Then, a doubt arises: as you confidently knows, in electrodynamics of guided media, we only study the primitives (*) solutions of waves(called "modes" which are "transversal magnetic TM, transversal electric TE and transversal electromagnetic TEM") and then we form combinations of these modes. What if there are others "modes" that we don't know about but which can actully arise?

In other words, are the primitves (*) a complete set of solutions (in the mathematical sense of completeness)?. Can any solution be found as combination of primitives? If so, how is the proof?

Thank you alexb.