Physical meaning of the radial index of Laguerre-Gauss beams

The Laguerre-Gauss modes are a class of fundamental and well-studied optical fields. These stable, shape-invariant photons - exhibiting circular-cylindrical symmetry - are familiar from laser optics, micro-mechanical manipulation, quantum optics, communication, and foundational studies in both class...

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Bibliographic Details
Published in:arXiv.org 2015-09
Main Authors: Plick, William N, Krenn, Mario
Format: Article
Language:English
Subjects:
Angular momentum
Beams (radiation)
Differential equations
Gaussian beams (optics)
Operators (mathematics)
Photons
Physical properties
Quantum optics
Quantum theory
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Summary:The Laguerre-Gauss modes are a class of fundamental and well-studied optical fields. These stable, shape-invariant photons - exhibiting circular-cylindrical symmetry - are familiar from laser optics, micro-mechanical manipulation, quantum optics, communication, and foundational studies in both classical optics and quantum physics. They are characterized, chiefly, by two modes numbers: the azimuthal index indicating the orbital angular momentum of the beam - which itself has spawned a burgeoning and vibrant sub-field - and the radial index, which up until recently, has largely been ignored. In this manuscript we develop a differential operator formalism for dealing with the radial modes in both the position and momentum representations, and - more importantly - give for the first time the meaning of this quantum number in terms of a well-defined physical parameter: the "intrinsic hyperbolic momentum charge".
ISSN:2331-8422
DOI:10.48550/arxiv.1509.06875