Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles

Alonso, Miguel A.

doi:10.1364/aop.3.000272

Cited by 148 publications

(97 citation statements)

References 152 publications

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“…The literature on the Wigner functions of optical vortices, Airy beams and their generalizations is extensivesee, for example, refs. [53][54][55][56][57][58][59]. Here we do not intend to make a comprehensive comparison of our results with those obtained in optics.…”

Section: Generalitiesmentioning

confidence: 99%

Scattering of wave packets with phases

Karlovets

2017

J. High Energ. Phys.

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A general problem of 2 → N f scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in (3 + 1) D, vortex particles with orbital angular momentum, the Airy beams, and their generalizations. A method is developed in which a number of events represents a functional of the Wigner functions of such states. Using width of a packet σ p / p as a small parameter, the Wigner functions, the number of events, and a cross section are represented as power series in this parameter, the first non-vanishing corrections to their plane-wave expressions are derived, and generalizations for beams are made. Although in this regime the Wigner functions turn out to be everywhere positive, the cross section develops new specifically quantum features, inaccessible in the plane-wave approximation. Among them is dependence on an impact parameter between the beams, on phases of the incoming states, and on a phase of the scattering amplitude. A model-independent analysis of these effects is made. Two ways of measuring how a Coulomb phase and a hadronic one change with a transferred momentum t are discussed.

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Section: Generalitiesmentioning

confidence: 99%

Scattering of wave packets with phases

Karlovets

2017

J. High Energ. Phys.

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“…The advantages of coherent and incoherent light, such as phase recovery of the diffracted field and speckle-noise reduction, can be combined by controlling the DoC of the involved light. On the other hand, the phase-space representation can be helpful for the design and characterization of optical systems, structurally stable beams, and spatially nonstationary fields [16].…”

Section: Discussionmentioning

confidence: 99%

“…Instead of the MI, its Fourier transform (FT) respect to the position difference r 1 − r 2 , known as Wigner distribution (WD) [15,16], can be used for beam description. The WD is a real 4D function but it may take negative values that also impedes its direct measurement.…”

Section: Introductionmentioning

confidence: 99%

Optical coherenscopy based on phase-space tomography

Cámara¹,

Rodrigo²,

Alieva³

2013

Opt. Express

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Abstract:Partially coherent light provides attractive benefits in imaging, beam shaping, free-space communications, random medium monitoring, among other applications. However, the experimental characterization of the spatial coherence is a difficult problem involving second-order statistics represented by four-dimensional functions that cannot be directly measured and analyzed. In addition, real-world applications usually require quantitative characterization of the local spatial coherence of a beam in the absence of a priori information, together with fast acquisition and processing of the experimental data. Here we propose and experimentally demonstrate a technique that solves this problem. It comprises an optical setup developed for automatized video-rate measurement and a method -phase-space tomographic coherenscopy-allowing parallel data acquisition, processing, and analysis. This technique significantly simplifies the spatial coherence analysis and opens up new perspectives for the development of tools exploiting the degrees of freedom hidden into light coherence.

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“…8 (Appendix E) have been constructed successfully based on this method. Since the real WDF of the light field has a more general definition in the nonparaxial regime [33], it is expected to have more to be explored in this regime compared with the above discussion in the future work.…”

Section: Design Of Light Beams In 3d Spacementioning

confidence: 99%

“…The physical meaning of the WDF in optics can be approximately interpreted as the intensity of a light ray with a specific position and direction. Particularly, the WDF has been exploited to study the propagation of Airy beams [32,33], which provides an intuitive picture to explain the novel characteristics of these accelerating beams. Since the propagation properties of accelerating beams are related to the WDF, a question naturally arises: Is it possible to construct accelerating beams simply by engineering the WDF?…”

Section: Introductionmentioning

confidence: 99%

Tailoring accelerating beams in phase space

et al. 2017

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This is the final published version of the article (version of record). It first appeared online via APS Physics at https://doi.org/10.1103/PhysRevA.95.023825 . Please refer to any applicable terms of use of the publisher. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms PHYSICAL REVIEW A 95, 023825 (2017) Tailoring accelerating beams in phase space An appropriate wave-front design will enable light fields that propagate along arbitrary trajectories, thus forming accelerating beams in free space. Previous strategies for designing such accelerating beams rely mainly on caustic methods, which start from diffraction integrals and deal only with two-dimensional fields. Here we introduce an alternate perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find that such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space, respectively. Moreover, this approach applies to the construction of both two-and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open a new route for construction of highly tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.

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Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles

Cited by 148 publications

References 152 publications

Scattering of wave packets with phases

Scattering of wave packets with phases

Optical coherenscopy based on phase-space tomography

Tailoring accelerating beams in phase space

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