he eh mode
a picture say more than words.
take a look at the plane normal to the propagating axis:
TEM: is the propagation mode for coax, stripline etc. it's a non-dispersive mode.
TE: in a waveguide, from a side to the opposite, E filed has 1 or more maximum and minimum.
TM: in a waveguide, from a side to the opposite, H describe 1 or more close circles
The number of maximum/minimum or circles are everytime an integer.
In waveguide, TE and TM are dispersive.
Into waveguide, surmoded propagation is generally unwanted.
HE and EH are hybrid modes. In this context, "Hybrid" means: combined with weighted amplitude and the correct phase. Some authors speaks about "balanced hybrid modes".
I.e. in circular waveguide, combining to TE11 a small portion TM11, you'll get HE11 that has the particularity to have E lines mutch more parallel than TE11.
This is very "good" mode to illuminate large antennas.
HE11 is generated (and propagate) into circular corrugated horn feeds and achieve the most advanced Xpol performances.
For more info, look IEEE papers by P.J.B. Clarricoats, or G.James