Spatial Characterization Of Two-Photon States - GAP-Optique

APPENDIX C
Methods for OAM
measurements
A real world oam application will require a compact tool able to separate the
different modes at the single photon level. A tool analogous to the beam splitter
for polarization, or to a diffraction grating for frequency. Such a tool probably
will be based on the two current methods to determine the oam of photons:
holographic and interferometric methods.
In a very simplistic way, an hologram is a record of the interference pattern
of two beams. When the hologram is illuminated with one of the beams,
the other beam can be reconstructed. Based on this principle, a computer
generated hologram of the interference of a lg mode with a Gaussian beam,
in conjunction with a single mode fiber can be used to detect that particular
lg mode [7, 51]. Even though this method works at single photon level, it
is restricted to a two-value response, reducing the effective dimensions of the
oam to two, as shown in figure C.1.
Reference [15] introduced an analyzer able to sort photons into even and
odd oam modes, using a Mach-Zender interferometer. With a phase shift in
one of the interferometer arms, the constructive and destructive interference
were so that odd modes go to one of the outputs, and even modes to the other,
as figure C.2 shows. By nesting several interferometers, and using holograms,
the authors proved that was possible to separate up to 2 n modes with (2 n − 1)
interferometers. This method works at single photon level, and can distinguish
many different oam modes, but it relies on the simultaneous stabilization of
different interferometers, which is challenging experimentally.
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