2.5 Propagation below the cutoff frequency

It was stated above that the electromagnetic wave propagates in a waveguide at a chosen waveguide mode only if its frequency is above the cutoff. In this part of the tutorial, the behaviour of an electromagnetic wave at a frequency below cutoff value will be investigated.

The below relations describes a propagation constant in case of lossless medium filling the waveguide:

If we consider a wave at a frequency below a cutoff value, the propagation constant is a complex number defined as follows:

Thus the propagation constant becomes strictly imaginary, what means that the wave inside the waveguide will be attenuated. This can be confirmed with wr340_1GHz.QWpro project. In this scenario the excitation frequency is set to 1 GHz. As it was calculated earlier in this tutorial, the cutoff frequency for the dominant TE₁₀ mode in WR-340 waveguide equals to 1.73 GHz, which means that in the considered case the waveguide is excited at the frequency below cutoff value. To investigate this phenomenon, run the electromagnetic simulation in QuickWave. Open field visualisation window using . In this case, for better visualisation the field envelope calculation has been enabled (by pressing ‘E’ button on the keyboard – for dynamic field observation ‘E’ button should be pressed). The display as in Fig. 20 should be seen.

Fig. 20 Ez component of electric field for TE10 mode in WR-340 waveguide at 1GHz

It is clearly seen that the envelope of Ez component rapidly decreases along the waveguide. The field amplitude is proportional to e^-^a^z ^z value.