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-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.
CREOL, The College of Optics &Photonics, University of Central Florida, Orlando, FL 32816, USA.
Lane
L
Martin
Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA.
Davood
D
Mardani
CREOL, The College of Optics &Photonics, University of Central Florida, Orlando, FL 32816, USA.
H Esat
HE
Kondakci
CREOL, The College of Optics &Photonics, University of Central Florida, Orlando, FL 32816, USA.
Walker D
WD
Larson
CREOL, The College of Optics &Photonics, University of Central Florida, Orlando, FL 32816, USA.
Soroush
S
Shabahang
CREOL, The College of Optics &Photonics, University of Central Florida, Orlando, FL 32816, USA.
Ali K
AK
Jahromi
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.|Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA.
Tanya
T
Malhotra
Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA.|Institute of Optics, University of Rochester, Rochester, NY 14627, USA.
A Nick
AN
Vamivakas
Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA.
George K
GK
Atia
CREOL, The College of Optics &Photonics, University of Central Florida, Orlando, FL 32816, USA.
Ayman F
AF
Abouraddy