Multichannel pulse dynamics in a stabilized Ginzburg-Landau system

Bragg solitons in systems with separated nonuniform Bragg grating and nonlinearity

The existence and stability of quiescent Bragg grating solitons are systematically investigated in a dual-core fiber, where one of the cores is uniform and has Kerr nonlinearity while the other one is linear and incorporates a Bragg grating with dispersive reflectivity. Three spectral gaps are identified in the system, in which both lower and upper band gaps overlap with one branch of the continuous spectrum; therefore, these are not genuine band gaps. However, the central band gap is a genuine band gap. Soliton solutions are found in the lower and upper gaps only. It is found that in certain parameter ranges, the solitons develop side lobes. To analyze the side lobes, we have derived exact analytical expressions for the tails of solitons that are in excellent agreement with the numerical solutions. We have analyzed the stability of solitons in the system by means of systematic numerical simulations. We have found vast stable regions in the upper and lower gaps. The effect and interplay of dispersive reflectivity, the group velocity difference, and the grating-induced coupling on the stability of solitons are investigated. A key finding is that a stronger grating-induced coupling coefficient counteracts the stabilization effect of dispersive reflectivity.

Direct observation of two-color pulse dynamics in passively synchronized Er and Yb mode-locked fiber lasers

We report direct experimental observation of interesting pulse synchronization dynamics in a cavity-combined Er and Yb mode-locked fiber lasers by measuring the relative position between the two-color pulses in the shared fiber section. The influence of the 1.03 μm pulse on the 1.56 μm single pulse as well as bound soliton pairs can be clearly identified as an effective phase modulation through the XPM effect with the walk-off effect taken into account. For the 1.56 μm single pulse under synchronization, the dependence of the relative position variation and the center wavelength shift on the cavity mismatch detuning is found analogous to the typical characteristics of FM mode-locked lasers with modulation frequency detuning. Moreover, depending on the cavity mismatch, the passively synchronized 1.56 μm bound soliton pairs are found to exhibit two different dynamical behaviors, i.e., phase-locked (in-phase) as well as non-phase-locked. The physical origins for these two kinds of bound soliton pairs are investigated experimentally by disclosing their locations with respective to the copropagating 1.03 μm pulse.

Solitons in a chain of parity-time-invariant dimers

Dynamics of a chain of interacting parity-time-invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrödinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anticontinuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear parity-time-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton's velocity.

Solitary pulses in linearly coupled Ginzburg-Landau equations

This article presents a brief review of dynamical models based on systems of linearly coupled complex Ginzburg-Landau (CGL) equations. In the simplest case, the system features linear gain, cubic nonlinearity (possibly combined with cubic loss), and group-velocity dispersion (GVD) in one equation, while the other equation is linear, featuring only intrinsic linear loss. The system models a dual-core fiber laser, with a parallel-coupled active core and an additional stabilizing passive (lossy) one. The model gives rise to exact analytical solutions for stationary solitary pulses (SPs). The article presents basic results concerning stability of the SPs; interactions between pulses are also considered, as are dark solitons (holes). In the case of the anomalous GVD, an unstable stationary SP may transform itself, via the Hopf bifurcation, into a stable localized breather. Various generalizations of the basic system are briefly reviewed too, including a model with quadratic (second-harmonic-generating) nonlinearity and a recently introduced model of a different but related type, based on linearly coupled CGL equations with cubic-quintic nonlinearity. The latter system features spontaneous symmetry breaking of stationary SPs, and also the formation of stable breathers.