Waveguide Junction TM/TE combination

[tworitdash]

TL;DR Summary

I have been verifying measurements from a commercial EM tool with equations implemented on MATLAB with 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.

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 $$\int\int_{S_{smaller-waveguide}} (E^{small}_{transverse} \times H^{large}_{transverse}) . \hat z dS$$, 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 ($$\rho$$) and the angular variables integral ($$\phi$$) 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.

 

[tech99]

Is it that the circular waveguide can support a choice of two polarisations which the small rectangular cannot?

 

[tworitdash]

Is it that the circular waveguide can support a choice of two polarisations which the small rectangular cannot?

Yes, the field equations have a cos (or) a sin term in the field equations for circular waveguides. Either way, it is right and I use it as cos.

I think you are asking the same as polarization here? Or do you mean TE and TM? TE and TM both are supported in both waveguides. I think I don't understand the question properly.