Kerr Spatiotemporal Self-Focusing in a Planar Glass Waveguide

Eisenberg, Henryk; Morandotti, Roberto; Silberberg, Yaron; Bar-Ad, S.; Ross, Duncan M.; Aitchison, J. S.

doi:10.1103/physrevlett.87.043902

Cited by 110 publications

(83 citation statements)

References 15 publications

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“…There appear multiple angular band gaps supporting the formation of spatial gap solitons, which possess tunable steering properties [10]. Recent experiments [11] demonstrated the effect of simultaneous spatial and temporal self-trapping of optical pulses in the form of optical light bullets [12].…”

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confidence: 99%

Slow-Light Optical Bullets in Arrays of Nonlinear Bragg-Grating Waveguides

Sukhorukov

Kivshar

2006

Phys. Rev. Lett.

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We demonstrate how to control independently both spatial and temporal dynamics of slow light. We reveal that specially designed nonlinear waveguide arrays with phase-shifted Bragg gratings demonstrate the frequency-independent spatial diffraction near the edge of the photonic bandgap, where the group velocity of light can be strongly reduced. We show in numerical simulations that such structures allow a great flexibility in designing and controlling dispersion characteristics, and open a way for efficient spatiotemporal self-trapping and the formation of slow-light optical bullets.PACS numbers: 42.79. Gn; 42.79.Dj; 42.65.Tg; 42.70.Qs Nonlinear response is the fundamental property of optical materials that leads to interaction of propagating optical waves and allows all-optical switching for various applications. Efficiency of nonlinear interactions can be greatly enhanced in the regime of light propagation with small group velocities [1]. The slow-light regime can be realized when the frequency is tuned close to the edge of a photonic bandgap where optical waves experience strong Bragg scattering from a periodically-modulated dielectric structure. These effects were studied extensively in the structures where the propagation direction is fixed by the waveguide geometry, including experimental observations of pulse propagation in fibers [2] and AlGaAs ridge waveguides [3] with Bragg gratings, or coupleddefect waveguides in photonic crystals with two-or threedimensional modulation of the refractive index (see, e.g., Refs. [4,5,6]). In particular, it was demonstrated that the group velocity and the corresponding pulse delay can be tuned all-optically in nonlinear photonic structures, and at the same time nonlinearity may compensate for pulse broadening due to dispersion [2].All-optical control of the spatial beam dynamics becomes possible in periodic two-(2D) or three-dimensional (3D) photonic structures, where light can propagate in various directions. The possibility for beam steering is inherently linked to the effect of beam spreading due to diffraction. Similar to pulses, nonlinearity can suppress beam spreading and support the formation of nondiffracting spatial optical solitons [7]. Recent studies have emphasized many unique properties of spatial solitons in periodic structures such as waveguide arrays or photonic lattices [8,9], where modulation in the transverse spatial dimension fundamentally affects the nonlinear wave dynamics. There appear multiple angular band gaps supporting the formation of spatial gap solitons, which possess tunable steering properties [10]. Recent experiments [11] demonstrated the effect of simultaneous spatial and temporal self-trapping of optical pulses in the form of optical light bullets [12].In this Letter, we address an outstanding key problem and demonstrate how to perform dynamical tunability over both the magnitude and direction of the speed of light through all-optical control in the slow-light regime. In order to realize an effective nonlinear control, it is necessary...

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confidence: 99%

Slow-Light Optical Bullets in Arrays of Nonlinear Bragg-Grating Waveguides

Sukhorukov

Kivshar

2006

Phys. Rev. Lett.

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“…The possibility of a real collapse in a 1D system is quite interesting by itself, and also because experimental observation of spatio-temporal self-focusing in nonlinear optical media is a subject of considerable interest, see, e.g., Ref. [25].…”

Section: Stability Of the Solitons And Spatiotemporal Collapsementioning

confidence: 99%

Singular and regular gap solitons between three dispersion curves

2002

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A general model is introduced to describe a wave-envelope system for the situation when the linear dispersion relation has three branches, which in the absence of any coupling terms between these branches, would intersect pair-wise in three nearly-coincident points. The system contains two waves with a strong linear coupling between them, to which a third wave is then coupled. This model has two gaps in its linear spectrum. As is typical for wave-envelope systems, the model also contains a set of cubic nonlinear terms. Realizations of this model can be made in terms of temporal or spatial evolution of optical fields in, respectively, either a planar waveguide, or a bulk-layered medium resembling a photonic-crystal fiber, which carry a triple spatial Bragg grating. Another physical system described by the same general model is a set of three internal wave modes in a density-stratified fluid, whose phase speeds come into close coincidence for a certain wavenumber. A nonlinear analysis is performed for zero-velocity solitons, that is, they have zero velocity in the reference frame in which the third wave has zero group velocity. If one may disregard the self-phase modulation (SPM) term in the equation for the third wave, we find an analytical solution which shows that there simultaneously exist two different families of solitons: regular ones, which may be regarded as a smooth deformation of the usual gap solitons in a two-wave system, and cuspons, which have finite amplitude and energy, but a singularity in the first derivative at their center. Even in the limit when the linear coupling of the third wave to the first two nearly vanishes, the soliton family remains drastically different from that in the uncoupled system; in this limit, regular solitons whose amplitude exceeds a certain critical value are replaced by peakons. While the regular solitons, cuspons, and peakons are found in an exact analytical form, their stability is tested numerically, which shows that they all may be stable. If the SPM terms are retained, we find that there may again simultaneously exist two different families of generic stable soliton solutions, namely, regular ones and peakons. Direct simulations show that both types of solitons are stable in this case.

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“…There were several proposals of how to stabilize multidimensional solitons [19][20][21][22][23][24][25][26][27][28]. Spatiotemporal compression [29][30][31], metastable 2D spatiotemporal solitons [24,32], and metastable discrete light bullets [33,34] were observed in pioneering experiments, the latter constituting the closest realization of a stable light bullet up until now. However, these quasiconservative bullets are only stable over a few characteristic lengths and are long-term unstable due to losses and Raman shifts.…”

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confidence: 99%

Observation of mode-locked spatial laser solitons

Gustave¹,

Radwell²,

Toomey³

et al. 2017

2017 Conference on Lasers and Electro-Optics Europe &Amp; European Quantum Electronics Conference (CLEO/Europe-EQEC)

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A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatiotemporal structures have a pulse length shorter than the cavity round-trip time and may pave the way to completely independent cavity light bullets. DOI: 10.1103/PhysRevLett.118.044102 Wave packets in general, and light wave packets in particular, do not remain confined to small regions in space or time, but have the natural tendency to broaden. In space this is due to diffraction and in time this is due to dispersion, at least in a medium. Although localization can be achieved by confining potentials (e.g., optical fibers and photonic crystals in optics), it was always the vision of researchers to obtain confinement by self-action. This is why the concept of solitary waves, or, more loosely speaking, of solitons, received a lot of attention over the last decades. A soliton is a wave packet in which the tendency to broaden is balanced by nonlinearities. Spatial and temporal solitons in one or two dimensions are known in many fields of science [1][2][3][4][5][6][7]. There was also early interest in three-dimensional (3D) self-localization, not least as a model for elementary particles [8]. However, early results [8] were discouraging as they indicated that stationary 3D localized states are not stable in a broad class of nonlinear wave equations. Significant interest continued in the theoretical and mathematical literature (e.g., Refs. [9][10][11][12][13][14][15]), but to our knowledge there is only evidence for 3D self-organized periodic patterns [16], but not for 3D self-localization.In optics, spatiotemporal localization of light, i.e., a "bullet" of light being confined in all three spatial dimensions (and time, because it is propagating), was considered as early as 1990 in the framework of a 3D nonlinear Schrödinger equation (NLSE) [17], but realized to be unstable due to the well-known blow-up experienced for cubic nonlinearities in more than one dimension [18,19]. There were several proposals of how to stabilize multidimensional solitons [19][20][21][22][23][24][25][26][27][28]. Spatiotemporal compression [29][30][31], metastable 2D spatiotemporal solitons [24,32], and metastable discrete light bullets [33,34] were observed in pioneering experiments, the latter constituting the closest realization of a stable light bullet up until now. However, these quasiconservative bullets are only stable over a few characteristic lengths and are long-term unstable due to losses and Raman shifts.This makes it attractive to look for solitons in dissipative optical systems in which losses are compensated by driving [5]. Indeed solitons can exist in two dimensions with a cubic nonlinearity within ...

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Kerr Spatiotemporal Self-Focusing in a Planar Glass Waveguide

Cited by 110 publications

References 15 publications

Slow-Light Optical Bullets in Arrays of Nonlinear Bragg-Grating Waveguides

Slow-Light Optical Bullets in Arrays of Nonlinear Bragg-Grating Waveguides

Singular and regular gap solitons between three dispersion curves

Observation of mode-locked spatial laser solitons

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