Propagation of partially coherent light with the Maxwell–Debye equation

Garnier, Josselin; Ayanides, Jean-Philippe; Morice, O.

doi:10.1364/josab.20.001409

Cited by 19 publications

(20 citation statements)

References 17 publications

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“…From this point of view, these ISs are of the same nature as the ISs predicted in plasma physics a long time ago in the framework of the Vlasov equation [27][28][29]. This analogy with nonlinear plasma waves has been also exploited in optics in different circumstances [30][31][32], in particular to interpret the existence of a threshold in the incoherent modulational instability as a consequence of the phenomenon of Landau damping [21].…”

Section: Introductionmentioning

confidence: 52%

“…A WT approach of the problem revealed that this type of IS can be described in detail in the framework of a Vlasov-like kinetic equation, which is shown to provide an "exact" statistical description of the highly nonlocal random wave system. We note that this Vlasov equation differs from the traditional Vlasov equation considered for the study of incoherent modulational instability and ISs in plasmas [28,29,58], hydrodynamics [59], and optics [21,[30][31][32], while its structure is analogous to that recently used to describe systems of particles with long-range interactions [60].…”

Section: Introductionmentioning

confidence: 89%

“…(1) thus leads to a closure of the hierarchy of the moment equations. More specifically, using statistical arguments similar as those in [31], one can show that, owing to the highly nonlocal response, the statistics of the incoherent wave turns out to be Gaussian. Then, contrarily to a conventional Vlasov equation, whose validity is constrained by the assumptions of (i) weakly nonlinear interaction and (ii) quasi-homogeneous statistics, the long-range Vlasov equation provides an exact statistical description of the random wave ψx; z in the highly nonlocal regime, ε ≪ 1.…”

Section: Long-range Responsementioning

confidence: 98%

“…This type of Vlasov equation was considered in various different fields to study incoherent modulational instability and ISs in plasmas [28,29,58], hydrodynamics [59], and optics [21,[30][31][32].…”

Section: Local Limitmentioning

confidence: 99%

See 3 more Smart Citations

Toward a wave turbulence formulation of statistical nonlinear optics

Garnier

Lisak²,

Picozzi³

2012

J. Opt. Soc. Am. B

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During this last decade, several remarkable phenomena inherent to the nonlinear propagation of incoherent optical waves have been reported in the literature. This article is aimed at providing a generalized wave turbulence kinetic formulation of random nonlinear waves governed by the nonlinear Schrödinger equation in the presence of a nonlocal or a noninstantaneous nonlinear response function. Depending on the amount of nonlocal (noninstantaneous) nonlinear interaction and the amount of inhomogeneous (nonstationary) statistics of the incoherent wave, different types of kinetic equations are obtained. In the spatial domain, when the incoherent wave exhibits fluctuations that are statistically homogeneous in space, the relevant kinetic equation is the wave turbulence (Hasselmann) kinetic equation. It describes, in particular, the process of optical wave thermalization to thermodynamic equilibrium, which slows down significantly as the interaction becomes highly nonlocal. When the incoherent wave is characterized by inhomogeneous statistical fluctuations, different forms of the Vlasov equation are derived, which depend on the amount of nonlocality in the system. This Vlasov approach describes, in particular, the processes of incoherent modulational instability and the formation of localized incoherent soliton structures. In the temporal domain, the noninstantaneous nonlinear response function is constrained by the causality condition. It turns out that the relevant kinetic equation has a form analogous to the weak Langmuir turbulence equation, which describes, in particular, the formation of nonlocalized spectral incoherent solitons. In the regime of a highly noninstantaneous nonlinear response and a stationary statistics of the incoherent wave, the weak Langmuir turbulence equation reduces to the Korteweg-de Vries equation. Conversely, in the regime of a highly noninstantaneous response in the presence of a nonstationary statistics, we derive a long-range Vlasov-like kinetic equation in the temporal domain, whose self-consistent potential is constrained by the causality condition. From a broader perspective, this work indicates that the wave turbulence theory may constitute the appropriate theoretical framework to formulate statistical nonlinear optics.

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Section: Introductionmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 89%

Section: Long-range Responsementioning

confidence: 98%

Section: Local Limitmentioning

confidence: 99%

See 2 more Smart Citations

Toward a wave turbulence formulation of statistical nonlinear optics

Garnier

Lisak²,

Picozzi³

2012

J. Opt. Soc. Am. B

Self Cite

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“…On the analogy of the non-diffracting optical beam [7][8][9][10][11][12][13][14], the complex coherence function should also have diffraction-free solutions. In recently, the correlated Schellmodel sources caused great attention [15][16][17][18][19][20][21][22][23][24][25]. In this paper, we experimentally demonstrate the coherence function and study its full-field distributions.…”

Section: Introductionmentioning

confidence: 99%

A comparison of diffracting and non-diffracting coherence functions based on full field spatial coherence visualization system

Zhao¹,

Takeda

Wang³

2015

SPIE Proceedings

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In this paper, we proposed a novel optical geometry for direct visualization of spatial coherence function. The full-field distribution of the coherence function from an incoherent circular aperture source is experimentally investigated. Meanwhile, the experiments of non-diffracting coherence function from an incoherent circular slit source have also been done. The experimental results show that the coherence function generated by an incoherent circular aperture source is in the form of Fresnel diffraction integral which diffracting during the propagation and the coherence function generated by an incoherent circular slit source is unaltered by propagating in free space.

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Optical Wave Turbulence in Fibers

Picozzi

Garnier

et al. 2017

Shaping Light in Nonlinear Optical Fibers

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Propagation of partially coherent light with the Maxwell–Debye equation

Cited by 19 publications

References 17 publications

Toward a wave turbulence formulation of statistical nonlinear optics

Toward a wave turbulence formulation of statistical nonlinear optics

A comparison of diffracting and non-diffracting coherence functions based on full field spatial coherence visualization system

Optical Wave Turbulence in Fibers

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