J.P. Berenger, “Numerical Reflection
of Evanescent Waves from
Perfectly Matched Layers” , IEEE
Antennas and P ropagation Symposium
Diges t, pp. 1888-1891, July
1997.

There is a good paper for your quesiton:

Haim Haskal, "Matrix Description of Waveguide Disdcontinuities in the Presence of Evanescent Modes,"
IEEE Transactions on Microwave Theory and Techniques,
pp. 184-188, March 1964

Using S-parameters for evenescent coupling between devices sounds like a theoretical exercise in futility (ie the smith chart breaks down). What is to be gained? Can your S-parameters reliably be characterized is the super-super fast changing world of evanescent decay? I think not as whatever cal standards you use would need the accuracy of an atomic clock. Best treat the coupling as what it really is inductive or capacitive. Throw in isolation (metal walls) and lossy material to snuff it out. I know the simualtors are pretty good, but I would not trust them here, not yet.

S Matrix including higher modes can improve accuracy. We can find a lot of papers about numeric simulation about microwave juntion. In the before, only dominant mode was considered. Now almost everyone considers higher modes. Maybe this approach is only for academic purpose and it is hard to measure something about higher modes. For rectangular waveguide, we can only measure S parameter for dominnat mode.

Of Course if you want to analyze waveguide discontinuities using the mode matching technique, considering the higher order modes is of the utmost concern, like doing fourier analysis, the fundemental frequency and harmonics combine to provide your time domain waveform. Fortunately, with HFSS mode matching is dead for the practicing engineer today.

What do you mean "Fortunately, with HFSS mode matching is dead for the practicing engineer today"? Do you mean that mode matching is not useful in mocrowave indurstry? I know HFSS is a simulation software but have never used it.

I only see it in the academic world research papers on reduced height InP trapatt oscillators and such. Most of the high dollar development work that I have seen is highly orientated to HFFS, non-linear microwave and simular modeling tools.   

What is basic theory behind HFFS? Maybe mode match theory (or somethig else, for example,equivalent circuit) is exactly foundation of this simulation tool. Some papers show that their results using mode match fit very well with results from HFFS.

Hi,

 thanks for showing your interest!

I found the Haim Haskal paper valuable I remember.

I used to work on a problem where we simulated pieces of waveguide junctions using the Finite Element Method (HFSS etc...) in the Frequency Domain (interesting comment there on the atomic clock, I was mostly looking at the fields in the frequency domain). This was indeed a problem of practical 'industrial' interest. The problem was that the excitation ports, i.e. truncation boundaries of the FEM model, were located close to geometric discontinuities in the model such that evanescent modes were necessarily present at the ports.

The analysis of a system of many connected junctions using circuit parameters (S-parameters for example) would then (perhaps) need to take into account also the evanescent modes. This is somewhat of a mode matching method, where the fields are to be made continuous at the intersecting ports by matching the modes on both sides of the intersection.

The simulators could model ports in a variety of ways (Perfectly Matched Layers, Impedance Boundary Condition, etc...), of which some would be appropriate for situations with multiple (incl. evanescent) modes.

Best luck,
Svea

For junction problem of rectangular waveguide, in junction area, both dominant mode and higher mode are considered using mode match(or something else, FEM,Equivalent circuit). After that, when we compare simulation data with experiment data, only dominant data is involved. The reason for this is that only dominant mode can propagate. But there is tricky behind this: higher mode consideration will effect the result of dominant data. This is why we should include higher mode in the calculation.

I would recommend a step backward.  What are S parameters?  They are a way of measuring a black box, and allowing limited design using that black box information.  When you measure something with evanescent modes, like a microstrip "T" embedded in 50 ohm transmission lines, the evanescent modes "die out" as the wave travel away from the discontinuity.  As the evanescent modes "die out", their energy combines with the real transmission modes, and looks like a fixed lumped reactance from a far distance.

So, if you now design something using that set of measured S parameters, your design will work wonderfully IF the next closest discontinuity is physically far enough so that 90% of the evanescent energy has died out by then.  If, as one usually finds, you are trying to use multiple discontinuities close together (such as a T junction, as stub, and the gate of a FET all withing 200 mils of each other), then the originally measured S parameters for each of those microstrip elements are now wrong, and you will find measured performance deviating from the predicted.

In those cases, you should do an Electromagnetic Field simulator (HFSS, etc) with all of the discontinuities shown all at once.

Thanks biff,

and wouldn't it be great in this case not having to redo the field calculations (e.g. in hfss), but to keep on doing algebra using generalized scattering parameters that include information about the evanescent modes? Also in real world applications.

That would be great.  But how would you do it?  The number and types of evanescent modes depends on the various loads present at any discontinuity.  As you change the loads, the boundary conditions change and new evanescent modes are formed, while the old ones are suppressed.  This is very different from linear transmission line analysis, where the forward and travelling waves are continuous with changes in the load impedances.  A good good example would be a waveguide circuit where the S parameters are measured, but then you want to add a mode suppression screw.  If the screw is in the right place, there may be no evanescent modes left.  How can you predict such an abrupt change?

Regarding Svea's concern:
*******
The problem was that the excitation ports, i.e. truncation boundaries of the FEM model, were located close to geometric discontinuities in the model such that evanescent modes were necessarily present at the ports.
*******
At this point, it might be feasible to switch from FEM to FDTD. Computation of S-parameters with the present evanescent modes is, e.g., a routine procedure in QuickWave-3D (www.qwed.com.pl).