The electromagnetic wave propagating in a (rectangular) waveguide is different
from a wave with the same frequency propagating in free space.
It can be seen as the sum of two such free-space waves, propagating diagonally
down the waveguide, bouncing of the sides as it goes.
This page provides an animation of this process, both in 3D and 2D.
This animation requires Javascript and WebGL support in your browser.
Show magnetic field
Above are four 2D top-views, from left to right: a plain wave in free space,
fictitious diagonal waves, and their sum (the actual field in the wave guide).
Here red is a positive electric field (pointing up in the 3D view, toward the viewer in the 2D view),
and blue negative.