Rectangular Waveguide Modes
A hollow rectangular waveguide carries only discrete TE and TM modes. Each has a cutoff frequency $f_c = (c/2)\sqrt{(m/a)^2 + (n/b)^2}$; above it the mode propagates at the guide wavelength $\lambda_g = 2\pi / \beta$ (longer than free space), below it $\beta$ is imaginary and the field is evanescent, carrying no power. The primary scene is physical: the transverse field map of the chosen mode in the $a \times b$ cross-section and a longitudinal strip showing the wave travelling down the guide or decaying when below cutoff. The side panel is the mode-cutoff spectrum with the operating frequency, so single-mode operation is visible.
WHAT TO TRY
- Raise the frequency past a mode cutoff (blue on the spectrum) and it begins to propagate; below cutoff it is evanescent and dies away. Only modes left of the operating line carry power.
- Watch the guide wavelength lambda_g stretch as you approach the TE10 cutoff: the wave slows along the guide and its wavelength diverges right at cutoff.
- Widen the guide and the cutoff frequencies drop, letting more modes through, the bandwidth-versus-single-mode trade-off at the heart of microwave plumbing.