Parallel_plate waveguide with sinusoidally perturbed boundaries

The method of multiple scales is used to obtain a uniformly valid asymptotic expansion for the propagation of TM modes on a parallel_plate waveguide with perfectly conducting boundary surfaces that are sinusoidally perturbed in the direction of propagation. The analysis shows that resonance occurs whenever the wave number of the wall distortion function is equal to the difference between the wave numbers of two propagating modes. It is further shown that the generated mode is the same order of magnitude as the excited mode due to resonance and that energy is continuously exchanged between the two modes as they propagate down the guide.