Generalized ray optics and orbital angular momentum carrying beams

Potocek, V. and Barnett, S. M. (2015) Generalized ray optics and orbital angular momentum carrying beams. New Journal of Physics, 17, 103034. (doi:10.1088/1367-2630/17/10/103034)

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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 free-space 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:1367-2630
ISSN (Online):1367-2630
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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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
549872Challenges in Orbital Angular MomentumMiles PadgettEngineering & Physical Sciences Research Council (EPSRC)EP/I012451/1P&A - PHYSICS & ASTRONOMY