Multimodal Calibration Technique for Waveguide Devices
The problem of performing measurements on waveguides when more than one mode is propagating dates back to the waveguide invention . Nonetheless, to date Vector Network Analyzers (VNA) just allow the measurement of monomodal waveguide devices, lacking of a calibration procedure allowing to recover the complete Generalized Scattering Matrix (GSM). There are actually many practical situations where dealing with multimode propagation is of paramount importance. A relevant case is the one of the low-pass filter, where often the stop-band includes a frequency range where more than one mode is propagating. In such a case, the current measurement approach requires to include a tapered waveguide ensuring the monomodality all over the desired frequency range. However, while the tapered waveguide is almost transparent for the fundamental mode, it is a reactive load for the higher order modes, so that the resulting measurement is often inconclusive. One more important case, often encountered in practice, is the one of waveguides having specific symmetries, such as cylindrical and square waveguides, where there are two fundamental, degenerate, modes with orthogonal polarization: in this case one has to rely on the quality of orthomode transducers to be inserted in the experimental setup; however orthomode transducers are themselves hard to characterize, and as matter of fact only recently a calibration approach has been developed to perform measurements of this kind of components . The general problem is the one of accessing and measure individual modes, disentangling the contribution of each mode to the total field. There is some contact point with a different problem, where however the term "mode" is usually used as well, namely the one of performing measurements on multifilar transmission lines, as in  where the calibration technique required the express exclusion of the degenerate case (modes having same propagation constant, as in TEM): most notably a common case is the one of recovering information about balanced devices from unbalanced measurements .
Here we have a different, twofold aim:
1) measurement of devices fed by waveguides in which there is more than one mode above cut-off,
2) measurement of devices fed by waveguides below cut-off.
In other words, the very goal is to make possible the measurement of the Generalized Scattering Matrix (GSM) of a given waveguide device, filling the gap existing between modern full wave analysis tools, that can compute it, and experiments.
In the past, the most explored idea was the one of exciting and filtering just the mode of interest. Here we propose a different point of view, where the multimodal device under test (DUT) is placed between two waveguide devices, aiming to excite all the modes we are interested in, thus, in a sense mixing up as much as possible all modes. Each device, that we will indicate as "converter", has on one side a multimodal port and on the other side several monomodal ports (as many as are the modes to be measured). The proposed calibration technique allows to remove completely the effect of the two converters, making accessible the GSM of the DUT from measurements made by a standard, monomodal VNA. Remarkably, the method works even on DUT having degenerate modes, and there is no restriction about the DUT but linearity.
Moreover, the technique allows to measure the propagation constants of waveguides featuring arbitrary cross-section
 G. C. Southworth, "Some Fundamental Experiments with Wave Guides", Proc. of the IRE vol. 25, no. 7, pp. 807–822, 1937.
 O.A. Peverini, R. Tascone, A. Olivieri, M. Baralis, R. Orta, G. Virone, "A microwave measurement procedure for a full characterization of ortho-mode transducers", IEEE Trans. Microw. Theory Tech., vol. 51, no. 4, pp. 1207-1213, April 2003.
 C. Seguinot, P. Kennis, J. F. Legier, F. Huret, E. Paleczny, L. Hayden, "Multimode TRL. A new concept in microwave measurements: theory and experimental verification", IEEE Trans. Microw. Theory Tech. , vol 46 no. 5, pp. 536-542, May 1998
 K. Anderson, "Balanced device characterization including test system calibration", patent US 2004/201383, 14th October 2004
Presentation at 2012 ESA Workshop on Filters
Video showing a practical calibration