How to identify TE and TM modes in rectangular waveguides

[reddvoid]

How to identify type of wave-guide mode here, like its TE or TM
TE01 , TE10, TM11, TE02, TE20 . ..
I read number of half wavelengths in x direction is the m and number of half-wavelengths in y direction is n. . .but I can't figure-out how . . .can somebody please explain

 

[the_emi_guy]

Try to find a better reference. I'm sure there must be some on the "net".

You are describing circular waveguide modes.
The first index denotes the number of variations circumferentially, the second index denotes the number of variations radially.

Your diagram shows the waveguide viewed from the side, only z-axis and radial variations are visible.

The TM11 guide will have variation in fields circumferentially, which is not visible in your diagram. The diagram is a view only at one specific rotational orientation.