As we can see below, the theory says that A,B coefficients depend on the excitation.
I have simulated a circular waveguide.
How do I need to excite my waveguide so I will see the A and B coefficients of the field change?
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Well, this sounds like it might be a homework problem, so I'll let you figure out a few more things: your field equations aren't just for the TE11 mode, but for a general n, and you haven't said what kc*rho is at the wall. One of your E components has to be zero at the wall, correct? There will be multiple choices for kc that will give you the wall boundary condition. One of those, plus a choice for n, will correspond to the TE11 mode. Also, when you plug those fields back into your Maxwell equations you should get a relation for kz and kc. Then you will have a few field solutions. Then the answer to your question of how to excite the field will be more obvious. You could put a wire probe in the radial direction in from the wall to excite a solution that has E radial peaking there. Or you could insert a magnetic loop at the wall that excites Hz where it peaks.
