TEM waves do not exist in waveguide. Is this the correct explanation- Both curl and divergence of TEM are zero inside the waveguide and because of the boundary conditions (electric field zero at every point of a hollow conductor), the only solution possible is zero i.e. trivial?
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TEM waves do exist in multi-conductor waveguides such as coaxial guides, in fact they exist in any homogeneous waveguide with more than one conductor. There are no propagating TEM, TE or TM modes if the cross section is inhomogeneous but at cutoff frequency the hybrid modes degenerate to the respective transversal modes.
