Propagation of partially coherent Gaussian Schell-model sources in nonlinear media

Nayyar, V. P.

doi:10.1364/josab.14.002248

Cited by 16 publications

(11 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several authors considered the case when the characteristic distance over which the nonlinear interaction between the field and the fluctuations of k 0 n nl (E)/n 0 takes place is much greater than the size of the region of longitudinal field correlation 0 ϭ k 0 0 2 , which is determined by the length of diffraction spreading of a characteristic inhomogeneity in the cross section of an incoherent beam. 12,16,17 Under such conditions the statistics are only slightly affected by the nonlinear effect, so that the fourth-order moments can be deduced from the secondorder moments according to the simple rules that are valid for Gaussian processes 18 and a closed-form equation for the AF can be obtained. Our framework is different because we take into consideration the slow nonlinear mechanism whose strength is much higher than the almost-instantaneous Kerr effect.…”

Section: Separation Of the Time Scalesmentioning

confidence: 99%

“…10 The case of the instantaneous nonlinear Schrödinger equation was addressed by Garnier et al 11 It was proved that the main contribution of the instantaneous nonlinearity is to break the Gauss-ian property of the statistical distribution and to enhance the local intensity fluctuations. Nayyar considered the propagation of the autocorrelation function (AF) of a GSM beam in a medium with third-order nonlinearity, 12 in the regime of rapid and weak nonlinearity. Here we consider a different regime, in which the nonlinearity has a greater amplitude but is slower than the coherence time of the pulse, and we also consider sources with general profiles and not only GSM sources.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Propagation of partially coherent light with the Maxwell–Debye equation

2003

View full text Add to dashboard Cite

We deal with the propagation of broadband Schell-model sources in nonlinear media with finite relaxation time. The approach is based on a study of the Wigner distribution function and on a separation of scales technique between the microscopic random fluctuations of the field and the macroscopic intensity profile. The regime in which the nonlinearity is strong and slow is considered. Precise results are obtained for the smalland large-scale characteristics of the pulse: optical intensity profile, speckle radius, and typical intensity profile of the speckle spots.

show abstract

Section: Separation Of the Time Scalesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Propagation of partially coherent light with the Maxwell–Debye equation

2003

View full text Add to dashboard Cite

show abstract

“…Advances in nonlinear optics and strong connections to the NLS motivate the effective interaction parameter used in our JWKB model. A deep theoretical understanding of the propagation and self-focusing of partially incoherent beams in nonlinear media, which can lead to spatial incoherent solitons, has been developed through several equivalent methods [104]: an infinite set of coupled nonlinear Schrödinger equations (coherent density approach) [105][106][107][108], propagation equation for mutual coherence function [109][110][111][112], and self-consistent multimode theory [113][114][115][116][117]. Similarities in the propagation equation for the mutual coherence method to the NLS allow for analytical techniques to be extended for partially incoherent regimes; e.g., derivation of an analytical expression for the collapse threshold of spatially partially coherent beans in inertial bulk Kerr media [118].…”

Section: Effective Mean-fieldmentioning

confidence: 99%

Macroscopic quantum tunneling escape of Bose-Einstein condensates

et al. 2017

View full text Add to dashboard Cite

Recent experiments on macroscopic quantum tunneling reveal a non-exponential decay of the number of atoms trapped in a quasibound state behind a potential barrier. Through both experiment and theory, we demonstrate this non-exponential decay results from interactions between atoms. Quantum tunneling of tens of thousands of 87 Rb atoms in a Bose-Einstein condensate is modeled by a modified Jeffreys-Wentzel-Kramers-Brillouin model, taking into account the effective time-dependent barrier induced by the mean-field. Three-dimensional Gross-Pitaevskii simulations corroborate a mean-field result when compared with experiments. However, with one-dimensional modeling using time-evolving block decimation, we present an effective renormalized mean-field theory that suggests many-body dynamics for which a bare mean-field theory may not apply.

show abstract

“…The progress was facilitated by the appearance of new methods for the treatment of incoherent localized beams in PR media: the coherent density method [4,5,9,14], the selfconsistent multimode method [2,7,8,11,13,15,18,19], and the mutual coherence function method [6,12]. They were developed independently to describe exactly such sorts of solitary waves in theory; however, it was soon demonstrated that these three seemingly different theoretical methods are equivalent to each other in inertial nonlinear media [21].…”

Section: Introductionmentioning

confidence: 99%

Interactions of incoherent localized beams in a photorefractive medium

et al. 2014

View full text Add to dashboard Cite

We investigate numerically interactions between two bright or dark incoherent localized beams in an strontium barium niobate photorefractive crystal in one dimension, using the coherent density method. For the case of bright beams, if the interacting beams are in-phase, they attract each other during propagation and form bound breathers; if out-of-phase, the beams repel each other and fly away. The bright incoherent beams do not radiate much and form long-lived well-defined breathers or quasi-stable solitons. If the phase difference is $\pi/2$, the interacting beams may both attract or repel each other, depending on the interval between the two beams, the beam widths, and the degree of coherence. For the case of dark incoherent beams, in addition to the above the interactions also depend on the symmetry of the incident beams. As already known, an even-symmetric incident beam tends to split into a doublet, whereas an odd-symmetric incident beam tends to split into a triplet. When launched in pairs, the dark beams display dynamics consistent with such a picture and in general obey soliton-like conservation laws, so that the collisions are mostly elastic, leading to little energy and momentum exchange. But they also radiate and breathe while propagating. In all the cases, the smaller the interval between the two interacting beams, the stronger the mutual interaction. On the other hand, the larger the degree of incoherence, the weaker the interaction.Comment: 6 pages, 5 figure

show abstract

Propagation of partially coherent Gaussian Schell-model sources in nonlinear media

Cited by 16 publications

References 46 publications

Propagation of partially coherent light with the Maxwell–Debye equation

Propagation of partially coherent light with the Maxwell–Debye equation

Macroscopic quantum tunneling escape of Bose-Einstein condensates

Interactions of incoherent localized beams in a photorefractive medium

Contact Info

Product

Resources

About