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Gori, F.; Santarsiero, Massimo; Vicalvi, S.; Borghi, Riccardo; Guattari, G.

doi:10.1088/0963-9659/7/5/004

Cited by 160 publications

(48 citation statements)

References 40 publications

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“…5 In fact, a single 2 3 2 matrix, called a beam coherencepolarization (BCP) matrix, is suff icient to yield a complete account of the second-order statistical properties of the f ield. 3 In scalar coherence theory, the van Cittert-Zernike theorem is a fundamental tool for studying the propagation processes of partially coherent fields. 5,6 Moreover, several partially coherent beams are generated starting from a primary spatially incoherent source.…”

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Use of the van Cittert–Zernike theorem for partially polarized sources

et al. 2000

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We introduce an extension of the van Cittert -Zernike theorem to spatially incoherent sources with partial polarization. We show through a simple example that fields generated by such sources can possess correlation matrices with interesting properties. In particular, we show that by suitable modulation of the polarization state across the incoherent source, the correlation between the orthogonal components of the field as well as the degree of polarization may drastically change on propagation. © 2000 Optical Society of America OCIS codes: 030.0030, 060.2380, 230.6080, 260.5430. There is currently an interest in optical beams that are both partially coherent from the spatial standpoint and partially polarized. -4Such beams can be described by an approximate version of the general tensorial theory of the electromagnetic f ield developed by Wolf. 5In fact, a single 2 3 2 matrix, called a beam coherencepolarization (BCP) matrix, is suff icient to yield a complete account of the second-order statistical properties of the f ield. 3In scalar coherence theory, the van Cittert-Zernike theorem is a fundamental tool for studying the propagation processes of partially coherent fields. 5,6 Moreover, several partially coherent beams are generated starting from a primary spatially incoherent source. 5,7,8 In such synthesis procedures the van Cittert -Zernike theorem plays a major role. We have observed that a spatially incoherent source can exhibit partial polarization and that the polarization state can change from one point to another across the source. Thus a suitable extension of the van Cittert -Zernike theorem to these sources should be sought. In this Letter we introduce such an extended version of the theorem. We then work out a specific example. It will be shown that the correlation functions appearing in the BCP matrix can behave in a rather different way with respect to each other. This will help the reader to appreciate the significance of the vectorial case. Furthermore, our results suggest that in the vectorial case, too, the van Cittert-Zernike theorem can serve as a useful tool in synthesis processes.We use a reference frame in which the z axis coincides with the mean direction of propagation of the beam. At a typical transverse plane, the vector r is used to specify the position of a point. Let us recall that, for a quasi-monochromatic field, the BCP matrix is def ined as 3 J͑r 1 , r 2 , z͒ ∑ J xx ͑r 1 , r 2 , z͒ J xy ͑r 1 , r 2 , z͒ J yx ͑r 1 , r 2 , z͒ J yy ͑r 1 , r 2 , z͒whereThe angle brackets denote time average, and E a ͑a x, y͒ is a Cartesian component of the time-dependent electric f ield. In the framework of scalar theory a spatially incoherent source is characterized by means of a d-like mutual intensity function, which expresses the fact that the fields at any two distinct points across the source plane are uncorrelated. 5In the same way we def ine a partially polarized, spatially incoherent source as one whose BCP matrix elements J ab have the formwhere d is the two-dimensional Dirac function...

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“…3 Since the f ield specified by Eqs. (8) and (9) is linearly polarized, there is a perfect correlation between any two f ield components at a typical source point.…”

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Use of the van Cittert–Zernike theorem for partially polarized sources

et al. 2000

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“…The seminal work on the subject was published by James [7], who showed that the degree of polarization of light beams may change upon propagation, depending on the spatial correlation properties of the light beam. Such an intrinsic connection between spatial coherence and partial polarization has been discussed in numerous later works (see, for example, [8][9][10][11][12]). …”

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confidence: 71%

Coherence–polarization mixing in resonance gratings

et al. 2012

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We show, using rigorous diffraction theory, that resonance gratings can be used to transfer partial spatial correlation to partial polarization even if the incident light beam is fully polarized. The phenomenon is based on the fact that either of the two orthogonal polarization components can be coupled into the leaky waveguide mode, leading to a strong phase delay, while the other one is reflected without being coupled into the grating. Numerical demonstrations are based on a Gaussian Schell-model beam and a grating analysis performed by rigorous Fourier modal method.

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“…However, since the formulation of the unified theory of coherence and polarization [10][11][12], several studies have been devoted to the question of how the HBT effect in random electromagnetic beams can be analyzed [13][14][15][16][17]. It is well known that the fundamental properties of these beams, such as their spectrum, degree of polarization, state of polarization, and degree of coherence, can all change significantly on propagation, even when the propagation is through free space [18][19][20][21][22][23][24]. However, until now a detailed investigation of the evolution of the HBT effect in random electromagnetic beams has been lacking.…”

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Hanbury Brown–Twiss effect with partially coherent electromagnetic beams

Visser

2014

Opt. Lett.

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We derive expressions that allow us to examine the influence of different source parameters on the correlation of intensity fluctuations (the Hanbury Brown-Twiss effect) at two points in the same cross section of a random electromagnetic beam. It is found that these higher-order correlations behave quite differently than the lower-order amplitude-phase correlations that are described by the spectral degree of coherence.

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Cited by 160 publications

References 40 publications

Use of the van Cittert–Zernike theorem for partially polarized sources

Use of the van Cittert–Zernike theorem for partially polarized sources

Coherence–polarization mixing in resonance gratings

Hanbury Brown–Twiss effect with partially coherent electromagnetic beams

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