TE10 is the dominant mode in rectangular waveguide. The subscripts m=1, n=0 indicate one half-wave variation of the electric field across the broad wall (width a) and zero variation across the narrow wall (height b). The cutoff frequency is fc = c/(2a), depending only on the broad dimension. For WR-90 waveguide (a = 22.86 mm): fc = 6.56 GHz. The usable single-mode bandwidth extends from fc(TE10) to fc(TE20) = c/a, giving a 2:1 frequency ratio. For WR-90: 6.56 to 13.12 GHz, with the recommended operating range of 8.2 to 12.4 GHz (X-band) to avoid excessive dispersion near cutoff and potential higher-mode excitation near the TE20 cutoff.

What is the difference between TE and TM modes?

TE (Transverse Electric) modes have Ez = 0 with a longitudinal Hz component. TM (Transverse Magnetic) modes have Hz = 0 with a longitudinal Ez component. Both mode families can propagate in rectangular and circular waveguides above their respective cutoff frequencies. In rectangular waveguide, TEmn modes exist for all m,n except m=n=0, while TMmn modes require both m and n to be non-zero (TM11 is the lowest TM mode). The dominant mode TE10 has the lowest cutoff of any mode, which is why rectangular waveguide dimensions are chosen so only TE10 propagates in the operating band. In circular waveguide, the dominant mode is TE11. TEM modes (both Ez=0 and Hz=0) cannot exist in hollow waveguides and require two conductors (coax, stripline).

How is the TE10 field distributed?

The TE10 electric field is purely y-directed (vertical across the narrow wall) and varies as sin(pi x/a) across the broad wall, with zero at the sidewalls and maximum at the center. The magnetic field has both x and z components: Hx varies as sin(pi x/a) (in-phase with Ey) and Hz varies as cos(pi x/a) (zero at center, maximum at walls). The wall currents flow on all four walls. On the broad walls, current flows in both x and z directions. On the narrow walls, current flows only vertically. The current pattern determines where slots can be cut for slot antennas and where the waveguide can be split without disrupting the mode. The TE10 mode has the lowest attenuation of any mode because the wall currents decrease with frequency above cutoff.

Waveguide Mode

TE Mode

/tee-ee/ — Transverse Electric (H-mode)

E_z = 0: electric field entirely transverse to propagation. H field has longitudinal component. TE_mn: m,n = half-wave variations across width (a) and height (b). Dominant TE₁₀: f_c = c/(2a), one half-sine E-field across broad wall. WR-90: f_c=6.56 GHz, operates 8.2-12.4 GHz (X-band). Single-mode BW: f_c to 2f_c (2:1 ratio). TE vs TM: TM requires both m,n ≠ 0.

Dominant: TE₁₀

f_c: c/(2a)

BW: 2:1

Understanding TE Modes

TE modes are the most commonly used propagation modes in rectangular waveguide systems. The defining characteristic is that the electric field lies entirely in the transverse plane (perpendicular to the direction of wave travel), with no longitudinal E-field component. This means E_z = 0 everywhere inside the waveguide. The magnetic field, however, has both transverse and longitudinal components, which is why TE modes are also called H-modes in European literature.

The TE₁₀ mode is by far the most important: it has the lowest cutoff frequency of any mode in rectangular waveguide, making it the dominant mode. Standard waveguide dimensions are chosen so that only TE₁₀ propagates in the operating band, ensuring single-mode operation. Higher-order modes (TE₂₀, TE₀₁, TE₁₁) are evanescent (non-propagating) below their cutoff frequencies and are deliberately suppressed.

TE Mode Equations

Cutoff frequency (rectangular):
f_c,mn = (c/2)√((m/a)²+(n/b)²)
TE₁₀: f_c = c/(2a)
TE₂₀: f_c = c/a = 2×f_c10
TE₀₁: f_c = c/(2b)

Guide wavelength:
λ_g = λ₀/√(1−(f_c/f)²)
Always longer than free-space λ

Wave impedance (TE):
Z_TE = η/√(1−(f_c/f)²)
η = 377Ω (free space)
Z_TE > 377Ω always

TE Mode Cutoff Order (WR-90)

Mode	f_c (GHz)	f_c/f_c10	m,n	Status in X-band
TE₁₀	6.56	1.00	1,0	Propagating (dominant)
TE₂₀	13.12	2.00	2,0	Evanescent
TE₀₁	14.76	2.25	0,1	Evanescent
TE₁₁/TM₁₁	16.16	2.46	1,1	Evanescent
TE₂₁	19.75	3.01	2,1	Evanescent

Common Questions

Frequently Asked Questions

What is TE10?

Dominant mode: m=1 (one half-sine across width a), n=0 (uniform across height b). f_c = c/(2a). WR-90 (a=22.86 mm): fc=6.56 GHz. Operates 8.2-12.4 GHz. E-field: sin(πx/a) across broad wall, zero at sidewalls, max at center. Lowest attenuation of any mode.

TE vs TM?

TE: Ez=0, Hz≠0 (H-mode). TM: Hz=0, Ez≠0 (E-mode). TE exists for all m,n except m=n=0. TM requires both m,n≠0 (TM11 lowest). Dominant mode is always TE (TE10 rectangular, TE11 circular). TEM (Ez=Hz=0): impossible in hollow waveguide, needs two conductors (coax).

TE10 field pattern?

Ey = sin(πx/a): zero at sidewalls, max at center. Hx = sin(πx/a), Hz = cos(πx/a). Wall currents on all 4 walls. Broad walls: x+z currents. Narrow walls: vertical only. Current pattern determines slot antenna placement and where waveguide can be split. Lowest-loss mode.

Related Terms

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Waveguide Systems

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