Waveguide TE/TM Mode Dispersion

Rectangular waveguide — cutoff frequencies and dispersion curves

TE modes
TM modes
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Physics: In a rectangular waveguide of width a and height b, electromagnetic modes are labeled TEmn (transverse electric) or TMmn (transverse magnetic). Each mode has a cutoff frequency fc = (c/2π)√[(mπ/a)² + (nπ/b)²], below which the mode is evanescent. Above cutoff, the dispersion relation is β² = (ω/c)² − (mπ/a)² − (nπ/b)², giving a hyperbolic curve. TE10 (m=1, n=0) is the dominant mode with the lowest cutoff. TM modes require both m≥1 and n≥1.