Standing wave ratio inside a waveguide If there were microwaves being transmitted through the waveguide in the image below out the horn, and I place a sheet of metal in front of the horn (perpendicular to the propagation of the waves), will the standing wave ratio inside the waveguide be 1?
I know a standing wave will be formed between the horn and the sheet of metal because the transmitted and reflected waves will combine, but I'm not sure if the reflected waves will  re-enter the waveguide through the horn. 
I say that I think the SWR will be 1 because the horn matches the impedance of the waveguide with the impedance of free-space. But this would mean measurements of the voltage of the wave inside the waveguide will be fixed and there would not be a standing wave inside. 

 A: If (part of) the wave is reflected back into the horn, that wave will interfere with the outgoing wave and produce a standing wave pattern.
The SWR will be "something greater than 1.0". How big it gets depends on the effectiveness of the reflection - if you get 100% reflection, you will get a perfect standing wave. But it's perfectly possible to have a "partial standing wave". If the amplitude of the outgoing wave is A, and you reflect a fraction fA, then the peak of the standing wave will have amplitude (1+f) A while the trough has amplitude (1-f)A, so the standing wave ratio will be
$$R = \frac{1+f}{1-f}$$
Which is a number between 1 and $\infty$. 

Note - I am assuming that $f=|f|$; if you chose $f$ to be negative, the above would give a confusing answer (because then the peak amplitude would not be (1+f)A ...)
A: Call the transmitted wave $t$ and its reflection from the metal $r$. Note first that this is a passive and reciprocal system, so the reflectivity and transmissivity are the same from both sides, $|S_{11}|=|S_{22}|$ and $|S_{12}|=|S_{21}|$. There are several discrete places where reflection may occur, starting from the left: at the $P_1$ backshort, at the $P_2$ launch probe, at the $P_3$ transition between the waveguide and the horn, and at the $P_4$ rim of the horn (I ignore the very small but continuous reflection from the wall's of the horn). When you place a sheet in front of the horn the wave $r$ will first reflect from $P_4$ the rim, then after passing into the horn it will suffer reflection from $P_3$ the transition between the waveguide and the horn, this reflection will interfere with the primary transmitted. The backshort is placed at a distance so that antenna probe in the waveguide is reasonably well matched but the match is not perfect so there will be some reflection from them. All these will contribute to the SWR and being positive SWR must be larger than one.
While it is true that the horn is an impedance transformer between the ether's $120\pi=377\Omega$ and whatever impedance the waveguide has. But no impedance match is perfect even at a single frequency, all those points $P_1,...P_4$ are potential discontinuities; a very good horn may have 40dB return loss or 1% reflectivity over a very narrow bandwidth. At any rate, over a nonzero bandwidth nothing can be matched perfectly even with lossless elements.
