# What is the general boundary condition of wave-guides?

1. Feb 3, 2015

### genxium

By wave-guides I refer to the device with (perfectly) conducting walls that enclose EM wave inside. I'm reading this tutorial here http://farside.ph.utexas.edu/teaching/em/lectures/node105.html and found this interesting boundary condition for wave-guides:

$E_{\parallel} = 0$ -- (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 :)

2. Feb 3, 2015

### HallsofIvy

Yes, those refer to the components of the E wave parallel and the B wave perpendicular to the wave guide. At the walls of the guide, those components must be 0.

3. Feb 4, 2015

### genxium

@HallsofIvy , thanks for the reply. So do conditions (1) & (2) hold for all shapes of wave-guides when the wall is (nearly) perfect conductor (i.e. the skin-depth of the propagating wave is much less than the thickness of wall) ?