Not a microwave expert, I only know enough about fields to be dangerous,
Seems to me, I was never explained the reason why traditional waveguide is rectangular, and the ratio that it is; but I can tell by inspection that it has to do with pushing the cross polarized mode to a much higher frequency, so that the TEM0,0 mode is fairly unperturbed over a usefully wide range. A perfectly square waveguide, of course, would support both vertical and horizontal polarizations in the same frequency range, which would give rise to weird interactions, reflections, "drool" and so on due to nonuniform perturbations between the modes (the square not being perfectly equal or perfectly, well, square; connectors, couplers and so on being not quite centered, and not quite parallel or perpendicular, as the case may be; etc.).
The same is true of a circular waveguide, of course.
I don't know about propagation outside of the main mode, though. There are higher modes (0,1, 1,0, etc.) but by nature and by design, those start an octave or so higher. I expect the usual time-space dualities apply, but I wouldn't know what to look at, as far as what defines those lobes or whatever.
Maybe... you're referring specifically to lobes in a power divider structure? So the periodic openings yield a Fourier transform that looks like, well, sampling or aliasing?
Tim
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