In a circular waveguide the dominant mode is

Some applications require dual polarization capability. Circular waveguide has this capability.

These analysis uses cylindrical coordinates.

In circular waveguide TE₁₁ mode has the lowest cut off frequency and is the dominant mode.

If D is diameter of waveguide

λ_c = 1.706 D for TE₁₁ mode

λ_c = 1.029 D for TE₂₁ mode

λ_c = 0.82 D for TE₀₁ mode

λ_c = 1.306 D for TM₀₁ mode.