Self‐Squeezing of Elliptically Polarized Light Propagating in a Kerr‐Like Optically Active Medium

Kielich, S.; Tanaś, R.; Zawodny, R.

doi:10.1002/9780470141434.ch13

Cited by 3 publications

(2 citation statements)

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“…This could be expected since in many models [19,23], for instance in the anharmonic oscillator model (for references see Ref. [94]), there occur third-order derivatives in the FPEs for the Wigner function (s = 0).…”

Section: Fokker-planck Equation a Raman Scattering Including Pump Dep...mentioning

confidence: 91%

“…85 of this series and references therein, for instance Refs. [93][94][95], as well as the reviews by Kielich et al [96], Leuchs [97], Loudon and Knight [98], Teich and Saleh [99,100], Zaheer and Zubairy [101] and the topical issues of the Journal of the Optical Society of America B [102] and the Journal of Modern Optics [103]. Squeezing properties of Raman scattering have been studied by Peřinová and et al Peřina, Kárská and Peřina [56], Levenson et al and Peřina and Křepelka [67,68].…”

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confidence: 99%

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Quantum-statistical theory of Raman scattering processes

Miranowicz¹,

Kielich²

2011

Preprint

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Raman scattering from a great number of phonon modes is described from a quantum-statistical point of view within the standing-wave model. The master equation for the completely quantum case, including laser pump depletion and stochastic coupling of Stokes and anti-Stokes modes, is derived and converted to classical equations: either into a generalized Fokker-Planck equation and an equation of motion for the characteristic function or into the master equation in Fock representation. These two approaches are developed both in linear and nonlinear régime. A detailed analysis of scattering into Stokes and anti-Stokes modes in linear régime, i.e., under parametric approximation, is presented. The existence of s-parametrized quasiprobability distributions, in particular the Glauber-Sudarshan P -function, is investigated. An analysis of Raman scattering into separate Stokes and anti-Stokes modes in nonlinear régime, thus including pump depletion, is given. The master equation in Fock representation is solved exactly for the complete density matrix using the Laplace transform method. Short-time solutions, steady-state solutions and approximate compact form solutions are obtained. Relations between the quasidistribution approach based on the Fokker-Planck equation and the density matrix approach based on the master equation in Fock representation are presented. The photocount distribution and its factorial moments as well as variances and extremal variances of quadratures are calculated in both approaches giving the basis for the analysis of the quantum properties of radiation such as sub-Poissonian photon-counting statistics and squeezing. A comparison of various statistical moments obtained from numerical calculations utilizing our exact solution of the master equation and from the approximate relations for short times, as well as obtained under parametric approximation, is presented graphically. Contents I. Introduction: Historical developments 2 II. Model and master equation 7 III. Multimode s-parametrized quasidistributions 14 IV. Photon-counting statistics and squeezing: definitions 16 V. Fokker-Planck equation 21 A. Raman scattering including pump depletion 21 B. Raman scattering without pump depletion 25 VI. Master equation in Fock representation 39 A. Raman scattering including pump depletion 40 1. Short-time solutions 40 2. Exact solutions 49 3. Long-time solutions 54

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Section: Fokker-planck Equation a Raman Scattering Including Pump Dep...mentioning

confidence: 91%