Self-similar interaction of slowly oscillating dispersion-managed solitons

Hause, A.; Hartwig, H.; Mitschke, F.

doi:10.1103/physreva.82.053833

Cited by 14 publications

(10 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3(c) subsequent behavior, and the complex interplay may result in a self-similar (fractal) structure of the parameter space. This behavior has been studied before [48]. With a view to applications of soliton molecules for data transmission, the energy region near E sol ≈ 11-16 pJ is preferred.…”

Section: A Global Parameter Dependencementioning

confidence: 99%

Two-soliton and three-soliton molecules in optical fibers

2013

Self Cite

View full text Add to dashboard Cite

An experimental study of bound states of two solitons and of three solitons in dispersion-managed fibers is presented. The existence regime and stability of such soliton molecules is investigated. With a programmable pulse shaper we can flexibly shape launch signals; received signals are detected in amplitude and phase, and in relative position and velocity. An equilibrium separation is demonstrated for both two-soliton and three-soliton soliton molecules. It is also shown that stable molecules are possible only with antiphase pulses. Both types of soliton molecule are viable for transmission in the same fiber, at the same wavelength. Together with single solitons this opens the possibility of quaternary data transmission in a soliton-based format.

show abstract

Section: A Global Parameter Dependencementioning

confidence: 99%

Two-soliton and three-soliton molecules in optical fibers

2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…A Gaussian ansatz as an approximation to a DM soliton shape captures the central part quite well and is therefore almost universally adopted (e.g., [42,43]); it is a reasonable ansatz to describe the ground state of soliton molecules [23,29]. It meets its limitations, however, when details of the wings count: The tails of Gaussian, sech, and "true-soliton" pulses are quite different, and any conclusions about higherorder equilibria or interactions between adjacent solitons are affected considerably.…”

Section: And a Metric Of The Nonlinearity Allocationmentioning

confidence: 99%

“…In this paper, we endeavor to draw a more complete picture. We use a perturbative treatment similar to that in [23,29], but with a refinement, to calculate interaction forces and equilibrium separations of adjacent solitons. We find conditions under which symmetric in-phase and opposite-phase DM soliton pairs of the same energy can have more than a single equilibrium separation.…”

Section: Introductionmentioning

confidence: 99%

Higher-order equilibria of temporal soliton molecules in dispersion-managed fibers

Hause

Mitschke

2013

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

Bound states of two or three solitons in dispersion-managed fibers (soliton molecules) were experimentally demonstrated recently. We investigate with a modified perturbation analysis whether the binding mechanism creates a unique stable equilibrium of the relative positions of the solitons in the molecule. Indeed, we find a multitude of equilibrium states, alternatingly stable and unstable. This holds for either case: nearest neighbor solitons having the same or the opposite phase. The number of equilibria are limited by the level of the radiation background. The state with the smallest separation and the highest binding energy ("ground state") always occurs for opposite-phase pulses; the lowest-order state for in-phase pulses is always unstable. Stable long-chain molecules can be built with a mixture of different nearest-neighbor equilibrium separations. Our results agree with our numerical simulations and experimental results, and connect well with certain results in the literature.

show abstract

“…Thus, solitary wave solutions behave like solitons, with the characteristics described above. In a more complex scenario, when the NLS equation presents nonintegrability, collision of solitary waves can show a complex structure since the collision outcome can depend on the initial conditions, presenting a fractal pattern [19][20][21][22][23][24][25][26]. Fractal structures in solitons' collisions are also reported in systems described by other equations, such as, in the ϕ 4 model [27,28], the sine-Gordon model [29][30][31][32][33], etc.…”

Section: Introductionmentioning

confidence: 99%

Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities

Teixeira

Cardoso

2016

Physics Letters A

View full text Add to dashboard Cite

In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enable us the possibility of controlling the scattering of solitons as well as the lifetime of bound states.

show abstract

Self-similar interaction of slowly oscillating dispersion-managed solitons

Cited by 14 publications

References 40 publications

Two-soliton and three-soliton molecules in optical fibers

Two-soliton and three-soliton molecules in optical fibers

Higher-order equilibria of temporal soliton molecules in dispersion-managed fibers

Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities

Contact Info

Product

Resources

About