Transverse modulational instability of periodic light patterns in photorefractive strontium barium niobate crystal

Apolinar-Iribe, A.; Korneev, N.; Vysloukh, Victor A.; Gómez-Sarabia, Cristina M.

doi:10.1364/ol.27.002088

Cited by 11 publications

(8 citation statements)

References 9 publications

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“…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.…”

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confidence: 99%

“…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.…”

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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Two-dimensional modulational instability in photorefractive media

Saffman¹,

McCarthy²,

Królikowski³

2004

J. Opt. B: Quantum Semiclass. Opt.

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“…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 selffocusing 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 one-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.…”

mentioning

confidence: 99%

“…Several previous studies of MI in the context of photorefractive media were limited to a one-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.…”

mentioning

confidence: 99%

Two dimensional modulational instability in photorefractive media

Saffman

McCarthy

Królikowski

2004

Nonlinear Guided Waves and Their Applications

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We study theoretically and experimentally the modulational instability of broad optical beams in photorefractive nonlinear media. The angular dependence of the growth rate of periodic perturbations is calculated. Our findings are confirmed by experimental measurements on a strontium barium niobate photorefractive crystal.Keywords: photorefractive nonlinear optics, self-focusing, instabilities 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 effort has 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 selffocusing 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 one-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 transverse breakup 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 two-dimensional anisotropic model of the photorefractive nonlinearity.Time independent propagation of an optical beam E(r, z) = (A/2)e i(kz−ωt) + c.c. in a nonlinear medium with a weakly varying index of refraction is governed by the parabolic equationHere r ...

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“…2, right half). The compression ratio was limited on the level five, approximately, by the development of transverse modulation instability [2]. The red light beam was trapped by this array of self-tightening photoinduced lattices.…”

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Laser beam guiding by periodic array of self-tightening photonic lattices

Korneev

Marroquin-Gutierrez

Aguilar³

CLEO/Europe. 2005 Conference on Lasers and Electro-Optics Europe, 2005.

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Photorefractive media are extraordinary candidates for experimental implementation of the lattice soliton concept, because such type of light-induced structures might operate in regimes of weak as well as strong coupling between neighboring wave-guides. Notice that photoinduced structures present possibilities to vary not only the lattice period and refractive index modulation depth but also the value and sign of nonlinearity. Spatial solitons have been demonstrated recently in arrays of optically induced waveguides [I].Here we report experimental results on low-intensity laser beam guiding by periodic array of self-tightening photoinduced lattices. The remarkable self-compression of periodic wave array during propagation in photorefractive SBN crystal (due to the drift-type focusing nonlinearity) is accompanied by decreasing of the lattice width and by growth of refractive index modulation depth. As result, coupling of low-intensity light-waves guided by neighboring lattices diminishes significantly and the number of modes potentially guided by individual lattice steadily decreases. Gradually periodical array of strongly-coupled multimode waveguides transforms into array of weakly-coupled singlemode ones, and this feature enriches possibilities of experimentation with lattice solitons, including the case of discrete spatial solitons. It worth noticing that self-compression is easily controlled by external voltage applied to photorefractive crystal and also that self-tightening of guiding lattices facilitates low-intensity laser beam launching conditions.In the experiment two beams derived from the frequency-doubled diode-pumped YAG:Nd+3 laser (532 am, 50mW) with extraordinary polarization were crossing inside the 6 mm long SBN photorefractive crystal at a small angle (10-2_ 10-3) producing interference fringes with a typical period of 100 gm (Fig.1, right half) that were not practically altered during propagation along the crystal. Additionally, the attenuated relatively wide beam of He-Ne laser ( 633nm, 10 mW) with the same polarization was fed in to the region of green beams intersection (Fig.1, left half, almost uniform input intensity distribution). Naturally that in the absence of the fringes, that form photoinduced lattices, the red beam passes without distortion. The high voltage (up to I kV) application along the c-axis of the crystal (perpendicularly to the fringes) results in the formation of the self-tightening waveguide array by green fringes (Fig. 2, right half). The compression ratio was limited on the level five, approximately, by the development of transverse modulation instability [2]. The red light beam was trapped by this array of self-tightening photoinduced lattices. Fig. 2 (left half) shows corresponding output intensity distribution. It can be seen that profiles of both output waves are not sinusoidal, rather described by elliptical functions, and initially strongly coupled photoinduced waveguides transform in to well separated and practically decoupled ones. Notice that if the read beam i...

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Transverse modulational instability of periodic light patterns in photorefractive strontium barium niobate crystal

Cited by 11 publications

References 9 publications

Two-dimensional modulational instability in photorefractive media

Two-dimensional modulational instability in photorefractive media

Two dimensional modulational instability in photorefractive media

Laser beam guiding by periodic array of self-tightening photonic lattices

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