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The most easy exitable mode is TE11. It's the most "robust" to unwanted modes and you may acheive a moderate BW.
TE11 may be exited by a E probe perpendicular to the sidewall (from a coax connector) or by an rectangular to circular transformer from the back wall (from a WR).
About the loss: the TE11 is a moderately low loss mode.
The lowest loss mode, TE01, is nearly impossible to exite, only few factories around the world produce launchers and only for narrow BW.
As you asked, I'll share some pictures of some Waveguide Circular feeding.
Unfortunately i cannot provide the dimensions, but as you may see the tapered version are 1 or more Lambda long, the step version has every step lamda/4 long.
For the design a Mode Matching code is the best, also HFSS may be used.
But... if you understand the concept... the pocket calculator may be enough.
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