if any of the m or n in case of TM MODE becomes zero then all the field components vanishes. Hence the waveguide has no relevence with TM01, TM10 or TM00 modes.
Therefore TM11 is the lowest order mode of all TMmn modes.
For similer reasons TE00 mode can not propagate through the waveguide.
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Because it has the lowest cut-off frequency (highest cut off wavelength) for a>b o
A square waveguide does not allow single mode operation as for example fc(TEmn)=fc(TEnm).
circular is easy to manufacture than rectangular As the name indicates the circular is circular in shape and rectangular is rectangular in shape its uses same modes that is Te and Tm I know this much only hope this helped u little bit atleast A: In principle waveguides act as the equivalent of wires for high frequency circuits. For such applications, it is desired to operate waveguides with only one mode propagating inside of the waveguide. With rectangular waveguides, it is possible to design the waveguide such that the frequency band over which only one mode propagates is as high as 2:1 (i.e. the ratio of the upper band edge to lower band edge is 2). With circular waveguides, the highest possible band width allowing only a single mode to propagate is only 1.3601:1. I found it on Wikileaks.
TE10
Arif Ullah khan utman kheel this is because for conductor E parallel is zero this means that the surface of the wave guide is at equipotential and this potential follow the laplace equation .it means that there is no maxima and minima inside the wave guide . this means that the electric field inside zero . hence the TEM do not exist in wave guide only TE and TM can be exist . if we place some conductor in the wave guide then the conductor inside will not be equipotential and the TEM waves can be exist . like in Coaxial cables