Binding mechanism of temporal soliton molecules

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke

Phys. Rev. A 78, 063817 – Published 10 December 2008

Abstract

Temporal optical soliton molecules were recently demonstrated; they potentially allow a further increase of data rates in optical telecommunication. We present a theoretical study aimed at an explanation of the mechanism responsible for the binding force. To this end we use a perturbation treatment in several variants. We find that the well-known soliton interaction as mediated by the optical Kerr effect, when suitably modified for chirped pulses, captures essential features like the existence of a stable equilibrium separation and small-scale oscillations around this point. Predictions of these models are compared to numerical simulations.

Received 9 September 2008

DOI:https://doi.org/10.1103/PhysRevA.78.063817

Authors & Affiliations

A. Hause, H. Hartwig, M. Böhm, and F. Mitschke^*

Universität Rostock, Institut für Physik, 18051 Rostock, Germany

^*fedor.mitschke@uni-rostock.de

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Vol. 78, Iss. 6 — December 2008

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Images

Figure 1
(a) Reconstructed field of a double pulse, after [18]. The temporal pulse shape (solid line) and the temporal phase function (bold, dashed line) is shown. The fitted quadratic phase functions (thin, dashed line) for the single pulses show intersection points where constructive interference takes place and secondary peaks appear. (b) Superposition (bold, solid line) of two linearly cirped Gaussian pulses (thin, solid line). The intersection points of the single temporal phase functions denote the same positions of the secondary peaks.Reuse & Permissions
Figure 2
Force acting on the single pulse $u$ according to (a) first-order perturbation theory, (b) higher-order perturbation theory, and (c) the modified potential model. Here the force $d ∕ d ζ ⟨ ω ⟩$ is given in units of $W (η ∕ π)$ . The lower figures are on an expanded vertical scale to show more detail. Seven cases are shown: opposite phase $(φ = π)$ for three chirp values, in phase for the same chirp values, and quadrature phase, unchirped. The pulse width parameter is $η = 0.454$ . Points on the horizontal axis, highlighted by arrows, mark stable equilibria. Positive (negative) values of the force imply repulsion (attraction) in the case of anomalous dispersion.Reuse & Permissions
Figure 3
Pulse width $T_{0}$ during propagation (solid line) and linear chirp parameter $β (z)$ (dashed line) as a function of distance $z$ over one period of the dispersion map. The dashed vertical lines mark the joints between fiber segments. The chirp-free points in the middle of each fiber segment are indicated by points. SSMF: standard single-mode fiber. IDF: inverse dispersion fiber.Reuse & Permissions
Figure 4
Evolution of $d ⟨ ω ⟩ ∕ d z$ in a single dispersion period. The behavior of double pulses with an initial separation of $σ = T_{0, z = 0}$ (dashed), $σ = 4.13 T_{0, z = 0}$ (solid line) und $σ = 6 T_{0, z = 0}$ (dotted line) is shown.Reuse & Permissions
Figure 5
Overview of the “forces” as obtained from the three models (linear perturbation, full perturbation, modified potential). The extended perturbation model shows an additional attraction of opposite phase DM solitons at very close separations. There is also an unstable equilibrium separation.Reuse & Permissions
Figure 6
Attraction of two DM solitons in dependence of their relative phase. The temporal profile is shown on a logarithmic power scale. A superposition of two solitons with parameters according to Table was propagated over 50 dispersion periods. Soliton pairs have the strongest attraction when they are in phase and the weakest when they have opposite phase.Reuse & Permissions

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