I just came across a nice answer on Quora, explaining visually how wave guide modes can be constructed from the condition of zero tangential fields in the wave guide walls.
In mathematical terms, this corresponds to a certain set of boundary conditions for the Maxwell equations resulting in a certain set of solutions. The physical reasoning is that for perfectly conductive walls, any non-zero tangential fields would induce infinite currents in them - therefore, the waves somehow "know" which modes to choose and which to avoid, or, as the author of the cited answer writes,
"One nice thing about the wave guide is that you don’t have to design the waves. You just stick an antenna in the wave guide and the field just finds the correct angle for each wave train. The waves simply propagate in a mode that they can."
Obviously, it wasn't the author's intent to personify waves as sentient beings who test out different modes and select only those consistent with physical laws. Still, both the mathematical as well as physical arguments kind of put the cart before the horse:
The boundary conditions are not axiomatically derived, but a conscious choice made by whoever sets up a theoretical calculation or simulation. They do not follow from the differential equations, but are chosen as parameters (correct me if I'm wrong).
Similarly, the physical argument against infinite currents inside the wave guide walls is a justification, but not an explanation of fundamental causes or underlying physical processes.
The question is therefore:
What is the real physical mechanism behind the emergence of distinct propagation modes inside wave guides? What rather than who decides in which modes waves can propagate and in which they cannot?
- Could it be that the "zero tangential fields" argument is factually wrong?
Meaning: If we (quote) "stick an antenna in the wave guide", could it be that there are indeed high-frequency currents induced inside the walls - or rather: in the wall surfaces - such that any modal components, whose tangential fields don't perfectly cancel out, simply dissipate as heat (resistive/absorptive loss) or leak out (radiative loss)?
Note that wave guides are in general fabricated from either highly conductive materials (usually metals) or have at least a highly conductive inner layer/coating (copper or even gold), both of which actually facilitates an effective induction of currents!*
A definite answer from someone with either experimental (e.g. RF/microwave research) or theoretical experience (e.g. FDTD simulation) would be much appreciated.
*Addendum: The choice of material actually depends on the frequency of the electromagnetic radiation and doesn't necessarily have to be a metal, but can be anything that is sufficiently conductive at the desired frequencies.