Tandem light bullets

Torner, Lluís; Carrasco, Sílvia; Torres, Juan P.; Crasovan, L.-C.; Mihalache, Dumitru

doi:10.1016/s0030-4018(01)01573-5

Cited by 58 publications

(30 citation statements)

References 23 publications

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“…Solitons (or, more properly, solitary waves) in Kerr-type focusing media are described by the cubic nonlinear Schrödinger (NLS) equation and they are known to be unstable in two and three dimensions because of the occurrence of the collapse of the wave packet (see, e.g., the review [4]). Various schemes to arrest the collapse were proposed such as the use of weaker saturable [5] or quadratic nonlinearities [6][7][8][9], or to use the concept of nonlinearity and group-velocity dispersion (GVD) management in tandem structures, which are composed of periodically alternating linear dispersive and quadratically nonlinear layers [10]. Other recent approaches use off-resonance two-level systems [11], self-induced-transparency media [12], inhomogeneous, dispersive nonlinear media (for example, a graded index Kerr medium [13]), or small negative fourth-order GVD to arrest the spatiotemporal collapse [14] (this scheme works only in two dimensions, that is, in a planar waveguide with pure Kerr nonlinearity).…”

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confidence: 99%

Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice

et al. 2004

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We investigate the existence and stability of three-dimensional spatiotemporal solitons in self-focusing cubic Kerr-type optical media with an imprinted two-dimensional harmonic transverse modulation of the refractive index. We demonstrate that two-dimensional photonic Kerr-type nonlinear lattices can support stable one-parameter families of three-dimensional spatiotemporal solitons provided that their energy is within a certain interval and the strength of the lattice potential, which is proportional to the refractive index modulation depth, is above a certain threshold value.

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confidence: 99%

Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice

et al. 2004

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“…For n 2 > 0, but n 4 < 0 this form describes the competition between self-focusing occurring at low intensity and self-defocusing taken on the high intensities. The opposite occurs for n 2 < 0, but n 4 > 0 (Torner et al 2001), and (4) assume the form…”

Section: Theoretical Framework and Numerical Proceduresmentioning

confidence: 99%

“…Numerous approaches for obtaining spatiotemporal solitons (light bullets) have been considered theoretically, e.g. by using saturation nonlinearity (Edmundson and Enns 1992;Akhmediev and Soto-Crespo 1993), nonlocal nonlinearity Mihalache et al (2006b), tandem structures that are composed of linear and nonlinear materials (Torner et al 2001), and through manipulating the diffraction and/or dispersion by periodic structures (Aceves et al 1994;Laedke et al 1994;Xu et al 2004;Sukhorukov and Kivshar 2006b). In this paper we propose an approach for propagation and stability of spatiotemporal solitons periodically modulated in planar waveguide and with cubic-quintic nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal optical solitons in planar waveguide with periodically modulated cubic-quintic nonlinearity

et al. 2010

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The propagation and stability of spatiotemporal optical solitons (or optical bullets) in a planar waveguide with periodically modulated cubic-quintic nonlinearity is studied numerically as a function of the amplitudes of modulation (A m ), the frequency of modulation (ω m ) and the propagation distance z. The optical spatiotemporal solitons are the result of the balance between the nonlinear parameters, of dispersion (dispersion length, L D ) and diffraction (diffraction length, L d ) with temporal and spatial auto-focusing behavior respectively. With the objective of ensure the stability and preventing the collapse or the spreading of pulses, in this study we explore the cubic-quintic nonlinearity with the optical fields coupled by XPM and take into account several values for the non linear parameter α and for amplitudes (A m ) and frequency (ω m ) of modulation as a function of the propagation distance z and we cause the collisions of two pulses (envelope of the optical field) to ensure that the optical pulse are solitons. After numerical analysis of parameter settings selected four conditions and for all we get stable solitons and this paper shown that, for a fixed amplitude and frequency of modulation we have stable spatiotemporal solitons.

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“…Another possibility is to consider periodic mismatch management, which corresponds to the situation with the QPM is implemented in the form of a superlattice, rather than a simple periodic lattice [26]. It is also relevant to mention theoretically investigated tandem systems, that offer a possibility to minimize the mismatch in a waveguide built as a periodic concatenation of linear and v ð2Þ -nonlinear segments, in the temporal [27,28] and spatiotemporal [29] domains alike (a v ð3Þ -counterpart of the tandems is represented by split-step systems [31][32][33][34]). The self-trapping of light in walkoff-compensating tandem structures was demonstrated experimentally in Ref.…”

Section: Introductionmentioning

confidence: 99%