Noise-induced perturbations of dispersion-managed solitons

We study noise-induced perturbations of dispersion-managed solitons by developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte-Carlo simulations and reconstruct the probability density functions of the solution parameters under the effect of noise.Comment: 12 pages, 6 figure

Oscillating tails of dispersion-managed soliton

Oscillating tails of dispersion-managed optical fiber system are studied for strong dispersion map in the framework of path-averaged Gabitov-Turitsyn equation. The small parameter of the analytical theory is the inverse time. An exponential decay in time of soliton tails envelope is consistent with nonlocal nonlinearity of Gabitov-Turitsyn equation, and the fast oscillations are described by a quadratic law. The pre-exponential modification factor is the linear function of time for zero average dispersion and cubic function for nonzero average dispersion.Comment: 6 pages, 4 figures; submitted to Jounal of the Optical Society of America

Optical pulse propagation in fibers with random dispersion

The propagation of optical pulses in two types of fibers with randomly varying dispersion is investigated. The first type refers to a uniform fiber dispersion superimposed by random modulations with a zero mean. The second type is the dispersion-managed fiber line with fluctuating parameters of the dispersion map. Application of the mean field method leads to the nonlinear Schr\"odinger equation (NLSE) with a dissipation term, expressed by a 4th order derivative of the wave envelope. The prediction of the mean field approach regarding the decay rate of a soliton is compared with that of the perturbation theory based on the Inverse Scattering Transform (IST). A good agreement between these two approaches is found. Possible ways of compensation of the radiative decay of solitons using the linear and nonlinear amplification are explored. Corresponding mean field equation coincides with the complex Swift-Hohenberg equation. The condition for the autosolitonic regime in propagation of optical pulses along a fiber line with fluctuating dispersion is derived and the existence of autosoliton (dissipative soliton) is confirmed by direct numerical simulation of the stochastic NLSE. The dynamics of solitons in optical communication systems with random dispersion-management is further studied applying the variational principle to the mean field NLSE, which results in a system of ODE's for soliton parameters. Extensive numerical simulations of the stochastic NLSE, mean field equation and corresponding set of ODE's are performed to verify the predictions of the developed theory.Comment: 17 pages, 7 eps figure

Parametric excitation of multiple resonant radiations from localized wavepackets

Fundamental physical phenomena such as laser-induced ionization, driven quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the control of new states of matter rely on time-periodic driving of the system. A remarkable property of such driving is that it can induce the localized (bound) states to resonantly couple to the continuum. Therefore experiments that allow for enlightening and controlling the mechanisms underlying such coupling are of paramount importance. We implement such an experiment in a special fiber optics system characterized by a dispersion oscillating along the propagation coordinate, which mimics "time". The quasi-momentum associated with such periodic perturbation is responsible for the efficient coupling of energy from the localized wave-packets sustained by the fiber nonlinearity into free-running linear dispersive waves (continuum), at multiple resonant frequencies. Remarkably, the observed resonances can be explained by means of a unified approach, regardless of the fact that the localized state is a soliton-like pulse or a shock front

Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4346--4369, July, 201