Hermite–Gaussian stationary solutions in strongly nonlocal nonlinear optical media

Zhong, Lanhua; Yang, Jing; Ren, Zhanmei; Guo, Qi

doi:10.1016/j.optcom.2016.09.021

Cited by 15 publications

(5 citation statements)

References 34 publications

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“…where the superscript * denotes the conjugate complex. We search the multi-peak solitons with the HG shape, so the trial solution q(x, z) for the variational problem is supposed to be [16,39]…”

Section: Variational Proceduresmentioning

confidence: 99%

Multi-peak solitons in nonlocal nonlinear system with sine-oscillation response

Zhong,

Dang,

et al. 2021

Preprint

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The multi-peak solitons and their stability are investigated for the nonlocal nonlinear system with the sine-oscillation response, including both the cases of positive and negative Kerr coefficients. The Hermite-Gaussian-type multi-peak solitons and the ranges of the degree of nonlocality within which the solitons exist are analytically obtained by the variational approach. This is the first time, to our knowledge at least, to discuss the solution existence range of the multi-peak solitons analytically, although approximately. The variational analytical results are confirmed by the numerical ones. The stability of the multi-peak solitons are addressed by the linear stability analysis. It is found that the upper thresholds of the peak-number of the stable solitons are five and four for the system with negative and positive Kerr coefficients, respectively.

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Section: Variational Proceduresmentioning

confidence: 99%

Multi-peak solitons in nonlocal nonlinear system with sine-oscillation response

Zhong,

Dang,

et al. 2021

Preprint

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“…where u N is a real function and b N is a real constant. It was numerically found that in the case with the exponential-decay response function u N ( x ) is of N -humps ( N = 1, 2, 3, …) HGT-structure 20 41 , specially, u 1 ( x ) has a single-hump Gauss-type shape. It was also proved that u N ( x )( N ≥ 2) can exist only when the parameters w m and b N satisfy 22 42 .…”

Section: Unstable Evolution Of Hgt Stationary Solutionsmentioning

confidence: 99%

“…The case of strongly nonlocal nonlinearity [ w m = 10 and w (0) = 1 unless otherwise stated] is considered. The unstable evolution 41 of the HGT stationary solutions ( N > 4)are given in Fig. 1 , where only solutions with N = 7 and 12 are displayed without loss of generality.…”

Section: Unstable Evolution Of Hgt Stationary Solutionsmentioning

confidence: 99%

Chaoticons described by nonlocal nonlinear Schrödinger equation

Zhong

Chen

et al. 2017

Sci Rep

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It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrödinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities are referred to as chaoticons because they exhibit not only chaotic properties (with positive Lyapunov exponents and spatial decoherence) but also soliton-like properties (with invariant statistic width and interaction of quasi-elastic collisions).

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“…Hence, a great variety of novel nonlocal solitons can be formed in nonlocal nonlinear media. For instance, ring dark and antidark solitons [20], gap solitons [21], elliptic Hermite-Gaussian [22], Hermite-Gaussian stationary solutions [23], vortex solitons [24] and spiraling elliptic solitons [25], etc.…”

mentioning

confidence: 99%

“…The higher-order soliton in the (1+1)-dimensional usual strong nonlocal nonlinear Schrödinger equation (α = 2) was proved to have a HG-shaped profile [22,23,26]. Therefore, we also choose the HG-shaped function as the initial input condition to obtain the stable soliton for 1 < α ≤ 2 by numerical iteration,…”

mentioning

confidence: 99%

Hermite-Gaussian–like soliton in the nonlocal nonlinear fractional Schrödinger equation

Wang

Zhang

et al. 2018

EPL

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The propagation of an optical beam in the nonlocal nonlinear fractional Schrödinger equation (NNFSE) was numerically investigated. The results reveal that the stability of beam propagation decreases as the Lévy index decreases in the local fractional case. However, the nonlocal response can effectively enhance the stability of beam propagation and leads to a completely stable solitons formation in the NNFSE. In addition, the shapes of fundamental mode solitons are determined by the Lévy indexes and nonlocalities. For the high-order solitons case, the shapes slightly vary with the change of nonlocality, but are strongly dependent on the Lévy index. Furthermore, the critical power of the stable soliton decreases as the Lévy index decreases since the decrease of the Lévy index will weaken the diffraction effect.

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Hermite–Gaussian stationary solutions in strongly nonlocal nonlinear optical media

Cited by 15 publications

References 34 publications

Multi-peak solitons in nonlocal nonlinear system with sine-oscillation response

Multi-peak solitons in nonlocal nonlinear system with sine-oscillation response

Chaoticons described by nonlocal nonlinear Schrödinger equation

Hermite-Gaussian–like soliton in the nonlocal nonlinear fractional Schrödinger equation

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