What is the lower bound for the wavelength concerning polarizing beam splitters?
Especially I ask for interferometer experiments with single photons. Of course I know that they exist for all wavelengths in the visible spectrum. But what when I want to use photons with a wavelength of 100 nm or 1 nm or even 0.1 nm?
Do polarizing beam splitters exist for this range?
I'm not very sure what the situation is with harder x-rays, but in the soft x-ray and extreme UV range doing this sort of thing is very hard, and as far as I'm aware there are no polarizing beam splitters in this range. In fact, starting with VUV at about 150nm, it is usually quite hard to get the light to do anything other than propagate in a straight(ish) line through a vacuum.
I know of one experiment which has successfully changed the polarization of radiation after it was generated in this range (specifically, ~20nm), by using an array of mirrors as a waveplate to change linear into circular polarization. There are slight polarization-dependent phase shifts upon reflection in each mirror, and they add up to the effect of a waveplate:
For more information, see the paper:
Polarization control of high order harmonics in the EUV photon energy range. B. Vodungbo et al. Opt. Express 19 no. 5, 4346-4356 (2011); HAL e-print.
One thing to note is that most of the experiment is done in a collinear configuration. The spectrometer is a grazing incidence diffraction grating, and the EUV is focused on it using a toroidal mirror which is also at grazing incidence. This is usually the way to go unless you need something rather specific, as mirrors for near-normal incidence can have rather low reflectivities:
Invited Review Article: Technology for Attosecond Science. F. Frank et al. Rev. Sci. Instrum. 83 no. 7, 071101 (2012); Researchgate (paywalled?) pdf.
The design of polarizing mirrors such as the ones used by Vodungbo et al. has been an important part of the experimental design of the XUV and synchrotron communities for over twenty years. One standard is multi-layer mirrors, and you can get a general picture of them from
Reflection circular polarizers for xuv light: a theoretical study. A Derossi et al. Pure Appl. Opt 3 no. 3, 269-278 (1994)
For a more modern study, in wavelengths just above 100 nm, try
Multilayer reflective polarizers for the far ultraviolet. J. I. Larruquert et al. In Damage to VUV, EUV, and X-ray Optics IV; and EUV and X-ray Optics: Synergy between Laboratory and Space III, Juha et al. (eds.), Proc. of SPIE 8777, 87771D (2013).
These are mirrors made of multiple layers of fused silica and various metal salts. In this range of not-too-extreme-UV, you can still get polarizances (the ratio of the differential reflectivity to the total reflectivity) as high as 99%.
However, as you descend into shorter wavelengths, you start taking a hit in the polarization sensitivity. The latest experiment that I'm aware of worked at about 40 nm wavelength, and they used a combination of three fused silica blanks to get a total polarizance over 90%:
Spin angular momentum and tunable polarization in high-harmonic generation. A. Fleischer et al.. Nature Photon. 8 no. 7, 543-549 (2014); arXiv:1310.1206.
(Shameless plug/full disclosure: I cowrote a News & Views piece on this paper, High-harmonic generation: Taking control of polarization, Nature Photon. 8, 501 (2014), which is nice.)
Now, these are all reflection polarizers, and they do not transmit any light. I'm not aware of any beam-splitting devices that transmit as well as reflect light, but the way I see it is this: a polarizing beam splitter would render these devices obsolete, by simply blocking one port; hence, the intense activity in creating these devices is good evidence that there are no PBSs available on this range.
If you do want to split your x-rays in two, you end up using a technique called 'split and delay', which essentially uses a mirror that only blocks half of the beam:
Design of an x-ray split- and delay-unit for the European XFEL. S. Roling et al. in X-Ray Free-Electron Lasers: Beam Diagnostics, Beamline Instrumentation, and Applications, eds. S. P. Moeller et al. Proc. of SPIE 8504, 850407 (2012).
Finally, if you're interested in quantum-optics experiments on the hard UV to x-ray range, you should really read
X-ray quantum optics. B.W. Adams et al. J. Mod. Opt. 60 no. 1, 2-21 (2013).
This may be closer to what you're interested in. The papers I cite above are mostly from my field, which is ultrafast science. We need the short wavelengths simply to support the short pulses we use, but there are many reasons to want such hard radiation, and many fields that do. In the end, though, you don't simply 'perform an interferometry experiment'; instead, you have some specific sort of goal in mind. What technology you need depends, therefore, on what you want to do - though of course if you need a hard x-ray PBS, then I would suggest you start looking for alternatives.
I don't know of polarizing x-ray beam splitters, and I suspect they don't exist, but I'm always very interested to be shown wrong.
It appears from a cursory search that working x-ray interferometers have been built, and are conceptually more similar to neutron interferometers than to optical interferometers. For neutrons there are polarizing supermirrors, but the other polarization state is absorbed, not transmitted. Unlike neutrons, x-rays can be produced polarized, so I suspect there's not as much research into polarizing x-rays.
In visible-wavelength optics there is symmetry between creating and analyzing polarization — you can use the same device for both cases. Here's an old patent for a rotating-mirror x-ray polarization analyzer which states "conventional transmission polarizers and analyzers do not exist for this wavelength region [vacuum UV and x-rays]." A recent paper or conference proceedings report describes a multiple Bragg diffraction analyzer which could conceivably have enough transmission to do what you're interested in, but I'm not prepared to evaluate it.
I also point out that neutron interferometry is done without reference to polarization and involves single neutrons (that is, the mean number of particles present at the interferometer at any moment is much less than one) and the fact that optical beamsplitters are frequently polarization-based is not an essential feature of optical interferometers either. Don't let the absence of a polarizing x-ray beam splitter distract you from your thoughts about short-wavelength single-particle interferometry.
