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I have only dealt with a rudimentary theoretical treatment of how light propagates inside a waveguide, such as those available in Griffiths.

One thing bugging me is that I still do not know how exactly an outside EM wave turns into whatever it is inside the waveguide. In particular, I am interested in what happens the moment an EM wave enters a waveguide. Does it get reflected in such a way that the allowed modes are formed, while the forbidden modes cancel out? Something like that.

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    $\begingroup$ Indeed, something like that. $\endgroup$
    – John Doty
    Commented Jul 9 at 0:38

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