EE 499 · Week 7 · Engineering view
Watch a Waveguide Mode Move
One mode, one rectangular guide, and the electric and magnetic fields drawn as vectors that you can watch evolve in space and in time. It draws the dominant TE10 mode of a rectangular guide, and lists the other modes the guide can carry at the chosen frequency.
Part of Week 7 · Fields Inside the Waveguide. New to waveguides? Start with the simplified 3D Waveguide Field Explorer →
Rectangular waveguide · TE10
Above cutoff — propagating- Cutoff fc
- GHz
- f / fc
- β
- rad/m
- α (decay)
- Np/m
- Free-space λ
- mm
- Guided λg
- mm
- Phase velocity
- Group velocity
Travelling wave. The pattern in the cross-section keeps its shape, and the whole field pattern advances along +z: watch the crests in the lower plot move to the right. The phase velocity vp = ω/β is faster than c; that is a speed of pattern, not of energy. Energy and information move at the group velocity vg, which is slower than c. Ey and Hx rise and fall at the same instant (with opposite signs, because E × H must point along +z), so power flows.
At cutoff, β = 0. Nothing advances along z and the fields are the same in every cross-section: the wave simply bounces between the two side walls (a transverse resonance). Ey and the magnetic field are 90° apart in time, so no net power flows. The magnetic field is purely longitudinal (Hz) here, and the guided wavelength is infinite. This is the limiting field pattern as f → fc.
Evanescent, not propagating. The pattern oscillates in time but never travels: the profile along z is a fixed decaying curve that rises and falls in place. The amplitude falls as e−αz. E and H are 90° apart in time, so the time-averaged power flowing along z is zero. Energy is stored in the field, not transmitted by it.
Other modes can propagate here. At this frequency the next mode is also above its cutoff, so a real guide would not be single-mode. This explorer is showing TE10 only.
TE10 is not the dominant mode for these dimensions (b is larger than a). A lower-cutoff mode exists.
Reduced-motion setting detected. The animation starts paused. Press Play, or drag the phase slider, to step through the cycle.
Modes of this guide, by cutoff
- Dominant mode
- Single-mode interval
- Next mode after the dominant
- Axial window shown
- mm
- Attenuation below cutoff
- dB/m
- Perfectly conducting walls and an air-filled, lossless guide, so there is no attenuation above cutoff.
- Arrow length is proportional to field magnitude, and E and H are each scaled to their own peak over the cross-section at z = 0, so each longest arrow is 1. E and H sizes cannot be compared with each other.
- Each arrow shows the instantaneous field at one point and one moment. Arrows in an axial view show only the components lying in that plane; the third component is the dot or cross.
- The animation shows the phase ωt in slow motion. A real X-band field completes 1010 cycles each second.
- One field pattern at one amplitude is drawn. Nothing here shows how the guide is excited.