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arXiv · 1511.07339

Fractional vortex Hilbert's Hotel

Greg Gbur
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Abstract

We demonstrate how the unusual mathematics of transfinite numbers, in particular a nearly perfect realization of Hilbert's famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a fractional vortex plate can be used, in principle, to create any number of "open rooms," i.e. topological charges, simultaneously. Fractional vortex plates are therefore demonstrated to create a singularity of topological charge, in which the vortex state is completely undefined and in fact arbitrary.

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Greg Gbur. 2015-11-23. Fractional vortex Hilbert's Hotel. https://arxiv.org/abs/1511.07339

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