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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Production for Superpositions of the Orbital Angular Momentum of Photons by Fork-Like Grating

Fengwei Ye, Yongping Li

Published Sep 19, 2002• 0 citations
Publisher

Abstract

Laguerre-Gaussian (LG) mode carries a well-defined orbit angular momentum. We design a fork-like grating to produce the superposition of two LG modes. It is useful in the high-dimensional quantum communication.
DOI
10.1117/12.471699

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Two different experimental techniques for preparing and analysing superpositions of Gaussian and Laguerre–Gaussian modes are presented. These involve exploiting an interferometric method in one case and using computer-generated holograms in the other. It is shown that by shifting a hologram with respect to an incoming Gaussian beam, different superpositions of the Gaussian and the Laguerre–Gaussian beam can be produced. An analytical expression connecting the relative phase, the amplitudes of the modes and the displacement of the hologram is given. The application of such orbital angular momenta superpositions in quantum experiments such as quantum cryptography is discussed.
In this work, a technique to produce spatial electromagnetic modes with definite orbital angular momentum is presented. The method is based in the construction of binary diffractive gratings generated by computer. In the classical regime the gratings produce the well known Laguerre-Gaussian modes distributions when illuminated by a plane wave. In the quantum regime the grating is placed in the signal path of a spontaneous parametric down conversion layout and the diffraction pattern, observed in the coincidence count rate, shows that the single photons are projected onto spatial states consistent with a Laguerre-Gaussian modes distribution.
Spatially structured photons have attracted a lot of attention in quantum photonics, where they often serve as powerful tools for investigating fundamental properties of light, and for realizing high-dimensional quantum states with beneficial properties in quantum information tasks such as cryptography or quantum simulations [1] . One way of describing any spatial structure, in the paraxial limit, is through orthogonal transverse-spatial modes e.g. Laguerre-Gaussian (LG) modes. A unique feature of higher order LG modes is their twisted phase front, to which a theoretically unbounded orbital angular momentum can be attributed.
We generated orbital angular momentum in atoms with a spin degree of freedom and coherently transferred it to a light field, which resulted in the generation of a Laguerre-Gaussian (LG) beam. In this method, atoms obtain orbital angular momentum through Larmor precession around the quadrupole field. Successive operations of quadrupole and homogeneous magnetic fields lead to a change of sign in the LG beam or even generation of superposition states of the LG beam with different indexes in real time. Possible applications to control orbital angular momentum of arbitrary photons are also discussed.
It is well known that Laguerre-Gaussian (LG) laser beams with orbital angular momentum (OAM), resulting from a phase singularity and created from the readily available Hermite-Gaussian (HG) laser beam, carry the potential for providing an unlimited number of orbital angular momentum states that could be used for enhanced processing of quantum info mation (QI). This paper presents a comprehensive set of experimentation on the fabrication and use of computer generated holograms to create LG beams from the HG profile of an ordinary He-Ne laser and characterization thereof in preparation for QI applications.