Pick a mode (TE10, TE20, …, TM11), set the guide dimensions a, b, and the operating frequency. The 2D cross-section shows the field pattern at the current time; the side view shows how the wave propagates (or evanesces) along z; the dispersion curve shows β(f) with the operating point marked. Drag f through the cut-off to see the field suddenly "wake up" and propagate.
Drag the frequency slider through fc to see the field "wake up" — below cut-off the mode is evanescent (decaying along z); above cut-off it propagates with wavelength λg.
① 2D cross-section — field pattern at the current (z, t)
The colored background shows |E| magnitude. Red arrows = E, blue arrows = H. The dominant TE10 mode has a single Ey lobe (vertical arrows, max at the center) and a single Hz loop.
E arrows (red, in cross-section) H arrows (blue, in cross-section) |E| background (low → high blue → red)
② Side view — Ey(z) at x = a/2, the center of the broad wall
Above cut-off: a propagating sinusoid with wavelength λg. Below cut-off: an evanescent decay exp(−α z) — the field amplitude collapses to zero as you move down the guide.
③ Dispersion — β(f) with cut-off marker
β = √(k² − kc²) above cut-off (square-root curve rising from fc); β = 0 below (mode is evanescent). The orange marker is the operating point.
Cut-off
fc
—
kc
—
λc
—
Status
—
Propagation
β (rad/m)
—
α (Np/m)
—
λg (mm)
—
vp (×10⁸ m/s)
—
vg (×10⁸ m/s)
—
Wave impedance + power
ηmode (Ω)
—
η0 = 377 Ω (free space)
377
⟨Pz⟩ (W, unit A)
—
⟨Pz⟩ (dB)
—
ηTE = η0·k/β > η0 (always above free-space impedance for a propagating TE mode). ηTM = η0·β/k < η0.