- #1

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##E_{\parallel} = 0## -- (1)

##B_{\perp} = 0## -- (2)

however what anchor ##\parallel## and ##\perp## are respecting is not mentioned in the tutorial but I suppose that it's the wall of wave-guide (please correct me if I get it wrong). By the way the tutorial assumes that the wave-guide is guiding the EM wave to propagate along the z-axis but the geometry of the cross-section is NOT specified.

My question is, are (1) and (2) the general boundary conditions for wave-guides? If so why isn't ##E_{\perp}## or ##B_{\parallel}## taken into consideration? I drew some pill-boxes but unfortunately I didn't come up with a convincing answer for myself.

In an engineering textbook I only learned to solve equations for rectangular wave-guide (with cross-section ##x \in [0, a], y \in [0, b]##) like assuming that the wave is propagating along the z-axis and ##E_z = 0## for TE wave and ##B_z=0## for TM wave then apply "separate variable" assumption to solve the rest of the unknowns.

Any help would be appreciated :)