Bell's measure in classical optical coherence

Kagalwala, Kumel H.; Giuseppe, Giovanni Di; Abouraddy, Ayman F.; Saleh, Bahaa E. A.

doi:10.1038/nphoton.2012.312

Cited by 234 publications

(226 citation statements)

References 35 publications

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“…Indeed, axially self-similar propagation becomes a generic feature of beams incorporating these correlations in their ST-spectrum. This work can thus be viewed as a generalization of burgeoning working on so-called 'classical entanglement' [48][49][50] to continuous DoFs of the optical field. Previous demonstrations of classical entanglement have been confined to date to discretized DoFs such as polarization and individual spatial or temporal modes.…”

Section: Resultsmentioning

confidence: 99%

Diffraction-free space–time light sheets

Kondakci¹,

Abouraddy²

2017

Nature Photon

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Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles restricted to one transverse dimension. Here, we demonstrate that the temporal degree of freedom can be exploited to efficiently synthesize onedimensional pulsed optical sheets that propagate self-similarly in free space. By introducing programmable conical (hyperbolic, parabolic, or elliptical) spectral correlations between the beam's spatio-temporal degrees of freedom, a continuum of families of axially invariant pulsed localized beams is generated. The spectral loci of such beams are the reduced-dimensionality trajectories at the intersection of the light-cone with spatio-temporal spectral planes. Far from being exceptional, self-similar axial propagation is a generic feature of fields whose spatial and temporal degrees of freedom are tightly correlated. These one-dimensional 'space-time' beams can be useful in optical sheet microscopy, nonlinear spectroscopy, and non-contact measurements.Diffractive spreading is a fundamental feature of freely propagating optical beams that is readily observed in everyday life. Diffraction sets limits on the optical resolution in microscopy, lithography, and photography; on the maximum distance for free-space optical communications and standoff detection; and on the precision of spectral analysis 1,2 . As a result, there has been a long-standing fascination with socalled 'diffraction-free' beams whose change in shape and scale during propagation is curbed when compared to other beams of comparable transverse size 3 . Monochromatic diffraction-free beams have sculpted two-dimensional (2D) transverse spatial profiles that confirm to Bessel 4 , Mathieu 5 , or Weber 6 functions, among other examples (see Refs. [7,8] for recent taxonomies). The situation is altogether different for monochromatic beams with one transverse dimension -or optical sheets -where there are only two possible diffraction-free solutions: the cosine wave that lacks spatial localization and the Airy beam that maintains a localized intensity profile but whose center-of-mass undergoes a transverse shift with propagation 9,10 . Indeed, a conclusive argument by Michael Berry 11 identified the Airy beam as the only such monochromatic one-dimensional (1D) profile. Optical nonlinearities can be exploited to thwart diffractive spreading 12,13 , and in some cases chromatic dispersion is required in the medium to restrain the diffraction of pulsed beams [14][15][16] . However, most applications require free-space diffraction-free beams.Here, we exploit the temporal degree of freedom (DoF) in conjunction with the spatial DoF to realize a variety of diffraction-free pulsed solutions having arbitrary 1D transverse profiles. By establishing a correlation between the spatial and temporal DoFs, diffractive spreading is reined-in and the time-averaged spatial profile propagates self-similarly. ...

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Section: Resultsmentioning

confidence: 99%

Diffraction-free space–time light sheets

Kondakci¹,

Abouraddy²

2017

Nature Photon

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299

283

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“…This measure has been experimentally examined by Kagalwala et al [24]. One fundamental problem of their formulation is that it varies under global unitary transformations.…”

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confidence: 99%

Revealing Hidden Coherence in Partially Coherent Light

et al. 2015

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Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a coherent beam, where each spatial mode bears different polarizations. Whereas a local unitary transformation of the system does not affect its coherence, global unitary transformations modifying both the system and its surroundings can enhance its coherence, transforming mutual correlations into coherence. The question naturally arises of what is the best measure that quantifies the correlations that can be turned into coherence, and how much coherence can be extracted. We answer both questions, and illustrate its application for some typical simple systems, with the aim at illuminating the general concept of enhancing coherence by modifying correlations. Introduction.-Coherence is one of the most important concepts needed to describe the characteristics of a stream of photons [1, 2], where it allows us to characterize the interference capability of interacting fields. However its use is far more general as it plays a striking role in a whole range of physical, chemical, and biological phenomena [3]. Measures of coherence can be implemented using classical and quantum ideas, which lead to the question of in which sense quantum coherence might deviate from classical coherence phenomena [4], and to the evaluation of measures of coherence [5][6][7].Commonly used coherence measures consider a physical system as a whole, omitting its structure. The knowledge of the internal distribution of coherence between subsystems and their correlations becomes necessary for predicting the evolution (migration) of coherence in the studied system. The evolution of a twin beam from the near field into the far field represents a typical example occurring in nature [8]. The creation of entangled states by merging the initially separable incoherent and coherent states serves as another example [7]. Or, in quantum computing the controlled-NOT gate entangles (disentangles) two-qubit states [9,10], at the expense (in favor) of coherence. Many quantum metrology and communication applications benefit from correlations of entangled photon pairs originating in spontaneous parametric down-conversion [11][12][13]. Even separable states of photon pairs, i.e. states with suppressed correlations, are very useful, e.g., in the heralded single photon sources [14,15]. For all of these, and many others, examples the understanding of common evolution of coherence and correlations is crucial.The Clauser-Horne-Shimony-Holt (CHSH) Bell's-like inequality [16][17][18] has been usually considered to quantify nonclassical correlations present between physically sepa-

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“…This analogy between polarization and purity has been discussed by some authors [6]. Some authors have suggested the use of Bell's measure, commonly used in tests of quantum non-locality, to quantify classical optical coherence (polarization) [7]. Others have suggested a particular measure of polarization in higher dimensions [8].…”

Section: Introductionmentioning

confidence: 99%

Measures of quantum state purity and classical degree of polarization

Gamel

James

2012

Phys. Rev. A

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There is a well known mathematical similarity between two dimensional classical polarization optics and two level quantum systems, where the Poincare and Bloch spheres are identical mathematical structures. This analogy implies classical degree of polarization and quantum purity are in fact the same quantity. We make extensive use of this analogy to analyze various measures of polarization for higher dimensions proposed in the literature, and in particular, the N = 3 case, illustrating interesting relationships that emerge as well the advantages of each measure. We also propose a possible new class of measures of entanglement based on purity of subsystems.

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Bell's measure in classical optical coherence

Cited by 234 publications

References 35 publications

Diffraction-free space–time light sheets

Diffraction-free space–time light sheets

Revealing Hidden Coherence in Partially Coherent Light

Measures of quantum state purity and classical degree of polarization

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