Documentation for 2D Waveguide Example

Hi,

Apologies if this is a somewhat stupid question, but is the documentation for the 2D Waveguide example accurate, specifically when discussing the components of the E field which are being solved for? The docs say that, when solving for the transverse magnetic mode in the 2D cavity, the unknown variable is the z component of the E field, however it was my understanding of TM modes that the electric field has a non zero component parallel to the direction of propagation, which I believe in this setup would be the x direction, should it not? Assuming that an EM wave enters the waveguide from the left and travelling to the right towards the absorbing boundary.

It has been a few years since I took an EM course so I am more than happy to be corrected, I feel as though the explanation of the physics setup in the docs are pretty lacking for this example.

Thanks