Explanation:

• The walls of the waveguides can be considered as nearly perfect conductors.
• Therefore, the boundary conditions require that electric field be normal i.e., perpendicular, to the waveguide walls.
• The magnetic fields must be tangential i.e., parallel to the waveguide walls. Because of these boundary conditions a zero subscript can exist in the TE mode but not in the TM mode. For e.g., TE10, TE01, TE20, etc. modes can exist in a rectangular waveguide but only the TM11, TM12, TM21 etc. modes canexist.
• Also the cut-off frequency relationship shows that the physical size of the waveguide determinesthe propagation of modes depending on the values of m and n.
• The minimum cut-off frequency for a rectangular waveguide is obtained for a dimension a>b for m= 1 and n= 0, i.e., TE10 mode is the dominant mode for a rectangular waveguide.(Since for TMmn modes m# 0or n# 0, the lowest order mode TE10 is the dominant mode for a> b.)