Analytical theory of dark nonlocal solitons

Kong, Qian; Wang, Qi; Bang, Ole; Królikowski, Wiesław

doi:10.1364/ol.35.002152

Cited by 56 publications

(36 citation statements)

References 28 publications

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“…This occurs, e.g., in media featuring strong thermal nonlinearity [12] or in nematic liquid crystals [13], where the nonlinear contribution to the refractive index depends on the intensity distribution in the transverse plane. It has been shown that dark solitons in one-dimensional (1D) settings exist in media with a defocusing nonlocal nonlinearity [14][15][16][17][18][19] while, in the case of stripes, transverse MI may be suppressed due to the nonlocality [20]. The smoothing effect of the nonlocal response was shown to occur even in the case of shock wave formation [20][21][22][23], or give rise to stable 2D solitons [24].…”

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Ring dark and antidark solitons in nonlocal media

Horikis

Frantzeskakis

2016

Opt. Lett.

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Ring dark and anti-dark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable continuous-wave background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvilli (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.In nonlinear optics, spatial dark solitons are known to be intensity dips, with a phase-jump across the intensity minimum, on top of a continuous-wave (cw) background beam. These structures may exist in bulk media and waveguides, due to the balance between diffraction and defocusing nonlinearity, and have been proposed for potential applications in photonics as adjustable waveguides for weak signals [1].In the two-dimensional (2D) geometry, spatial dark solitons, in the form of stripes, are prone to the transverse modulation instability (MI) [2], which leads to their bending and their eventual decay into vortices [3]. However, the instability band of the dark soliton stripes, may be suppressed if the stripe is bent so as to form a ring of particular length. This idea led to the introduction of ring dark solitons (RDSs) [4], whose properties have been studied both in theory [5,6] and in experiments [7], and potential applications of RDS to parallel guiding of signal beams were proposed [8]. RDSs have also been predicted to occur in other physically relevant contexts, such as atomic Bose-Einstein condensates [9] and polariton superfluids [10,11].While the above results rely on the study of nonlinear Schrödinger (NLS) models with a local nonlinearity, there exist many physical settings where the use of NLS models with a nonlocal nonlinearity are more appropriate. This occurs, e.g., in media featuring strong thermal nonlinearity [12] or in nematic liquid crystals [13], where the nonlinear contribution to the refractive index depends on the intensity distribution in the transverse plane. It has been shown that dark solitons in one-dimensional (1D) settings exist in media with a defocusing nonlocal nonlinearity [14][15][16][17][18][19] while, in the case of stripes, transverse MI may be suppressed due to the nonlocality [20]. The smoothing effect of the nonlocal response was shown to occur even in the case of shock wave formation [20][21][22][23], or give rise to stable 2D solitons [24]. Here we should note that, generally, pertinent nonlocal models do not possess soliton solutions in explicit form (other than the weakly nonlinear limit [25]). As such, various techniques have been used to analyze soliton dynamics and interactions, with the most common one being the variational approximation, where a particular form of the solution is chosen [13,[26][27][28][29]. However, to the best of our knowledge, RDSs in nonlocal medi...

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confidence: 99%

Ring dark and antidark solitons in nonlocal media

Horikis

Frantzeskakis

2016

Opt. Lett.

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“…For the sake of simplicity and analytical tractability and without loss of generality, however, we consider here the rectangular profile for the nonlocal response function [39,52,70,72]:…”

Section: Dark Solitons Interactions With General Nonlocal Casementioning

confidence: 99%

“…Although (12) is only a phenomenological model, it also can describe the general properties of the nonlocal media very well. In particular, with such a model of nonlocal response function, the solutions of dark solitons can be obtained analytically in the whole range of nonlocality [39,52,70,72]. Substituting (4) and (12) into the Lagrangian density (11) and integrating over the whole spatial coordinate x, we can obtain the averaged Lagrangian of the following form…”

Section: Dark Solitons Interactions With General Nonlocal Casementioning

confidence: 99%

The interaction of dark solitons with competing nonlocal cubic nonlinearities

Chen

Shen

Kong

et al. 2015

J Opt

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The interaction of dark solitons under competing cubic nonlinearities is investigated with an arbitrary degree of nonlocality. Employing the approximately variational technique, the analytical relations for the interaction of dark solitons is obtained in the whole range of degree of nonlocality. It is shown that the competing self-focusing nonlinearity enhances the repulsive force of the interaction, whereas, the competing self-defocusing nonlinearity strengthens the attractive force of the interaction. All the analytically theoretical results have also been demonstrated by direct numerical simulations with split step Fourier transform.

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“…The nonlocality allows the refractive index of a material at a particular point to be related to the beam intensity over a finite volume surrounding that point, which is distinctly different from the conventional local nonlinearity. Subsequently various soliton solutions of the nonlocal nonlinear Schrödinger equation are obtained in theory, such as Gaussian and higher-order Gaussian solitons [3][4][5][6][7], vortex solitons [11][12][13][14], dark solitons [15,16], dipole solitons [17,18], surface solitons [19,20], and so on. Their propagation dynamics is studied deeply, even some have been observed in experiments [11,16,19].…”

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“…Variational approach is a valid method to solve some nonlinear equations, and it is introduced into optics firstly by Anderson [21]. For the nonlocal nonlinear Schrödinger equation, some soliton solutions are obtained by applying this method [15,18,20,22,23]. Recently, Aleksić et al [24] studied the fundamental solitons in (1 + 2)-dimensional highly nonlocal nematic liquid crystals using the variational approach.…”

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Dynamics of dipole breathers in nonlinear media with a spatial exponential-decay nonlocality

2015

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By applying the variational approach, the analytical expression of dipole breathers is obtained in nonlinear media with an exponential-decay nonlocal response. The parameters of the width, the amplitude, the phase-front curvature, and the phase of the complex amplitude of the dipole breathers are all given in analytical expressions. It is found that the input power plays a key role in the evolution of dipole breathers, whose magnitude decides the change of the beam width (compressed or broadened) during propagation. The physical reason for the evolution of dipole breathers is analyzed in detail. Numerical simulations are also carried out, and the analytical solutions are in good agreement with numerical simulations.

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Analytical theory of dark nonlocal solitons

Abstract: We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe the dark solitons, for the first time, in the whole range of degree of nonlocality.Comment: to be published in Optics Letter

Cited by 56 publications

References 28 publications

Ring dark and antidark solitons in nonlocal media

Ring dark and antidark solitons in nonlocal media

The interaction of dark solitons with competing nonlocal cubic nonlinearities

Dynamics of dipole breathers in nonlinear media with a spatial exponential-decay nonlocality

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