Pulse Propagation In Optical Fibers Research Articles

Wide vector solitons in systems with time- and space-modulated nonlinearities

In this work we apply point canonical transformations to solve some classes of two coupled nonautonomous nonlinear Schrödinger equations with specific cubic and quintic-time- and space-dependent-nonlinearities. The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of nonautonomous nonlinear Schrödinger equations. The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities.

Numerical simulation of nonlinear pulse propagation in optical fibers with randomly varying birefringence

This paper is concerned with the evolution of nonlinear pulses driven by random polarization mode dispersion (PMD). The evolution of the slowly varying envelopes is governed by the stochastic Manakov equation, which has been derived as the limit of the Manakov PMD equation. The aim in this work is to investigate the effect of the PMD on Manakov’s solitons and soliton wave-train propagation. I also study the statistical property of the differential group delay (DGD), and, using Monte Carlo simulations, I compute its probability density function. For linear pulses with zero group-velocity dispersion, I propose an algorithm, based on importance sampling, to estimate the outage probability, i.e., the probability that the value of the DGD exceeds an acceptance level.

Butterfly-shaped pulse in optical fibers with variable group-velocity dispersion

Butterfly-shaped pulse in optical fibers with variable group-velocity dispersion is reported for the first time. The nonlinear Schrödinger equation, which describes the pulse propagation in optical fibers with variable group-velocity dispersion, is investigated, and the analytic solution for this equation is derived. The cosine dispersion profile of optical fibers is suggested to obtain the butterfly-shaped pulse. The physical effects affecting the butterfly-shaped pulse properties is discussed.

Rogue Waves of the Fokas–Lenells Equation

The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in the leading asymptotic order the nonlinear Schr\"odinger (NLS) equation results). Here we present an explicit analytical representation for the rogue waves of the FL equation. This representation is constructed by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution. when certain higher-order nonlinear effects are considered, the propagation of rogue waves in optical fibers is given.

Linear and nonlinear propagation of optical Nyquist pulses in fibers

We present an analytical and numerical description of optical Nyquist pulse propagation in optical fibers in the presence of dispersion and nonlinearity. An optical Nyquist pulse has a profile given by the sinc-like impulse response of a Nyquist filter, which has periodic zero-crossing points at every symbol interval. This property makes it possible to interleave bits to an ultrahigh symbol rate with no intersymbol interference in spite of the strong overlap between adjacent pulses. We analyze how this periodic zero-crossing property is maintained or affected by the fiber dispersion and nonlinearity, and show that it is better maintained against nonlinearity in the presence of normal dispersion.

Adaptive step size Gill method for the modeling of ultrashort pulse propagation in optical fiber

An adaptive step size Gill method is proposed to numerically solve the normal and generalized nonlinear Schrödinger equations. In this method, the Gill algorithm in the interaction picture and the conservation quantity error (CQE) method are used for integration scheme and adaptive step size control, respectively. Numerical simulations of the propagation of second-order soliton and soliton collision show that the proposed method can reduce the round-off error in the process of computation. The adaptive step size Gill method exhibits the expected global fourth-order accuracy for the problems studied. It is an efficiently alternative method for the modeling of ultrashort pulse propagation in optical fiber. In addition, we adopt a more accurate Raman response function (MA-RRF) in the simulation of supercontinuum generation. The results illustrate that the MA-RRF is necessary to provide a more accurate description of the Raman-induced frequency shift effect in supercontinuum generation.

Simulations of pulse propagation in optical fibers using graphics processor units

Several simple cases of pulse propagation in optical fibers have been simulated using a graphics processor unit. Comparisons with simulations in a computer processor unit are also reported. Speedups from 4 to 36 have been obtained by different numerical methods, reaching a similar accuracy both in computer processor unit and in graphics processor unit, working with double-precision floating point numbers. Best results are achieved in simulations when the number of points in t grid rises. Therefore, the results indicate that graphics processor units could be a good tool to improve numerical simulations of pulse propagation in fibers.

Research on the nonlinear pulse propagation by numerical analysis

Based on the computation approaches of numerical analysis in electromagnetic, the nonlinear pulse propagation in optical fiber is investigated in this paper. The transforming rule of the shape and spectrum of Gauss pulse are also researched in chirped and non-chirped scenarios from the nonlinear Schrödinger equation (NLSE). Analyzing the transient wave behavior in time domain and frequency domain respectively, the compression effect of chirp is also presented at different propagation distance. Then by the nonlinear Schrödinger equation, we discuss a specific solution in the quasi soliton without distortion, which has the stable propagation properly, and do the numerical simulation in soliton wave. Finally, by selecting proper fiber structure parameters and adjusting the width in soliton pulse, the soliton communication system can be optimized.

An Efficient Approach for Time-Domain Simulation of Pulse Propagation in Optical Fiber

A novel approach is proposed for split-step time-domain simulation of pulse propagation in optical fiber. In this approach, a Fourier series expansion method is introduced for time-domain digital filter extraction from any given fiber transfer function. With such extracted filter coefficients and a double Tukey window function, the filter length can be optimized for a given error tolerance. This method is validated by comparing our simulation results with that obtained from the well-known split-step frequency-domain method. Through several simulation examples, we find that this solution technique is much more efficient than other existing time-domain approaches-as much as 92% of the computation time can be saved. It even outperforms the well-known split-step frequency-domain fast Fourier transform method in terms of the computation efficiency, under the condition that the input signal samples are huge-a situation we often meet in dealing with wavelength division multiplexing systems. Moreover, we find that the truncation effect at the computation window edge introduced by the time-domain algorithm is less severe than the aliasing effect associated with the frequency-domain method, not to mention that we can eliminate the truncation error by using a sliding window, only at a small cost on computation time.

Dark solitons in optical fiber with inhomogeneous effects

We study the nonlinear wave propagation in an inhomogeneous optical fiber core in the normal dispersive regime. In order to include the inhomogeneous physical effects, the nonlinear Schrödinger equation (NLSE), which governs the solitary pulse propagation in optical fiber, is modified by adding terms for phase modulation and power gain or loss. The modified NLSEs are bilinearized and exact dark soliton solutions are obtained. The results are discussed.

Collisions and turbulence in optical rogue wave formation

We discuss optical rogue wave generation in terms of collisions and turbulence processes. Simulations of picosecond pulse propagation in optical fibres show rogue soliton generation from either third-order dispersion or Raman scattering independently. Simulations of rogue soliton emergence with dispersive perturbation in the long-distance limit are also presented.

Efficient Adaptive Step Size Method for the Simulation of Supercontinuum Generation in Optical Fibers

The use of an adaptive step size selection significantly reduces the computational effort for the numerical solution of the generalized nonlinear SchrOumldinger equation (GNLSE). The most commonly employed adaptive step size method is based on the estimation of the local error by applying step size doubling and local extrapolation. While this method works well in combination with the globally second-order split-step Fourier (SSF) integration scheme, it can be significantly improved when the highly accurate fourth-order Runge-Kutta in the interaction picture (RK4IP) method is used for integration, which was recently introduced into the nonlinear optics field. It is demonstrated that the local error can then be estimated using a conservation quantity error (CQE) without the necessity of step size doubling. The CQE method for solving the GNLSE is explained in detail, and in addition the concept is transferred to the normal nonlinear Schrodinger equation and extended to include linear loss. The RK4IP-CQE combination proves to be the most efficient algorithm for the modeling of ultrashort pulse propagation in optical fiber, reducing the computational effort by up to ~50% relative to the local error method.

Exactly Solvable Model for Nonlinear Pulse Propagation in Optical Fibers

The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation, which was first derived by means of bi‐Hamiltonian methods in [1]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as a model for nonlinear pulse propagation in monomode optical fibers when certain higher‐order nonlinear effects are taken into account; (b) We show that the equation is equivalent, up to a simple change of variables, to the first negative member of the integrable hierarchy associated with the derivative NLS equation; (c) We analyze traveling‐wave solutions.

Impact of GVD on the Performance of 2-D WH/TS OCDMA Systems Using Heterodyne Detection Receiver

SUMMARY In this paper, a novel model of Gaussian pulse propagation in optical fiber is proposed to comprehensively analyze the impact of Group Velocity Dispersion (GVD) on the performance of two-dimensional wavelength hopping/time spreading optical code division multiple access (2-D WH/TS OCDMA) systems. In addition, many noise and interferences, including multiple access interference (MAI), optical beating interference (OBI), and receiver’s noise are included in the analysis. Besides, we propose to use the heterodyne detection receiver so that the receiver’s sensitivity can be improved. Analytical results show that, under the impact of GVD, the number of supportable users is extremely decreased and the maximum transmission length (i.e. the length at which BER ≤ 10−9 can be maintained) is remarkably shortened in the case of normal single mode fiber (ITU-T G.652) is used. The main factor that limits the system performance is time skewing. In addition, we show how the impact of GVD is relieved by dispersion-shifted fiber (ITU-T G.653). For example, a system with 32 × 1G bit/s users can achieve a maximum transmission length of 111 km when transmitted optical power per bit is − 5d Bm.

Femtosecond Pulse Propagation in Optical Fibers Under Higher Order Effects: A Collective Variable Approach

Employing collective variable approach, femtosecond pulse propagation has been investigated in optical fibers using the higher order nonlinear Schrodinger equation. In order to view the pulse dynamics along the propagation distance, variation of different pulse parameters, called collective variables, such as pulse amplitude, width, chirp, pulse center and frequency has been investigated by numerically solving the set of ordinary equations obtained from collective variable approach.

Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

In case of the nonlinear Schr\"odinger equation with designed group velocity dispersion, variable nonlinearity and gain/loss; we analytically demonstrate the phenomenon of chirp reversal crucial for pulse reproduction. Two different scenarios are exhibited, where the pulses experience identical dispersion profiles, but show entirely different propagation behavior. Exact expressions for dynamical quasi-solitons and soliton bound-states relevant for fiber communication are also exhibited.

Nonlinear pulse propagation in optical fibers using second order moments

We present simple yet efficient formulae for the propagation of the second order moments of a pulse in a nonlinear and dispersive optical fiber over many dispersion and nonlinear lengths. The propagation of the temporal and spectral widths, chirp and power of pulses are very precisely approximated and quickly calculated in both dispersion regimes as long as the pulses are not high order solitons.

Time-Frequency (Wigner) Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers

Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD) and self-phase modulation (SPM) are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking) are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers), providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems.

Parallel Split-Step Fourier Methods for the Coupled Nonlinear Schr�dinger Type Equations

The nonlinear Schrodinger type equations are of tremendous interest in both theory and applications. Various regimes of pulse propagation in optical fibers are modeled by some form of the nonlinear Schrodinger equation. In this paper we introduce parallel split-step Fourier methods for the numerical simulations of the coupled nonlinear Schrodinger equation that describes the propagation of two orthogonally polarized pulses in a monomode birefringent fibers. These methods are implemented on the Origin 2000 multiprocessor computer. Our numerical experiments have shown that these methods give accurate results and considerable speedup.

A broad-band digital filtering approach for time-domain Simulation of pulse propagation in optical fiber

A broad-band digital filtering approach for the simulation of pulse propagation in the optical fiber has been developed. Unlike the most popular frequency-domain split-step method, the pulse propagation is realized by letting the signal samples pass through a preextracted digital filter where the convolution is simply made by a series of operations that consist of shift and multiplication only. It also differs from the existing time-domain split-step method in a sense that the digital filter is extracted to match the frequency-domain fiber linear transfer function in the full bandwidth range rather than in a reduced portion. This approach is verified through comparisons made with the conventional frequency-domain split-step method and is applied to the simulation of multiple-channel narrow-pulse propagation over the long-haul fiber. The main advantage brought by this approach lies in that the simulator is fully realized in a "data-flow" fashion; that is, the signal (long sample stream) is treated sample by sample, rather than block (a collection of neighboring samples) by block. Matching the fiber frequency-domain response over the full bandwidth does not require any further reduction on the propagation step since the error can be controlled through the filter length. The authors' preliminary effort on the filter length reduction on a given error reveals that a savings on both memory and computation time is also achievable in comparison with the frequency-domain split-step method.