Propagation of light beams in anisotropic nonlinear media: From symmetry breaking to spatial turbulence

Мамаев, А. В.; Saffman, M.; Anderson, Donald G.; Zozulya, A. A.

doi:10.1103/physreva.54.870

Cited by 167 publications

(74 citation statements)

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“…Spatial perturbations with nonzero q y components have much weaker growth rates and will play an important role only after the 1D structure with q y ≈ 0 has reached sufficiently high intensity [18]. Then the full 2-dimensional break-up and subsequent filamentation of the beam will follow [23,25]. However, the full analysis of such a process is beyond the scope of the present paper.…”

Section: Figmentioning

confidence: 93%

“…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.…”

mentioning

confidence: 99%

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Two-dimensional modulational instability in photorefractive media

Saffman¹,

McCarthy²,

Królikowski³

2004

J. Opt. B: Quantum Semiclass. Opt.

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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 ...

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Section: Figmentioning

confidence: 93%

mentioning

confidence: 99%

Two-dimensional modulational instability in photorefractive media

Saffman¹,

McCarthy²,

Królikowski³

2004

J. Opt. B: Quantum Semiclass. Opt.

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“…When an intense light beam propagates in a nonlinear medium, it can experience filamentation effects, leading to periodic spatial distributions [168], or develop into self-trapped states of light, or solitons. The self-focusing action of the nonlinearity compensated by diffraction results in self-sustained bright spatial solitons [12], which can exist as isolated states or form complex ensembles, sometimes interacting in a particle-like fashion [169][170][171][172][173][174][175].…”

Section: Mirrorless Configurationmentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

174

156

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This book is devoted to the formation and dynamics of localized structures (vortices, solitons) and of extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. Theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given.

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“…Yv, 42.65Tg, 42.65.Sf. Wide (∼1 mm) Gaussian beams launched in a photorefractive (PR) crystal in the self-focusing regime tend to break into spatially disordered arrays of filaments, owing to transverse modulational instabilities [1]. However, ordered arrays of Gaussian beamlets (∼10 µm), launched in conditions appropriate to the generation of spatial screening solitons [2], form much more stable solitonic lattices.…”

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confidence: 99%

Solitonic lattices in photorefractive crystals

et al. 2003

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Two-dimensional spatial solitonic lattices are generated and investigated experimentally and numerically in an SBN:Ce crystal. An enhanced stability of these lattices is achieved by exploiting the anisotropy of coherent soliton interaction, in particular the relative phase between soliton rows. Manipulation of individual soliton channels is achieved by use of supplementary control beams.PACS numbers: 05.45. Yv, 42.65Tg, 42.65.Sf. Wide (∼1 mm) Gaussian beams launched in a photorefractive (PR) crystal in the self-focusing regime tend to break into spatially disordered arrays of filaments, owing to transverse modulational instabilities [1]. However, ordered arrays of Gaussian beamlets (∼10 µm), launched in conditions appropriate to the generation of spatial screening solitons [2], form much more stable solitonic lattices. Weakly interacting pixel-like arrangements of solitons that can individually be addressed are interesting for applications as self-adaptive waveguides [3,4].Adaptive waveguides are of particular interest in alloptical information processing for their potential to generate large arrays, as well as for allowing many configurations with different interconnection possibilities. Spatial optical solitons are natural candidates for such applications, owing to their ability for self-adjustable waveguiding and versatile interaction capabilities, as demonstrated in light-induced Y and X couplers, beam splitters, directional couplers and waveguides. In addition to such few-beam configurations, the geometries with many solitons propagating in parallel-the so-called soliton pixels, arrays, or lattices-have been suggested for applications in information processing and image reconstruction [5,6,7,8]. Recently several groups demonstrated the formation of quadratic arrays of solitons in parametric amplifiers [8,9] and PR media, with coherent [7,10] and incoherent [4] beams.In this communication we combine the properties of spatial PR solitons to form pixel-like lattices, to investigate experimentally and numerically the generation and interactions in large arrays of spatial solitons. We achieve improved stability of solitonic lattices by utilizing anisotropic interaction between solitons, in particular the phase-dependent interaction between solitonic rows. We manipulate individual or pairs of solitons using incoherent and phase-sensitive control beams.Creation of solitonic lattices requires stable noninteracting propagation of arrays of self-focusing beams. A crucial feature in the parallel propagation of PR spatial solitons is their anisotropic mutual interaction [11]. Because the refractive index modulation induced by a single soliton reaches beyond its effective waveguide, phasedependent coherent as well as separation-dependent incoherent interactions, such as repulsion or attraction, may appear between the neighboring array elements. These interactions also affect the waveguiding characteristics of an individual solitonic channel. Therefore, the separation between solitons and their nearest-neighbor (NN) a...

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Propagation of light beams in anisotropic nonlinear media: From symmetry breaking to spatial turbulence

Abstract: We investigate theoretically and experimentally breakup and subsequent spatial dynamics of ͑1ϩ1͒and ͑2ϩ1͒-dimensional beams in bulk media with an anisotropic photorefractive nonlinear response. ͓S1050-2947͑96͒02207-X͔

Cited by 167 publications

References 32 publications

Two-dimensional modulational instability in photorefractive media

Two-dimensional modulational instability in photorefractive media

Transverse Patterns in Nonlinear Optical Resonators

Solitonic lattices in photorefractive crystals

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