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Journal of Modern Optics

Measurement of the orbital angular momentum at photon level via the spatial probability distribution

Alcenísio J. Jesus‐Silva, E. J. S. Fonseca, Jandir M. Hickmann

Published Jul 20, 2012• 7 citations
Publisher

Abstract

We demonstrate that by diffracting light at single photon level with orbital angular momentum (OAM) by an equilateral triangular aperture, it is possible to determine their OAM amount by simply counting the number of maxima in the side of a generated triangular shaped hexagonal lattice in the spatial photon probability distribution. The sign of the OAM is obtained by the orientation of the latticed triangle. We also show that by changing the aperture size it is possible to discriminate OAM state superpositions.

DOI
10.1080/09500340.2012.705344

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We demonstrate that by diffracting light at single photon level with orbital angular momentum (OAM) by an equilateral triangular aperture, it is possible to determine their OAM amount by simply counting the number of maxima in the side of a generated triangular shaped hexagonal lattice in the spatial photon probability distribution. The sign of the OAM is obtained by the orientation of the latticed triangle. We also show that by changing the aperture size it is possible to discriminate OAM state superpositions.
This work presents a single-pass diffraction experiment that demonstrates that single photons in a vortex beam in passing through three slits arranged in an equilateral triangle can interfere with themselves and provide quantitative information of their total amount of orbital angular momentum (OAM) they carry. For the experiment presented the aperture has been reduced to a very thin triangular slit. A vortex beam is created by a diffractive optical element (DOE) and then it is made to pass through the slit. This work is considered as an extension to the Young double slit experiment.
The double-slit at single photon or electron level is the ubiqutous quantum interference experiment with the path phase playing a key role. On the other hand, photon's orbital angular momentum (OAM) brings a new dimension to interference problems with the spiral phase degree of freedom. In this work, we use OAM's two dimensional properties to extended the double-slit to a triple-slit configuration in the shape of an equilateral triangle, obtaining a triangular latticed single-photon counting interference pattern. In order to understand this interference pattern in terms of wave-particle duality, we have to take into account that, in contrast with the parallel double and triple slit cases, the azimuthal phase also plays a fundamental role, being undistinguishable from path phase.
Detection of photons in orbital angular momentum (OAM) superposition states is crucial to verification of OAM entanglement. In the past this has been realized by laterally shifting a hologram designed to remove a charge 1 phase singularity at its center. Such a laterally shifted hologram converts a beam with an off-center singularity (similar to that created by superposing an m = 0 beam and an m = 1 beam, where in is the OAM mode number) into a Gaussian beam, which is then filtered through a single mode fiber (SMF). However, it has been shown that a photon detected by this method is not a simple superposition of a photon in the m = 0 Gaussian mode and the m = 1 mode detected with an unshifted hologram, making it necessary to apply complicated analysis. One problem is that the radial distributions of the detected m = 0 and 1 components as determined by the SMF change as the hologram is shifted. Another, possibly more serious problem is the mixing of other OAM components. To overcome this problem we propose a new scheme for the detection of OAM superposition states consisting of a hologram and a path interferometer. The hologram is designed so that the output is equally distributed between the 0th and 1st order diffraction beams. The 0th order is the input beam itself, whose m = 0 Gaussian component is filtered through an SMF. In the 1st order beam the m = 1 component is converted to m = 0 and is filtered through a second SMF. The filtered beams now have the same spatial distribution, and can be superposed by a beam splitter. By inserting attenuators and phase modulators within the interferometer, superpositions with varying amplitude ratios and relative phases can be detected without shifting the hologram.
We use photon OAM's two-dimensional properties to extend the double-slit to a two-dimensional triple-slit configuration in the shape of an equilateral triangle, obtaining a bidimensional triangular interference pattern at photon level, whose size depends on the OAM amount. We also show that for this pattern, in contrast with the parallel two- and three-slit cases, the azimuthal phase plays a fundamental role, being undistinguishable from the path phase. Our results confirm that only pairs, here associated to path and azimuthal phases, contribute to the two-dimensional photon detection probability, as established by Born's rule.
We study theoretically the orbital angular momentum (OAM) density in arbitrary scalar optical fields, and outline a simple approach using only a spatial light modulator to measure this density. We demonstrate the theory in the laboratory by creating superpositions of non-diffracting Bessel beams with digital holograms, and find that the OAM distribution in the superposition field matches the predicted values. Knowledge of the OAM distribution has relevance in optical trapping and tweezing, and quantum information processing.
We report the experimental preparation of optical superpositions of high orbital angular momenta (OAM). Our method is based on the use of a spatial light modulator to modify the standard Laguerre-Gaussian beams to bear excessive phase helices. We demonstrate the surprising performance of a traditional Mach-Zehnder interferometer with one inserted Dove prism to identify these superposed twisted lights, where the high OAM numbers as well as their possible superpositions can be inferred directly from the interfered bright multiring lattices. The possibility of the present scheme working at the photon-count level is also shown using an electron multiplier CCD camera. Our results hold promise in high-dimensional quantum-information applications when high quanta are beneficial.