Angular and radial mode analyzer for optical beams

Abouraddy, Ayman F.; Yarnall, Timothy M.; Saleh, Bahaa E. A.

doi:10.1364/ol.36.004683

Cited by 28 publications

(26 citation statements)

References 13 publications

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“…For a discrete modal basis indexed by n (Equation 1), is periodic in α with period 2 π . Furthermore, Λ can be generalized to two transverse coordinates and is applicable to a continuous basis3334.…”

Section: Concept Of a Generalized Optical Delaymentioning

confidence: 99%

“…We introduce the concept of a generalized delay (GD): an optical transformation characterized by a continuous, real order-parameter that can be tuned to produce – once placed in one arm of an interferometer – an interferogram that reveals the modal weights in a prescribed functional basis via harmonic analysis. We find that GDs correspond to optical implementations of fractional transforms in the case of discrete modal bases3334. For example, it can be shown34 that the GD associated with Hermite Gaussian (HG) modes is the fractional Fourier transform3536, whereas that associated with radial LG modes37 is the fractional Hankel transform3839.…”

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confidence: 96%

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Basis-neutral Hilbert-space analyzers

Martin

Mardani

Kondakci

et al. 2017

Sci Rep

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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.

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Section: Concept Of a Generalized Optical Delaymentioning

confidence: 99%

mentioning

confidence: 96%

Basis-neutral Hilbert-space analyzers

Martin

Mardani

Kondakci

et al. 2017

Sci Rep

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“…An alternative setup that does not alter the OAM state during the measurement procedure is a Mach-Zehnder interferometer with a Dove prism in each arm [22,23], but to measure 2 n states requires 2 n -1 interferometers. A modified Mach-Zehnder interferometer can also be described to determine both the angular and radial mode content of scalar optical fields [24] but such systems are known to be sensitive to alignment [24]. Digital holograms are also used to extract the azimuthal modal content of optical fields for the reconstruction of its amplitude, phase and OAM density [25].…”

Section: Introductionmentioning

confidence: 99%

Efficient sorting of Bessel beams

Mhlanga

Dudley

McDonald

et al. 2013

Complex Light and Optical Forces VII

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Abstract:We demonstrate the efficient sorter of Bessel beams separating both the azimuthal and radial components. This is based upon the recently reported transformation of angular to transverse momentum states. We separately identify over forty azimuthal and radial components, with a radial spacing of 1588 m −1 , and outline how the device could be used to identify the two spatial dimensions simultaneously.

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“…The principle of this method may be extended to other DOFs (such as optical orbital angular momentum or other spatial modes,) by using appropriate projective measurements [15,16]. This result hinges on the fact that the vector space describing the properties of an electromagnetic field having multiple DOFs [5,17] is the direct product of the vector spaces corresponding to each DOF.…”

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confidence: 99%

Two-point optical coherency matrix tomography

2014

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The two-point coherence of an electromagnetic field is represented completely by a 4×4 coherency matrix G that encodes the joint polarization-spatial-field correlations. Here, we describe a systematic sequence of cascaded spatial and polarization projective measurements that are sufficient to tomographically reconstruct G--a task that, to the best of our knowledge, has not yet been realized. Our approach benefits from the correspondence between this reconstruction problem in classical optics and that of quantum state tomography for two-photon states in quantum optics. Identifying G uniquely determines all the measurable correlation characteristics of the field and, thus, lifts ambiguities that arise from reliance on traditional scalar descriptors, especially when the field's degrees of freedom are correlated or classically entangled.

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Angular and radial mode analyzer for optical beams

Cited by 28 publications

References 13 publications

Basis-neutral Hilbert-space analyzers

Basis-neutral Hilbert-space analyzers

Efficient sorting of Bessel beams

Two-point optical coherency matrix tomography

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