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No, it is not possible to have both E and H have components in direction of propagation.
If z is direction of propagation and Ez and Hz denote the components of E and H in the direction of propagation, then for
TEM : Ez = 0 ; Hz =0 ( TEM modes do not exist in a waveguide, for TEM mode to propagate atleast two conductors should be present )
TE : Ez = 0 ; Hz exists
TM : Ez exists ; Hz = 0
The rough explanation is this one:
Imagine that the field is vertical. The two lateral metallic walls force a null of the electric field over this two walls. But the shape of the field is required to be sin/cosinusidal (from the wave equation in cartesian coordinates). Is imposible to fit a sinus/cosinus when two nulls are located at distance smaller than half a wavelength.
Sir, frankly speaking, i think this a very vague view....because acoording to this if the wave guide is even greater than half wavelentgh but samller than wavelentgh..
then how will it fit the negative part of th field..
and with another point of waves if assumed as photons...we have no restrictions upon the dimension criteria..?