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Basis-neutral Hilbert-space analyzers

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-mo...

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Detalles Bibliográficos
Autores principales: Martin, Lane, Mardani, Davood, Kondakci, H. Esat, Larson, Walker D., Shabahang, Soroush, Jahromi, Ali K., Malhotra, Tanya, Vamivakas, A. Nick, Atia, George K., Abouraddy, Ayman F.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5366812/
https://www.ncbi.nlm.nih.gov/pubmed/28344331
http://dx.doi.org/10.1038/srep44995
Descripción
Sumario: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.