We propose a method to controllably generate six kinds of nonlinear waves on continuous waves, including the one- and multi-peak solitons, the Akhmediev, Kuznetsov-Ma, and Taijiri-Watanabe breathers, and stable periodic waves. In the nonlinear fiber system with third-order dispersion, we illustrate their generation conditions by the modified linear stability analysis, and numerically generate them from initial perturbations on continuous waves. We implement the quantitative control over their dynamical features, including the wave type, velocity, periodicity, and localization. Our results may provide an effective scheme for generating optical solitons on continuous waves, and it can also be applied for wave generations in other various nonlinear systems.
The dispersion-managed (DM) optical system with step-wise periodical variation of dispersion is studied in the framework of path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by iterating the path-averaged equation. The dependence of soliton parameters on dispersion map strength is investigated together with the oscillating tails of soliton.
We study the stability and the dynamics of many-soliton molecules in dispersion-managed (DM) optical fibers with focus on five-and seven-soliton molecules by analytical and numerical means. In particular we calculate the binding force, pulse durations and equilibrium separations using a variational approach. Predicted pulse shapes are in good agreement with those found by numerical simulations of the underlying nonlinear Schrödinger equation. Within limitations soliton molecules with up to seven solitons possibly allow to encode three bits of data per clock period.
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent parallel calculations of fast Fourier transforms on multiple CPUs. The algorithm allows one to implement numerical simulations M/2 times faster than a direct numerical simulation by a split-step method, where M is a number of CPUs in parallel network.
We investigate the stability of $N$-soliton molecules in dispersion-managed optical fibers with focus on the recently realized 2- and 3-soliton molecules. We calculate their binding energy using an averaged nonlinear Schr$\rm{\ddot o}$dinger equation. A combination of variational and numerical solutions to this equation shows that it describes well the intensity profiles and relative separations of the experimental molecules. Extending the calculation to larger values of $N$, the binding energy per soliton is found to saturate at N $N\ge7$.
The existence regimes and dynamics of soliton molecules in dispersion-managed (DM) optical fibers have been studied. Initially we develop a variational approximation (VA) for description of periodic dynamics of a soliton molecule within each unit cell of the dispersion map. The obtained system of coupled equations for the pulse width and chirp allows to find the parameters of DM soliton molecules for the given dispersion map and pulse energy. Then by means of a scaling transformation and averaging procedure we reduce the original nonlinear Schrödinger equation (NLSE) with piecewise-constant pe…
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 Schrödinger 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 pert…
The effect of retaining the material dispersion terms in the nonlinear coupled mode equations (NLCME) that describe light propagation in fiber Bragg gratings is analyzed. It is found that dispersion is responsible for new instabilities of the uniform states and gives rise to new complex spatio temporal dynamics that is not captured by the standard NLCME formulation. A detailed analysis of the effect of dispersion on the linear stability characteristics of the uniform solutions is presented and some numerical integrations of the NLCME with dispersion are also performed in order to corroborate t…
We investigate the dynamics of a ring cavity made of photonic crystal fiber and driven by a coherent beam working near the resonant frequency of the cavity. By means of a multiple-scale reduction of the Lugiato-Lefever equation with high order dispersion, we show that the dynamics of this optical device, when operating close to the critical point associated with bistability, is captured by a real order parameter equation in the form of a generalized Swift-Hohenberg equation. A Swift-Hohenberg equation has been derived for several areas of nonlinear science such as chemistry, biology, ecology, …
Short range correlated uniform noise in the dispersion coefficient, inherent in many types of optical fibers, broadens and eventually destroys all initially ultra-short pulses. However, under the constraint that the integral of the random component of the dispersion coefficient is set to zero, or pinned, periodically or quasi-periodically along the fiber, the nature of the pulse propagation changes dramatically. For the case that randomness is added to constant positive dispersion, the pinning restriction significantly reduces pulse broadening. If the randomness is added to piecewise constant …
In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schrödinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.
We show that the use of a dispersion oscillating fiber in passive cavities significantly extend modulational instability to novel high-frequency bands, which also destabilize the branches of the steady response which are stable with homogeneous dispersion. By means of Floquet theory, we obtain exact explicit expression for the sideband gain, and a simple analytical estimate for the frequencies of maximum gain. Numerical simulations show that stable stationary trains of pulses can be excited in the cavity.
We study resonant radiation generated by bound solitons in a twin-core fiber near zero-dispersion wavelength, in the presence of higher order dispersion terms. We propose a theoretical description of dispersive wave generation mechanism and derive resonance conditions. The presence of third order dispersion term leads to generation of polychromatic dispersive radiation and transition from the regime of center of mass oscillations to the regime of amplitude oscillations. Such a transition is not reproduced in the case of symmetric fourth order dispersion.
We address the generation and interaction of dispersion-managed dissipative solitons (DMDS) in a model of fiber lasers with the cubic-quintic nonlinearity, multiphoton absorption and gain dispersion. Both anomalous and normal segments of the dispersion map include random dispersion fluctuations. Effects of the gain dispersion, higher-order nonlinearity and randomness on the generation of DMDS are demonstrated. The solitons exhibit breather-like evolution, and are found to be robust, up to a certain critical level of the random-dispersion component, which is sufficiently high. The roles of mult…
We report on the observation of dispersion-managed (DM) dark soliton emission in a net-normal dispersion erbium-doped fiber laser. We found experimentally that dispersion management could not only reduce the pump threshold for the dark soliton formation in a fiber laser, but also stabilize the single dark soliton evolution in the cavity. Numerical simulations have also confirmed the DM dark soliton formation in a fiber laser.
In this theoretical study, we show that a simple endlessly single-mode photonic crystal fiber can be designed to yield, not just two, but three zero-dispersion wavelengths. The presence of a third dispersion zero creates a rich phase-matching topology, enabling enhanced control over the spectral locations of the four-wave-mixing and resonant-radiation bands emitted by solitons and short pulses. The greatly enhanced flexibility in the positioning of these bands has applications in wavelength conversion, supercontinuum generation and pair-photon sources for quantum optics.
We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue wave in nonlinear fibers. We find the rogue wave with these higher order effects has identical shape with the well-known one in nonlinear Schr$\ddot{o}$dinger equation. However, the quintic nonlinear term and nonlinear dispersion effect affect the velocity of rogue wave, and the evolution of its phase.
We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. This perturbation leads to the appearance of low frequency MI side lobes that grow with the strength of the perturbations, whereas they are faded by randomness in their position. If the random perturbations exhibit a finite average value, they can be compared with periodically perturbed fibers, where Arnold tongues appear. In that case…
We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression for the position of the gain bands, and we provide simple analytical estimates of the gain and of the bandwidths of those sidebands. An experimental validation of those results has been realized in several microstructured fibers specifically manufactured for that purpose. The dispersion landscape of those fibers is a comb of Gaussian pulses having widths muc…
It is known that eigenvalues of Zakharov-Shabat problem can be used to encode a signal in soliton communication lines. We propose to use dispersion oscillation fiber as a new versalite tool to control the eigenvalues. A fiber with sine-wave variation of the core diameter can be used to manage both real and imaginary parts of the eigenvalues. Change of real part of the eigenvalues results in a splitting of an optical breather into two distinct pulses propagating with the different group velocities. Change of imaginary parts of the eigenvalues allows to realize a reverse process of merge of two …
A recent communication [Opt. Commun. doi:10.1016/j.optcom.2010.06.076 (2010)] presents experimental results in which dark pulses are observed in a dispersion-managed (DM) net-anomalous dispersion fiber laser. Disagreement on the formation mechanism proposed in this communication, we would like to indicate a more accurate explanation in order to clarify some potential misunderstanding on dark pulses in fiber lasers.
Bloch oscillations of spatio-temporal light wave packets in arrays of nonlinear fibers with high-order dispersion are studied. The light wave experiences discrete spatial diffraction along the waveguide array coordinate together with continuous temporal dispersion including higher order terms. When a gradient in the waveguide light confinement strength is considered, the wave packet features robust long-lived Bloch oscillations with temporal and spatial spreading in the presence of a Kerr nonlinearity. The effect of the spatial Bloch oscillations on the emission of the dispersive radiation by …
An exact solitary wave solution is presented for the nonlinear Schrodinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The stability of this soliton-like solution with sech2 shape is proven by the sign-definiteness of the operator and an integral of the Sobolev type. The main criteria governing the existence of such stable localized pulses propagating in optical fibers are also formulated. A unique feature of these soliton-like optical pulses propagating in a fiber with higher order dispersion is that their …
We develop the scheme of dispersion management (DM) for three-dimensional (3D) solitons in a multimode optical fiber. It is modeled by the parabolic confining potential acting in the transverse plane in combination with the cubic self-focusing. The DM map is adopted in the form of alternating segments with anomalous and normal group-velocity dispersion. Previously, temporal DM solitons were studied in detail in single-mode fibers, and some solutions for 2D spatiotemporal "light bullets", stabilized by DM, were found in the model of a planar waveguide. By means of numerical methods, we demonstr…
The nonlinear Schrödinger equation with variable coefficients has applications in numerous areas of physics,specifically in the context of nonlinear optics and Bose-Einstein condensate. Apart from the usual bright and dark-soliton solutions, the so-called rational soliton solutions are perceived to have tremendous impact in futuristic applications and understanding many natural phenomena. In this work, we have studied various orders of rational solution of the variable coefficient nonlinear Schrödinger equation. It is possible to extract the first and the second-order controlled KM-like breath…
Noise-like pulses (NLP) are extremely sought after in many fields. Here, we experimentally and numerically investigated the generation of noise-like pulses in an all-normal-dispersion fiber laser with weak spectrum filtering. With the insertion of the grating as a tunable spectrum filter, the laser operates at a stable dissipative soliton state with a 3.84 ps duration. Replacing the grating with a mirror, NLPs with double-scale intensity autocorrelation trace is ultimately attained. Numerical simulations are performed in detail and demonstrated that with the absence of a spectrum filter, the s…
It is known that after a particular distance of evolution in fiber lasers, two (input) asymmetric soliton like pulses emerge as two (output) symmetric pulses having same and constant energy. We report such a compensation technique in dispersion managed fiber lasers by means of a semi-analytical method known as collective variable approach (CVA) with including third-order dispersion (TOD). The minimum length of fiber laser, at which the output symmetric pulses are obtained from the input asymmetric ones, is calculated for each and every pulse parameters numerically by employing Runge-Kutta four…
