On small beams with large topological charge

Mario Krenn, Nora Tischler, Anton Zeilinger

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    23 Citations (Scopus)
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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.
    Original languageEnglish
    Pages (from-to)033012-1-033012-6
    Number of pages6
    JournalNew Journal of Physics
    Publication statusPublished - 3 Mar 2016

    Bibliographical note

    Copyright the Publishers 2016. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


    • Laguerre-Gauss modes
    • nonparaxial
    • diffraction limit
    • focussing
    • visibility
    • Rayleigh criterion


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