega_{mn}=c\pi\sqrt{m^2/a^2+n^2/b^2}$}
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 $c/(2a)$.