Calculators › Transmission Lines

Waveguide Mode Visualizer

Pick a TE or TM mode and watch its field pattern move down the guide — the transverse E-field in cross-section, and the H-field / wall surface-current pattern on the broad (top) and narrow (side) walls. Set a frequency below cutoff to see the mode decay as an evanescent field instead of propagating.

Waveguide & Mode
Quick mode select
Mode type
m / n
/
⚠ TM: m≥1, n≥1. TE₀₀ invalid.
Waveguide dimensions
Broad Wall a
mm
Narrow Wall b
mm
Fill εr
—
Operating frequency
Frequency f
WR presets
Cutoff & Propagation
—
Mode—
Cutoff Freq (fc)—GHz
Operating f—GHz
f / fc ratio—
Guide Wavelength λg—mm
Playback
Speed
Instantaneous phase ωt — all three views below are the same instant
Cutoff & propagation
fc=(c/2π√εr)·kc,   kc=√((mπ/a)²+(nπ/b)²)
f>fc: β=√(k²−kc²) → travelling wave, λg=2π/β
f<fc: α=√(kc²−k²) → evanescent, decays as e^(−αz)
Mode Field Animation — TE₁₀

The small box next to each title shows exactly which face of the guide you're looking at (highlighted in cyan). All three views below update together, frozen at the same instant.

Field direction & strength (longer = stronger)
Background colour = sign of the longitudinal field (cyan +, red/pink −)
Amber fade = evanescent decay along z (δ = 1/α decay length; only shown below cutoff)
Cross-Section (End View)
E-field (arrows) + Hz (background colour: cyan +, red −)
Top Wall — Broad Wall (a)
Surface current / H-field looking down at y=0, along the guide axis z
Side Wall — Narrow Wall (b)
Surface current / H-field looking at x=0, along the guide axis z
Need the numbers too?

This page is the visual/intuition tool. For wave impedance, phase & group velocity, and exact numeric values, use the full calculator:

📐 Rectangular Waveguide Calculator →

Visualizing Waveguide Modes

A rectangular waveguide can carry infinitely many field patterns, or modes, each labelled TEmn or TMmn. The indices m and n count how many half-cycles the field completes across the broad wall (a) and narrow wall (b) respectively. Every mode has its own cutoff frequency — below it, the mode cannot propagate at all and instead decays exponentially along the guide as an evanescent field. Above cutoff, the pattern travels down the guide at the guide wavelength λg, unchanged in shape.

Why look at the top and side walls?

The transverse E-field picture in cross-section is the one every textbook shows, but it only tells half the story. The tangential H-field on the inside of the broad and narrow walls is exactly equal to the surface current density there (Js = n̂ × H) — it's the pattern that determines where you can safely cut a slot in the wall for a slot antenna or a directional coupler without disturbing the mode, and why TE10 forms the closed current loops you'll see in any waveguide slot-antenna textbook figure.

Above vs. below cutoff

Set the operating frequency below the mode's cutoff frequency (fc) and the top and side wall patterns stop travelling — instead you'll see the field pulse in place while its amplitude dies away along z. That's the direct, visual meaning of "evanescent": the mode still exists as a solution to Maxwell's equations inside the guide, it just can't carry energy away from where it was launched.