Complex wave-field reconstruction by means of the Page distribution function

Gase, R.; Gase, Torsten; Blüthner, K.

doi:10.1364/ol.20.002045

Cited by 8 publications

(1 citation statement)

References 11 publications

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“…The determination of the coherent modes 1 of a partially coherent beam and of their relative weights represents a key problem in characterizing real laser beams and sources, and several methods have been proposed to solve such a problem in the scalar case. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] In view of the current interest in light beams that are both partially polarized and partially coherent, [20][21][22][23][24][25][26][27][28] it is desirable to extend the coherent-mode representation to the case of vectorial electromagnetic beams. In the present paper, we show that such an extension can be carried out in a more or less straightforward way.…”

Section: Introductionmentioning

confidence: 99%

Coherent-mode decomposition of partially polarized, partially coherent sources

et al. 2003

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It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.

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Section: Introductionmentioning

confidence: 99%

Coherent-mode decomposition of partially polarized, partially coherent sources

et al. 2003

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Measurement of the Page function of an ultrashort laser pulse

Michelmann

Wagner

Feurer

et al. 2001

Optics Communications

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Phase-space distributions and the classical component of quantum observables

Luis

2003

Phys. Rev. A

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We analyze the relation between the classical part of quantum observables and the distributions representing quantum states and observables on the classical phase space. We determine in which conditions such a relation can be established, and the proper phase-space distribution required for this purpose. DOI: 10.1103/PhysRevA.67.064101 PACS number͑s͒: 03.65.Sq, 03.65.Ca, 03.65.Ta The representation of quantum states and observables by distributions on the classical phase space provides a distinguished tool to analyze fundamental aspects of the quantum physics, specially concerning the fuzzy boundary between the classical and quantum theories. For example, they can be used to determine how nonclassical is a quantum state ͑the so-called nonclassical depth͒ ͓1͔.Some recent works have put forward a decomposition of quantum observables into the sum of classical and nonclassical components ͓2,3͔. This splitting presents surprising and interesting properties concerning quantum fluctuations, uncertainty relations, and other fundamental aspects of the quantum theory ͓2-4͔. In particular, it has been shown that the classical part of the linear momentum ͑with respect to position͒ coincides with a local average of the Wigner function.This connection suggests a natural and fruitful relation between classical parts and classical-like description of quantum physics. In this work we study this correspondence in a more general framework by examining the case of arbitrary observables beyond linear momentum. On the one hand, when we consider arbitrary functions of momentum we find that the classical part is the local average of a phasespace distribution different from the Wigner function. ͑Natu-rally, for linear momentum such a distribution and the Wigner function give the same result.͒ On the other hand, if we consider arbitrary joint functions of position and momentum, we find that no phase-space correspondence of this kind can be established. where is the density matrix of the system. For definiteness, in what follows we focus on the case that the reference observable A is the Cartesian position of a onedimensional system, AϭX, while B will be arbitrary in principle. Incidentally, when AϭX, the classical parts are closely related to the de Broglie-Bohm approach to quantum mechanics, as discussed in Refs. ͓4,5͔. Moreover, when B is the linear momentum P, the classical part becomes proportional to the probability current density, which is a very intuitive result. In particular, for pure states ͉͘where (x)ϭ͗x͉͘ as usual. In Refs. ͓2,3͔ it has been shown that P c X can be suitably related to the Wigner function as a kind of a local expectation value of the form

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Complex wave-field reconstruction by means of the Page distribution function

Cited by 8 publications

References 11 publications

Coherent-mode decomposition of partially polarized, partially coherent sources

Coherent-mode decomposition of partially polarized, partially coherent sources

Measurement of the Page function of an ultrashort laser pulse

Phase-space distributions and the classical component of quantum observables

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