The mode in a rectangular waveguide which has the lowest cut-off frequency is called a dominant mode. For rectangular waveguide, the dominant mode is TE10 , which is the lowest possible mode. Whereas, two or more modes having same cut-off frequency but different field configuration are called degenerate modes.
TE denotes the Transverse Electric modes of a waveguide. Here, the electric field vector will be always perpendicular to the direction of propagation.
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