[tworitdash]

I have been verifying measurements from a commercial EM tool with equations implemented on MATLAB with the Mode Matching Technique for S parameters in the case of waveguide junction problems. I found in the literature that if the smaller waveguide has a TM mode (smaller waveguide surface is a sub-set of the larger waveguide in this case) and the larger has a TE mode, then the coupling is 0 no matter which kind of waveguide it is. It is shown in the paper here .

it says no matter what the waveguide structure is if the smaller waveguide has a TM mode and the larger has a TE mode, then the coupling (Inner cross product




, where z is the direction of propagation) should be 0.


First I derived the equations analytically for a circular waveguide where I saw it is true indeed and the reverse is also true (small waveguide with TE and large with TM). It is interesting to notice that when (S - TM and L -TE, I am referring S for small and L for large), the integrals of radial variables (ρ) and the angular variables integral (ϕ) are both 0 and when (S - TE and L -TM) only the angular variables integral is 0. Anyway, as one of them at least is 0 always, the inner cross product is 0 always for both configurations. As this is lossless, I also assume that the reverse also has to be true.

However, in rectangular waveguide structures in all literature I reviewed, it is said that only (S - TM and L -TE) has 0 coupling and not necessarily the opposite is true.

I don't understand why such a thing happen. What is the physical significance of this?