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  • On small beams with large topological charge

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    KrennPUB1604.pdf (1.217Mb)
    Author(s)
    Krenn, Mario
    Tischler, Nora
    Zeilinger, Anton
    Griffith University Author(s)
    Tischler, Nora
    Year published
    2016
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    Abstract
    Light beams can carry a discrete, in principle unbounded amount of angular momentum. Examples of such beams, the Laguerre–Gauss modes, are frequently expressed as solutions of the paraxial wave equation. The paraxial wave equation is a small-angle approximation of the Helmholtz equation, and is commonly used in beam optics. There, the Laguerre–Gauss modes have well-defined orbital angular momentum (OAM). The paraxial solutions predict that beams with large OAM could be used to resolve arbitrarily small distances—a dubious situation. Here we show how to solve that situation by calculating the properties of beams free from the ...
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    Light beams can carry a discrete, in principle unbounded amount of angular momentum. Examples of such beams, the Laguerre–Gauss modes, are frequently expressed as solutions of the paraxial wave equation. The paraxial wave equation is a small-angle approximation of the Helmholtz equation, and is commonly used in beam optics. There, the Laguerre–Gauss modes have well-defined orbital angular momentum (OAM). The paraxial solutions predict that beams with large OAM could be used to resolve arbitrarily small distances—a dubious situation. Here we show how to solve that situation by calculating the properties of beams free from the paraxial approximation. We find the surprising result that indeed one can resolve smaller distances with larger OAM, although with decreased visibility. If the visibility is kept constant (for instance at the Rayleigh criterion, the limit where two points are reasonably distinguishable), larger OAM does not provide an advantage. The drop in visibility is due to a field in the direction of propagation, which is neglected within the paraxial limit. Our findings have implications for imaging techniques and raise questions on the difference between photonic and matter waves, which we briefly discuss in the conclusion.
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    Journal Title
    New Journal of Physics
    Volume
    18
    Issue
    3
    DOI
    https://doi.org/10.1088/1367-2630/18/3/033012
    Copyright Statement
    ©2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is an Open Access article distributed under the terms of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) License (https://creativecommons.org/licenses/by/3.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
    Subject
    Quantum Physics not elsewhere classified
    Physical Sciences
    Publication URI
    http://hdl.handle.net/10072/172491
    Collection
    • Journal articles

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