Hi, StopTigidare!
In practice, usually 2 types of WG feeds are used - both unbalanced due to coaxial cable nature which is mostly used to be a feeding line:
- probe. This basically excites E field and thus should be oriented in E-field peak of desired waveguide mode. Advatage is simplicity when built.
- "trapeze" (very close to loop mentioned by flatulent). It's usually more frequency-wide than probe and can cover all the band of dominant mode (in rect. WG 1:2 band TE10 - TE20). For good frequency response it should be carefully designed and optimized (you will need some cones when crossing from coaxial inner feed to trapeze).
Both of those feeds are well described in literature.
I have one project with trapeze transition in MWS, if you're interested, I can PM it to you.
I have also a nice MWS example of sector slotted 15dBi WG antenna.
BTW, why you are interested also in TM modes (or generally high-order ones)? They won't give you advantage in common applications...
Kind regards,
eirp