Nonpropagating mode at waveguide cutoff ($k_x=0,v_g=0$)

For a membrane waveguide branch ${\omega }^2=v^2[k_x^2+(n\pi /b{)}^2]$, the exact cutoff has zero longitudinal wavevector and zero group velocity. It is not a traveling channel carrying finite longitudinal energy flux. Modes strictly below cutoff are evanescent; amplitudes of the permitted above-cutoff modes depend on the transverse excitation profile.