Basis-Neutral Hilbert-Space Analyzers

Abstract

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes-a critical task for spatial-mode multiplexing and quantum communication-basis-specific principles are invoked that are altogether distinct from that of 'delay'. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis-exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a 'delay' obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a 'Hilbert-space analyzer' capable of projecting optical beams onto any modal basis.

Publication Date

3-27-2017

Publication Title

Scientific Reports

Volume

7

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1038/srep44995

Socpus ID

85016151803 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85016151803

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