Dispersion-managed Fiber Systems Research Articles

Symmetrical reversal transmission of Airy pulses in dispersion-managed fiber systems.

Based on the dispersion management technology, the transmission characteristics of Airy pulses in optical fiber systems are studied theoretically and numerically. The results show that the group velocity dispersion and third-order dispersion that change periodically along the transmission direction of the optical fiber can prolong the transmission of pulses. Under the action of periodically varying group velocity dispersion, the symmetrical reversal of the Airy pulse can be realized which the shape of the pulse keeps invariable and the tail converses after the inversion. When the periodic third-order dispersion effect is also considered, the periodically symmetrical reversal of the Airy pulse happens and the pulse can be regenerated periodically at the certain transmission distance. Adjusting the parameters of the third-order dispersion, the inversion position and the period can be manipulated. In addition, it is found that the tight focusing of the Airy pulse is also controllable.

Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber

We investigate the soliton dynamics in tapered parabolic index fibers via symbolic computation for a variety of dispersion profiles to inspect how a specific dispersion profile controls the optical soliton. By means of AKNS procedure, Lax pair is constructed for nonlinear Schrödinger equation with variable coefficients. Using obtained Lax pair, multi-soliton solutions are generated via Darboux transformation technique. Using multi-soliton solutions, soliton dynamics in tapered parabolic index fiber with the hyperbolic, Gaussian, exponential, and linear profiles are discussed. Results obtained in this study will be of certain potential application on construction of the nonlinear optical devices by soliton control. Results obtained in this study will be of certain value to the studies on the propagation and application of the soliton in the tapered parabolic index fiber and dispersion-managed fiber system.

Vector Breathers in an Averaged Dispersion-Managed Birefringent Fiber System* *Supported by the Science and Technology Department of Henan Province under Grant No. 142300410043, and by the Education Department of Henan Province under Grant No. 13A140113

A variable-coefficient coupled nonlinear Schrödinger equation in an averaged dispersion-managed birefringent fiber is investigated. Based on the one-to-one correspondence between variable-coefficient and constant-coefficient equations, an analytical breather solution is derived. As an example to exhibit dynamical behaviors of solution, its controllable excitations including rear excitation, peak excitation and initial excitation are discussed.

Controllable Nonautonomous Rogue Waves in the Modified Nonlinear Schrödinger Equation with Distributed Coefficients in Inhomogeneous Fibers

Abstract Under investigation in this paper is an inhomogeneous modified nonlinear Schrödinger (MNLS) equation describing the ultrashort pulse dynamics with the distributed dispersion, self-phase modulation, self-steepening, and linear gain/loss. Nonautonomous rogue waves for the inhomogeneous MNLS equation are constructed via the modified Darboux transformation with the inhomogeneous parameters. The dynamical behaviours and main characteristics of the nonautonomous rogue waves in inhomogeneous fibers are discussed by analysing certain physical quantities. The inhomogeneous effects on the evolution of rogue waves are considered by virtue of the presented rational solutions with distributed coefficients. It is found that the group velocity dispersion (GVD) and linear gain/loss coefficients have effects on the trajectories and amplitudes of the rogue waves, respectively. Additionally, an intriguing composite rogue wave of the inhomogeneous MNLS equation is revealed, owing to the proper choice of the GVD coefficient. Our results could be useful for controlling the rogue waves in the dispersion-managed fiber system.

Double Wronskian solutions of a nonlinear Schrödinger equation in an averaged dispersion-managed fiber system

A nonlinear Schrödinger equation in the presence of chirp and loss terms, which describes the optical solitons in an averaged dispersion-managed (DM) fiber system with fiber losses, is studied via symbolic computation. N-soliton solutions are constructed and verified with the Wronskian technique. Analytic one-, two- and three-soliton solutions are discussed. The soliton has a linear frequency chirp. Soliton width increases exponentially while soliton amplitude, energy and speed decrease exponentially along the DM fiber. As the chirp-loss coefficient increases, soliton width gets wider, while soliton amplitude, energy and speed become smaller. Interactions between the two solitons and among the three solitons are discussed and illustrated. For the larger initial soliton separations, interactions result in some smaller envelopes, which soon disappear due to the chirp-loss effect. When the soliton separations almost reaches zero, solitons interact quasi-periodically along the DM fiber, while each soliton undergoes broadening and decaying.

Dark and antidark soliton solutions in the modified nonlinear Schrödinger equation with distributed coefficients in inhomogeneous fibers

We study a modified nonlinear Schrödinger model with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss, which describes the ultrashort pulse propagating dynamics in inhomogeneous fibers. The dark and antidark soliton solutions are obtained with Hirota's bilinear method. The propagation dynamics and collision behaviors of the dark and antidark soliton pulses in inhomogeneous fibers are discussed by analyzing some important physical quantities and through graphical illustration. The inhomogeneous effects on the evolution and interaction for dark and antidark solitons are considered by virtue of the presented soliton solutions with distributed coefficients. Our analytical results could be applied to research on dark and antidark solitons in the dispersion-managed fiber system.

Ultrashort soliton pulses in the modified nonlinear Schrödinger equation with distributed coefficients in inhomogeneous fibers

This paper investigates a variable-coefficient modified nonlinear Schrodinger model for describing the ultrashort pulse dynamics with the distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. Under specified soliton management conditions, the bright one- and two-soliton solutions are analytically derived by the Hiroa bilinear method. Dynamical behaviors and main features of the ultrashort pulse propagation in inhomogeneous fibers are discussed by analyzing some important physical quantities. Additionally, interactions of two neighboring ultrashort pulses with varying management parameters are investigated in detail. Results obtained in this paper will be of certain value to the studies on the propagation and application of the ultrashort pulse in the dispersion-managed fiber system.

Effective method of characterization of the phase and intensity profiles of asymmetrically distorted light pulses in optical fiber systems

We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems, under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse’s profile is asymmetrically distorted with respect to its center-of-mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, which allow a fair characterization of the intensity and phase of all types of light pulses, including those which are asymmetrically distorted. We illustrate the effectiveness of the upgraded parameters by applying them to a meticulous characterization of light pulses in a dispersion-managed optical fiber system in which third-order dispersion is acting as a strong perturbation.

Effective characterization of the phase and intensity profiles of asymmetrically distorted light pulses in optical fiber systems

We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse's profile is asymmetrically distorted with respect to its center of mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, that allow a fair characterization of the intensity and phase of all types of light pulses, including those that are asymmetrically distorted. We illustrate the effectiveness of the upgraded parameters by applying them to a meticulous characterization of light pulses in a dispersion-managed optical fiber system in which third-order dispersion is acting as a strong perturbation.

Effectiveness of Nonlinear Optical Loop Mirrors in Dispersion-Managed Fiber Communication Systems Compensated by Chirped Fiber Gratings With Group Delay Ripples

We examine the effectiveness of using nonlinear optical loop mirrors (NOLMs) to reduce the intersymbol interference in dispersion-managed (DM) fiber communication systems compensated by chirped fiber gratings (CFGs) with group delay ripples (GDR). We show that the use of NOLMs can enhance the transmission performance by more than one order of magnitude in the presence of amplifier noise and random variations in the parameters of the GDR in CFGs. We found that transoceanic transmissions can be achieved when NOLMs are included in the DM optical fiber transmission line compensated by CFGs with GDR whose parameters vary randomly along the transmission line.

ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM

We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

Design of dispersion-managed fiber systems for transmitting chirp-free Gaussian pulses

We present a general method to analytically design a dispersion-managed (DM) fiber system for any desired fiber (dispersion, nonlinearity and losses) and pulse (width and energy) parameters. This analytical design allows one to transmit chirp-free Gaussian pulses (for very long distances) in almost all kinds of DM fiber systems that have appeared so far in the literature, including systems with dispersion map length greater, equal or shorter with respect to the amplification period.

Generalized Riccati equation rational expansion method and its application

By directly extending the Riccati equation rational expansion method, a new method is developed for constructing a series of exact analytical solutions of an averaged dispersion-managed fiber system equation (ADmE), including some new rational formal soliton-like solutions, triangle-like solutions and rational solutions.

Dynamics of nonstationary return-to-zero pulses in dispersion-managed systems

We describe an analytical framework for return-to-zero (RZ) propagation in dispersion-managed fiber systems. The pulses may generally not follow the same periodicity as that of the dispersion map (i.e., nonstationary evolution), which can complicate the design and monitoring of such systems. We show that a phase-plane representation of pulses is useful in identifying as well as predicting the salient features of this multiscale and nonlinear evolutionary behavior. Numerical calculations of RZ pulse-train propagation over 4000 km are carried out to demonstrate the correspondence of theory and simulation

Radiating and nonradiating behavior of hyperbolic-secant, raised-cosine, and Gaussian input light pulses in dispersion-managed fiber systems

We address the problem of optical light pulses, called dressed pulses, which do not match the stationary pulse profile of a dispersion-managed (DM) fiber system and we theoretically analyze the associated radiation. Comparing hyperbolic-secant, raised-cosine, and Gaussian pulse envelopes, we show that the general radiation figure is highly sensitive to the input pulse profile. As common general features for these pulse profiles, we find a rich variety of dynamical states that includes weak-, moderate-, and strong-radiation states, depending on the map strength of the DM fiber system. We demonstrate the existence of two intervals of map strengths where the emitted radiation is of considerably low level. The first interval falls in a region of small map strengths where pulses are weakly dressed. In contrast, the second window of low radiation appears in the map strength region corresponding to strongly dressed pulses. As a major difference with respect to the pulse profile, we find that light pulses with Gaussian input profile produce less radiation in the fiber system than hyperbolic-secant or raised-cosine pulses can do. In particular, at the lower edge of the second window of low radiation, Gaussian light pulses with large initial dressing acquire the best ability to execute a stable nonradiative propagation over transoceanic distances.

Soliton Pulse Propagation in Averaged Dispersion-managed Optical Fiber System

The dynamics of nonlinear pulse propagation in an averaged dispersion-managed soliton system is governed by a variable coefficient nonlinear Schrodinger equation (NLSE). For a special set of parameters the variable coefficient NLSE is completely integrable. The same variable coefficient NLSE is also applicable to optical fiber systems with phase modulation or pulse compression. For such variable coefficient NLSE, solitary waves have been computed earlier in the literature either by the inverse scattering transform or the Backlund transformation. The Hirota bilinear method is shown to be applicable here too, and this modified format is employed to compute the exact bright and dark soliton solutions and the periodic waves solutions. The analysis is also extended to the coupled variable coefficient NLSEs. The merit of the Hirota bilinear approach is demonstrated clearly as periodic and solitary waves are obtained even for nonintegrable coupled systems. The validity of the new solutions is verified directly and independently by the software Mathematica.

Radiating and nonradiating dispersion-managed solitons

Using spectral analysis, we present the salient features of the radiating behavior of optical solitons in dispersion-managed fiber systems. Depending on the map strength of the system, we find a rich variety of dynamic states that includes weak, moderate, and strong radiation states. We establish the existence of a critical map strength at which a Gaussian-shaped light pulse with a large initial dressing undergoes highly stable nonradiative propagation over transoceanic distances.

Radiating and non-radiating trains of light pulses in dispersion-managed optical fiber systems

We show theoretically that the radiation picture of small trains of closely packed light pulses with Gaussian input profile, exhibits both some similar features and some fundamental differences when compared to the radiating behavior of a solitary pulse in a dispersion-managed optical fiber system. For small map strengths, the pulse trains strongly radiate away energy, and there, the total amount of radiated energy increases linearly as a function of the length of the pulse train. For large map strengths, the amount of radiated energy increases rather smoothly as a function of the length of the pulse train. We establish the existence of a map strength region, in which light pulses with initially Gaussian-shaped profile executes a non-radiative propagation over transoceanic distances.

Optimal span length in high-speed transmission systems with hybrid Raman–erbium-doped fiber amplification

We show, using nonlinearity management, that the optimal performance in high-bit-rate dispersion-managed fiber systems with hybrid amplification is achieved for a specific amplifier spacing that is different from the asymptotically vanishing length corresponding to ideally distributed amplification [Opt. Lett. 15, 1064 (1990)]. In particular, we prove the existence of a nontrivial optimal span length for 40-Gbit/s wavelength-division transmission systems with Raman-erbium-doped fiber amplification. Optimal amplifier lengths are obtained for several dispersion maps based on commonly used transmission fibers.

Exact Soliton Solutions To An Averaged Dispersion-Managed Fiber System Equation

By introducing a set of ordinary differential equations which possess q-deformed hyperbolic function solutions, and a new ansatz, a method is developed for constructing a series of exact analytical solutions of some nonlinear evolution equations. The proposed method is more powerful than various tanh methods, the secq-tanhq-method, generalized hyperbolic-function method, generalized Riccati equation expansion method, generalized projective Riccati equations method and other sophisticated methods. As an application of the method, an averaged dispersion-managed (DM) fiber system equation, which governs the dynamics of the core of the DM soliton, is chosen to illustrate the method. With the help of symbolic computation, rich new soliton solutions are obtained. From these solutions, some previously known solutions obtained by some authors can be recovered by means of some suitable choices of the arbitrary functions and arbitrary constants. Further, the soliton propagation and solitons interaction scenario are discussed and simulated by computer.