Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation

Dyachenko, Alexander; Newell, Alan C.; Pushkarev, A. N.; Захаров, В. Е.

doi:10.1016/0167-2789(92)90090-a

Cited by 425 publications

(634 citation statements)

References 19 publications

Supporting

Mentioning

614

Contrasting

Unclassified

Order By: Relevance

“…Such a blow-up behavior may result in wave collapse and optical turbulence (cf. [4], [5] and [15]). Due to the positive sign of µ j 's, the system (1.1) is of two-component self-focusing nonlinear Schrödinger equations having an increasing tendency for the solution to be trapped in regions of highest intensity.…”

Section: Introductionmentioning

confidence: 99%

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Lin

Wei

2006

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Conventionally, to learn wave collapse and optical turbulence, one must study finite-time blow-up solutions of one-component self-focusing nonlinear Schrödinger equations (NLSE). Here we consider simultaneous blow-up solutions of two-component system of self-focusing NLSE. By studying the associated self-similar solutions, we prove two components of solutions blow up at the same time. These self-similar solutions may come from solitary wave solutions with multi-bumps forming abundant geometric patterns which cannot be found in one-component self-focusing NLSE. Our results may provide the first step to investigate optical turbulence in two-component system of NLSE.

show abstract

Section: Introductionmentioning

confidence: 99%

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Lin

Wei

2006

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…This so called modulational instability (MI) phenomenon, has been extensively studied because of its importance as a factor limiting the propagation of high power beams. Filamentation may also be identified as the first stage in the development of turbulent fluctuations in the transverse profile of a laser beam [2]. In addition, MI is often considered as a precursor for the formation of spatial and/or temporal optical solitons.…”

mentioning

confidence: 99%

Two-dimensional modulational instability in photorefractive media

Saffman¹,

McCarthy²,

Królikowski³

2004

J. Opt. B: Quantum Semiclass. Opt.

View full text Add to dashboard Cite

We study theoretically and experimentally the modulational instability of broad optical beams in photorefractive nonlinear media. We demonstrate the impact of the anisotropy of the nonlinearity on the growth rate of periodic perturbations. Our findings are confirmed by experimental measurements in a strontium barium niobate photorefractive crystal.PACS numbers: 42.65. Hw, 42.65.Jx A plane wave propagating in a medium with focusing nonlinearity is unstable with respect to the generation of small scale filaments [1]. This so called modulational instability (MI) phenomenon, has been extensively studied because of its importance as a factor limiting the propagation of high power beams. Filamentation may also be identified as the first stage in the development of turbulent fluctuations in the transverse profile of a laser beam [2]. In addition, MI is often considered as a precursor for the formation of spatial and/or temporal optical solitons. As far as optics is concerned, MI has been studied in media with various mechanisms of nonlinear response including cubic [1], quadratic [3], nonlocal [4,5] and inertial [6,7] types of nonlinearity. Importantly, MI is not restricted to nonlinear optics but has also been studied in many other nonlinear systems including fluids [8], plasmas [9] and matter waves [10].In the context of optical beam propagation in nonlinear materials MI has usually been considered in media with spatially isotropic nonlinear properties. Recently a great deal of theoretical and experimental efforts have been devoted to studies of nonlinear optical effects and soliton formation in photorefractive crystals [11,12,13]. While these media exhibit strong nonlinearity at very low optical power their nonlinear response is inherently anisotropic [14]. The anisotropy causes a number of observable effects including astigmatic self-focusing of optical beams [15], elliptically shaped solitary solutions [16], geometry-sensitive interactions of solitons [17], and fixed optical pattern orientation [18].Several previous studies of MI in the context of photorefractive media were limited to a 1-dimensional geometry where the anisotropy is absent [19,20,21], and the physics is similar to the standard saturable nonlinearity [22]. On the other hand, in a real physical situation where one deals with finite sized beams, the anisotropic aspects of the photorefractive nonlinear response are expected to play a significant role. Some previous work [23,24] already indicated the importance of anisotropy in the transversal break-up of broad beams propagating in biased photorefractive crystals. However, no detailed analysis of this phenomenon was carried out. In this paper we study the MI of optical beams in photorefractive media taking into account the full 2-dimensional anisotropic model of the photorefractive nonlinearity.Time independent propagation of an optical beam E(r, z) = (A/2)e ı(kz−ωt) + c.c. in a nonlinear medium with a weakly varying index of refraction is governed by the parabolic equationHere r = (x, y) and z are ...

show abstract

“…The horseshoe of the homoclinic crossings creates the disorder following the fusion of two peaks. A phenomenon similar to the merging of peaks was found in a continuous non-integrable NLS equation [7]. Unlike solitons in integrable systems, collisions of solitary solutions of nonintegrable equations lead to a transfer of power from the weaker soliton to the stronger one while low amplitude waves are radiated.…”

Section: Discrete Nls Equationmentioning

confidence: 90%

“…This behavior is usually encountered on time scales that are short enough so that generic nonintegrable contributions to the dynamics may be neglected. Significant changes occur on time scales where the nonintegrability is relevant [6], [7]. The solution's shape becomes more irregular [8], [9], [10], [11] and the periodic breathing of the peaks turns into a more persistent state.…”

Section: Introductionmentioning

confidence: 99%

Localization and coherence in nonintegrable systems

Rumpf

Newell

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asymptotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved quantities leads naturally to localized and coherent structures. If the phase space is compact, the final equilibrium state is governed by entropy maximization and the coherent structures are stable lumps. In systems where the phase space is not compact, the coherent structures can be collapses represented in phase space by a heteroclinic connection of some unstable saddle to infinity.

show abstract

Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation

Cited by 425 publications

References 19 publications

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Two-dimensional modulational instability in photorefractive media

Localization and coherence in nonintegrable systems

Contact Info

Product

Resources

About