Potocek, V. and Barnett, S. M. (2015) Generalized ray optics and orbital angular momentum carrying beams. New Journal of Physics, 17, 103034. (doi:10.1088/13672630/17/10/103034)

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Abstract
In classical optics the Wolf function is the natural analogue of the quantum Wigner function and like the latter it may be negative in some regions. We discuss the implications this negativity has on the generalized ray interpretation of freespace paraxial wave evolution. Important examples include two classes of beams carrying optical orbital angular momentum—Laguerre–Gaussian (LG) and Bessel beams. We formulate their defining eigenfunction properties as phase–space symmetries of their Wolf functions, whose analytical form is shown, and discuss their interpretation in the ray picture. By moving to a more general picture of partly coherent fields, we find that new solutions displaying the same symmetries appear. In particular, we find that mixtures of Gaussian beams (thus fully describable using classical ray optics) can mimic the basic properties of LG beams without the need for negativity, and are not restricted to quantized values of angular momentum. The quantization of both the l and p parameters and negativity of the Wolf function are both inevitable and, indeed, arise naturally when a requirement on the purity of the solution is added. This work is supplemented by a set of computer animations, graphically illustrating the interpretative aspects of the described model.
Item Type:  Articles 

Keywords:  Wigner function quantum optics orbital angular momentum 
Status:  Published 
Refereed:  Yes 
Glasgow Author(s) Enlighten ID:  Potocek, Dr Vaclav and Barnett, Professor Stephen 
Authors:  Potocek, V., and Barnett, S. M. 
Subjects:  Q Science > QC Physics 
College/School:  College of Science and Engineering > School of Physics and Astronomy 
Research Group:  Quantum Theory 
Journal Name:  New Journal of Physics 
Publisher:  Institute of Physics Publishing Ltd. 
ISSN:  13672630 
ISSN (Online):  13672630 
Copyright Holders:  Copyright © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaf 
First Published:  First published in New Journal of Physics 17:103034 
Publisher Policy:  Reproduced under a creative commons license 
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