Rectangular Waveguide – TEmn Mode Visualizer
Interactive field plots for arbitrary TE modes with propagation along +z.
Electric Field (E) – Cross‑section (xy‑plane)
Arrows show (Ex, Ey) direction & magnitude. Red = high intensity.
Magnetic Field (H) – Cross‑section (xy‑plane)
Arrows show (Hx, Hy) direction & magnitude. Blue = high intensity.
E‑field in x‑z plane (y = b/2)
Horizontal arrows: Ex (in‑plane). Color: total |E| intensity.
H‑field in x‑z plane (y = b/2)
Arrows: (Hx, Hz) in plane. Color: total |H| intensity.
E‑field in y‑z plane (x = a/2)
Vertical arrows: Ey (in‑plane). Color: total |E| intensity.
H‑field in y‑z plane (x = a/2)
Arrows: (Hy, Hz) in plane. Color: total |H| intensity.
Surface Current Density (Js) on Top Wall (y = b)
Color intensity: magnitude of Js (red = high).
📐 TEmn Field Equations
Ey = -jωμ (mπ/a) H0 sin(mπx/a) cos(nπy/b) e-jβz / kc2
Hx = -jβ (mπ/a) H0 sin(mπx/a) cos(nπy/b) e-jβz / kc2
Hy = -jβ (nπ/b) H0 cos(mπx/a) sin(nπy/b) e-jβz / kc2
Hz = H0 cos(mπx/a) cos(nπy/b) e-jβz
Cutoff wave number: kc = √[(mπ/a)² + (nπ/b)²]
Cutoff frequency: fc = c kc / (2π)
Propagation constant: β = √[k² - kc²] (real above cutoff)
📝 Description & Applications
Rectangular waveguides support TEmn and TMmn modes. TE10 is the dominant mode with lowest cutoff. Higher‑order modes allow more complex field patterns and are used in mode converters, filters, and multi‑mode systems.
Applications: High‑power microwave transmission, radar feed networks, satellite communications, particle accelerators.
Advantages: Low loss, high power handling. Disadvantages: Large size at lower frequencies, dispersion.
Limitation: Single‑mode bandwidth limited by next higher mode cutoff.