Lattice solitons in nonlinear Schrödinger equation with coupling-to-a-mean-term

Bağcı, Mahmut; Bakırtaş, İlkay; Antar, Nalan

doi:10.1016/j.optcom.2016.09.005

Cited by 11 publications

(13 citation statements)

References 43 publications

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“…Conversely, the increase in peak amplitude can be delayed by increasing anisotropy parameter ν and lattice depth of the real part p re (see panels (b) and (c)). These results consistent with previous studies that have demonstrated stability of two dimensional solitons that are generated by the NLSM system with periodic [31], quasi-periodic [32] and pPT -symmetric [33] lattices.…”

Section: Nonlinear Evolution Of Vortex Solitonssupporting

confidence: 93%

“…In [31], it was also shown that, collapse will eventually occur in a lattice-free NLSM system, and collapse of the solitons are expedited by increasing values of ρ and ν in the lattice-free medium.…”

Section: Nonlinear Evolution Of Vortex Solitonsmentioning

confidence: 99%

“…Recently, the existence of ground-state solution for the NLSM system was demonstrated and collapse dynamics were investigated [30] and it was shown that wave collapse in the NLSM system can be arrested by self-rectification [22]. Latterly, collapse of the NLSM system has been arrested by real periodic [31], quasiperiodic [32] and pPT -symmetric [33] external lattices. The general NLSM system is defined as [22,28,29]…”

Section: Introductionmentioning

confidence: 99%

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Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response

Bağcı

2021

Journal of Mathematical Sciences and Modelling

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Vortex solitons in parity-time (PT ) symmetric and partially PT (pPT ) symmetric azimuthal lattices are demonstrated for a media with quadratic nonlinear response. Stability properties of the vortices are investigated comprehensively by linear spectra and nonlinear evolution of the governing equations, and it is shown that, although the existence domain of the PT -symmetric and pPT -symmetric lattices are identical, the stability region of PT -symmetric lattice is narrower than that of the pPT -symmetric lattice. It is also observed that deeper real part in the azimuthal potentials supports stability of vortex solitons, whereas deeper imaginary part and strong quadratic electro-optic effects impoverish stability properties of the vortices. Moreover, it is shown that there are different stability properties of vortices in pPT -symmetric azimuthal potentials for different vorticity values, while there is no such difference for vortices in PT -symmetric potentials.

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Section: Nonlinear Evolution Of Vortex Solitonssupporting

confidence: 93%

Section: Nonlinear Evolution Of Vortex Solitonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response

Bağcı

2021

Journal of Mathematical Sciences and Modelling

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“…It is noteworthy that, as demonstrated in previous studies [44,45], due to the anisotropy of the ML-NLSM system, steady state solutions do not possess radial symmetry. In the other words, the ML-NLSM model generates astigmatic fundamental solitons.…”

Section: B Numerical Existence Of the Fundamental Solitonsmentioning

confidence: 61%

“…Ablowitz et al [36][37][38] derived from first principles NLSM type equations describing the evolution of the electromagnetic field in quadratic nonlinear media. Recently, in [44], it was demonstrated that optical wave collapse can be arrested in the NLSM system by adding an external potential (lattice) to the model.…”

Section: Introductionmentioning

confidence: 99%

Spatio-Temporal Mode-locking in Quadratic Nonlinear Media

Bağcı,

Kutz

2020

Preprint

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A new theoretical model is developed to characterize spatio-temporal mode-locking (ML) in quadratic nonlinear media. The model is based on the two-dimensional nonlinear Schrödinger equation with coupling to a mean term (NLSM) and constructed as an extension of the master mode-locking model. It is numerically demonstrated that there exists steady state soliton solutions of the ML-NLSM mode-locking model that are astigmatic in nature. A full stability analysis and bifurcation study is performed for the ML-NLSM model and it is manifest that spatio-temporal mode-locking of the astigmatic steady-state solutions is possible in quadratic nonlinear media.

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Asymmetric propagation of solitons in nonlinear media with gradual nonlocality

Weng¹,

Chen²,

Tang³

et al. 2020

J. Opt.

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We investigate the propagation of solitons in homogeneous nonlocal nonlinear media and in media with gradual nonlinear nonlocality. We calculate the width and the maximum amplitude of solitons during propagation and demonstrate that solitons will propagate asymmetrically in the medium with gradual nonlinear nonlocality. Moreover, the propagation of solitons in the nonlinear medium with gradual nonlocality is independent of the forms of monotonically gradual nonlocalities. Finally, we investigate the ratio of width magnification quantitatively and demonstrate that the soliton with a particular input power maintains its width in one direction and suffers strong expansion in another direction.

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Lattice solitons in nonlinear Schrödinger equation with coupling-to-a-mean-term

Cited by 11 publications

References 43 publications

Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response

Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response

Spatio-Temporal Mode-locking in Quadratic Nonlinear Media

Asymmetric propagation of solitons in nonlinear media with gradual nonlocality

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