Waveguide modes
The wave we have chosen to analyze is a special solution of the field equations. There are many more. Each solution is called a waveguide “mode.” For example, our $x$-dependence of the field was just one-half a cycle of a sine wave. There is an equally good solution with a full cycle; then the variation of $E_y$ with $x$ is as shown in Fig. 24–14. The $k_x$ for such a mode is twice as large, so the cutoff frequency is much higher. Also, in the wave we studied $\FLPE$ has only a $y$-component, but there are other modes with more complicated electric fields. If the electric field has components only in $x$ and $y$—so that the total electric field is always at right angles to the $z$-direction—the mode is called a “transverse electric” (or TE) mode. The magnetic field of such modes will always have a $z$-component. It turns out that if $\FLPE$ has a component in the $z$-direction (along the direction of propagation), then the magnetic field will always have only transverse components. So such fields are called transverse magnetic (TM) modes. For a rectangular guide, all the other modes have a higher cutoff frequency than the simple TE mode we have described. It is, therefore, possible—and usual—to use a guide with a frequency just above the cutoff for this lowest mode but below the cutoff frequency for all the others, so that just the one mode is propagated. Otherwise, the behavior gets complicated and difficult to control.