The single mode condition of rectangular waveguides is derived by using a simple ray-optics approach, which relies on geometrical ray tracing principles as in classical optics. Light propagation through such a waveguide can be approximately simplified as reflections within two planes of incidence. By employing the mode equations for different polarizations, a relation that shows the single-mode cut-off as a function of the waveguide dimensions is readily obtained.
"Ray-Optics Analysis of Single Mode Condition for Optical Waveguides with Rectangular Cross-Section," Progress In Electromagnetics Research,
Vol. 135, 81-89, 2013. doi:10.2528/PIER12102901