A waveguide is a structure that causes a wave to propagate in a chosen direction. It is accomplished by an intimate connection between the fields of the wave and the currents and charges on the boundaries, or by some condition of reflection at the boundary.

Various higher order modes can propagate in either rectangular or circular guiding structures. The TE10 mode is the dominant mode in a rectangular waveguide and represents the lowest order mode the waveguide is capable of supporting.

In waveguides the electric and magnetic fields are confined to the space within the guides. Thus no power is lost to radiation. Since the guides are normally filled with air, dielectric losses are negligible. However, there is some power lost to heat in the walls of the guides, but this loss is usually very small.

It is possible to propagate several modes of electromagnetic waves within a waveguide. The physical dimensions of a waveguide determine the cutoff frequency for each mode. If the frequency of the impressed signal is above the cutoff frequency for a given mode, the electromagnetic energy can be transmitted through the guide for that particular mode with minimal attenuation. Otherwise the electromagnetic energy with a frequency below cutoff for that particular mode will be attenuated to a negligible value in a relatively short distance. This grammatical use of cutoff frequency is opposite that used for coaxial cable, where cutoff frequency is for the highest useable frequency. The dominant mode in a particular waveguide is the mode having the lowest cutoff frequency. For rectangular waveguide this is the TE10 mode. The TE (transverse electric) signifies that all electric fields are transverse to the direction of propagation and that no longitudinal electric field is present. There is a longitudinal component of magnetic field and for this reason the TEmn waves are also called Hmn waves. The TE designation is usually preferred. Figure 4 shows a graphical depiction of the E field variation in a waveguide for the TE10, TE10, and TE30 modes.

As can be seen, the first index indicates the number of half wave loops across the width of the guide and the second index, the number of loops across the height of the guide - which in this case is zero. It is advisable to choose the dimensions of a guide in such a way that, for a given input signal, only the energy of the dominant mode can be transmitted through the guide. For example, if for a particular frequency, the width of a rectangular guide is too large, then the TE20 mode can propagate causing a myriad of problems. For rectangular guides of low aspect ratio the TE20 mode is the next higher order mode and is harmonically related to the cutoff frequency of the TE10 mode. It is this relationship together with attenuation and propagation considerations that determine the normal operating range of rectangular waveguide.

Figure 4 - TE waveguide modes
(EW and Radar Systems Engineering Handbook)
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