Manakov Solitons Research Articles

Collisions of optical ultra-short vector pulses

Asymptotic two-pulse solutions of a modified (via attaching a nonlinear derivative term) vector nonlinear Schrödinger equation (MVNSE) are analyzed using the Hirota (bilinearization) method. This equation is known to describe the propagation of ultra-short optical pulses in nonlinear fibers (in particular, in the optical-crystal fibers). Some pulse-parameter regimes of applicability of the solutions to study the pulse collisions are estimated. It is found, for these regimes, that the collision of ultra-short vector pulses of almost equal velocities results in a transformation of their polarizations similar as that of the Manakov solitons whenever the pulse-interaction effects can be neglected.

Statistics of a noise-driven Manakov soliton

We investigate the statistics of a vector Manakov soliton in the presence of additive Gaussian white noise. The adiabatic perturbation theory for a Manakov soliton yields a stochastic Langevin system which we analyse via the corresponding Fokker-Planck equation for the probability density function (PDF) for the soliton parameters. We obtain marginal PDFs for the soliton frequency and amplitude as well as soliton amplitude and polarization angle. We also derive formulae for the variances of all soliton parameters and analyse their dependence on the initial values of polarization angle and phase.

Quantum lattice representations for vector solitons in external potentials

A quantum lattice algorithm is developed to examine the effect of an external potential well on exactly integrable vector Manakov solitons. It is found that the exact solutions to the coupled nonlinear Schrodinger equations act like quasi-solitons in weak potentials, leading to mode-locking, trapping and untrapping. Stronger potential wells will lead to the emission of radiation modes from the quasi-soliton initial conditions. If the external potential is applied to that particular mode polarization, then the radiation will be trapped within the potential well. The algorithm developed leads to a finite difference scheme that is unconditionally stable. The Manakov system in an external potential is very closely related to the Gross–Pitaevskii equation for the ground state wave functions of a coupled BEC state at T = 0 K .

Quantum theory of Manakov solitons

A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schrodinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.

Manakov solitons in centrosymmetric photorefractive materials

Abstract It is shown that dark–dark, bright–bright, and dark–bright Manakov solitons can be formed in centrosymmetric photorefractive materials, provided that two mutually incoherent incident optical beams have the same wavelength and their total intensity is much lower than the sum of the background intensity and the dark irradiance. It also found that the intensity full width at half maximum of these Manakov solitons is inversely proportional to the value of the external bias field.

Manakov solitons in biased photorefractive polymer

Summary The coupled equations for the incoherently coupled soliton pairs in biased photorefractive polymer are provided. It is shown that the coupled soliton equations reduce to Manakov equations when the total intensity of two coupled solitons is much lower than the background illumination. The bright-bright, dark-dark, and grey-grey soliton pair solutions of these Manakov equations are obtained, and the characteristics of these Manakov solitons are also discussed.

Suppression of Manakov soliton interference in optical fibers.

In this paper, we study the interaction of two vector solitons in the Manakov equations that govern pulse transmission in randomly birefringent fibers. Under the assumptions that these solitons initially are well separated and having nearly the same amplitudes and velocities but arbitrary polarizations, we derive a reduced set of ordinary differential equations for both solitons' parameters. We then solve this reduced system analytically. Our analytical solutions show that, when two Manakov solitons have the same amplitude and phases, their collision distance steadily increases as their initial polarizations change from parallel to orthogonal. In particular, the collision distance at orthogonal polarizations is of the order of the square of the collision distance at parallel polarizations. When the Manakov solitons have different amplitudes, a quasiequidistant bound state can be formed. The degrees of position and amplitude oscillations in this bound state diminish as the initial polarizations change from parallel to orthogonal. With a combination of launching Manakov solitons along orthogonal polarizations and at unequal amplitudes, Manakov-soliton interference is almost completely suppressed. These theoretical results are in excellent agreement with our direct numerical simulations.

Manakov Soliton Pairs in Biased Photovoltaic PhotorefractiveCrystals

We study, theoretically, incoherently coupled screening-photovoltaic soliton pairs inbiased photovoltaic photorefractive crystals. Itis shown that when the total intensity of two coupled solitons is much lowerthan the effective dark irradiance, the coupled soliton equations reduce tothe Manakov equations. The dark-dark, bright-bright and dark-bright solitonpair solutions of these Manakov equations are obtained under an appropriateexternal bias field and a photovoltaic field, and the characteristics ofthese Manakov soliton pairs are also discussed in detail.

Self-bending of the coupled spatial soliton pairs in a photorefractive medium with drift and diffusion nonlinearity.

The propagation of two incoherently coupled laser beams (coupled soliton pairs) in the photorefractive crystal with drift and diffusion components of nonlinear response is investigated. By the effective particles method we have shown that not only the well-known Manakov's soliton pairs but also asymmetric pairs can propagate undistorted in photorefractive crystal with diffusion nonlinearity along the parabolic trajectory for the definite relations of propagation constants. We numerically found the exact profiles of the specific multihump soliton solutions that are possible only in the photorefractive medium with nonlocal diffusion response. The stability properties and specific features of pair collisions are analyzed.

Manakov solitons and polarization mode dispersion.

The effect of polarization mode dispersion (PMD) on Manakov solitons and dispersion managed solitons is treated analytically and by numerical simulation. In the analytic approach the internal motion of the Manakov soliton is represented as a damped harmonic oscillator. The PMD functions as a white noise source driving the oscillations. It is shown that the solitons can withstand PMD up to a certain instability threshold for which an analytic expression is obtained. This threshold is also evaluated for dispersion managed solitons. (c) 2000 American Institute of Physics.

Solitons and polarization mode dispersion

Analytical expressions are presented for Manakov solitons perturbed by polarization mode dispersion (PMD). Comparison is made with computer simulations. Dispersion-managed solitons are also studied. It is concluded that at high bit rates solitons are superior to linear return-to-zero propagation with regard to PMD.

One-dimensional spatial solitons in AlGaAs waveguides

We present experimental results on one-dimensional (1-D) spatial solitons in AlGaAs waveguides. Three distinct types of spatial solitons have been observed: namely the fundamental soliton, the Manakov soliton, and the vector soliton. The fundamental soliton is the simplest form of 1-D soliton which consists of a single polarization. The properties of waveguiding and ‘robustness’ are experimentally studied. Vector solitons which result from the complex interplay between the two orthogonally polarized beams due to self-phase modulation, cross-phase modulation, and four-wave mixing effects are studied. The complex beam dynamics and polarization behaviour of the vector solitons are experimentally studied. Manakov solitons which are a special case of the vector soliton exist when the ratio between the self-to-cross-phase modulation is one and the four-wave mixing effects becomes zero are demonstrated experimentally and the basic properties discussed. Finally, some soliton interactions such as trapping and dragging are reported and possible applications of soliton interactions are discussed.

Coupled photorefractive spatial-soliton pairs

We provide a comprehensive experimental and theoretical study of incoherently coupled photorefractive spatial-soliton pairs in all three possible realizations: bright–bright, dark–dark, and dark–bright. We also show that when the total intensity of two coupled solitons is much lower than the effective dark irradiance, the coupled soliton pair is reduced to Manakov solitons. In all cases, mutual trapping of both components in the coupled soliton pair is verified by analyzing, experimentally and numerically, the beam evolution after decoupling.

Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers

We develop perturbation theory for the soliton of the Manakov equation, and apply it to the problem of soliton propagation in randomly birefringent fibers. We calculate both the slow evolution of the soliton parameters (through second order for two of them) as well as the radiation emitted by the soliton. Our analytical results agree well with the corresponding numerical results of earlier studies. We also relate results obtained with perturbation theory with those obtained from the intuitive picture of the dynamics of the soliton components as interacting quasiparticles.

AlGaAs below half bandgap: a laboratory for spatial soliton physics

The nonlinear third order parameters for AlGaAs have been measured at wavelengths near half the semiconductor bandgap, around 1550 nm. It was found in waveguides that the nonlinear refractive index coefficient was the same to within 10% for both TE and TM polarized modes, and that the ratio of the cross-phase to the self-phase modulation coefficient is approximately unity. Such fortuitous values, along with this material's low multiphoton absorption, have allowed us to study spatial solitons and their interactions under ideal conditions. An experimental geometry was found in which the four-wave-mixing term through which orthogonally polarized beams exchange energy was effectively zero. For orthogonally polarized beams, the deflection and trapping by a spatial soliton of either a weak beam or another spatial soliton have been investigated and all-optical switching demonstrated. Furthermore, Manakov solitons which consist of two orthogonally polarized components of arbitrary relative intensity were observed for the first time in slab waveguides.