Pulse Propagation In Optical Fibers Research Articles

Exact Schrödinger Solitons in Optical Fibers in the Presence of Space Dependent Damping or Amplification

It is shown that the nonlinear Schrödinger equation describing pulse propagation in optical fibers in the presence of a properly space-tailored damping or amplification is exactly integrable. A simple transformation of variables is given which transforms the inhomogeneous nonlinear Schrödinger equation into the standard form with constant coefficients, thus generating new explicit bright and dark soliton solutions in the cases of anomalous and normal dispersion, respectively.

Explicit Variational Solution of the Cubic-Quintic Nonlinear Schrödinger Equation for Pulse Propagation in Optical Fibers

With a variational method, we study the cubic-quintic nonlinear Schrödinger equation for pulse propagation in optical fibers. Anomalous dispersion that gives rise to fundamental bright solitary waves is considered. It is shown that within the specified limits, the present variational model demonstrates (for 1 picosecond pulse) good agreements with its analytical equivalent. It is proved that for negative coefficient of the fifth-order nonlinearity existence of the two-state solitary wave solution is a peculiarity of the variational formulation.

Characterizing Pulse Propagation in Optical Fibers around 1550 nm Using Frequency-Resolved Optical Gating

The ultrashort pulse measurement technique of frequency-resolved optical gating (FROG) has been used to characterize the propagation of picosecond pulses at wavelengths around 1550 nm in a variety of different optical fibers used in communications applications. In this paper, we review the use of the FROG technique for ultrashort pulse measurements, discussing in particular several practical issues of importance for accurate results at wavelengths around 1550 nm. We describe the use of FROG measurements to characterize pulse distortion in standard, dispersion-shifted, and erbium-doped optical fiber, and show how they provide direct measurements of complex intensity and phase evolution arising from the interplay of fiber nonlinearity and dispersion. We also discuss the application of the FROG technique to accurately measure the dispersive and the nonlinear parameters of optical fibers, and we present results for standard single-mode fiber in good agreement with specifications.

Soliton propagation in optical devices with two-component fields: a comparative study

The problem of solitonlike pulse propagation in optical fiber devices with two-component fields is studied. Two examples, viz., propagation of pulses in birefringent optical fibers and in nonlinear couplers, are considered. It is shown that radiation processes play an essential role in the soliton dynamics in two-component field fiber devices. Radiation influences the transformation of the main pulses in different ways in the two cases considered. The influence of radiation is stronger when the soliton is closer to the point of bifurcation or the separatrix and weaker when it is far from it.

Stochastic simulation of pulses in nonlinear-optical fibers with random birefringence

Numerical simulations of nonlinear pulse propagation in optical fibers with randomly varying birefringence are presented. For short-length-scale randomness the dominant effect is due to phase-velocity birefringence and produces a probabilistic uncertainty that increases with propagation distance for the expected value of the pulse’s polarization state. An approximate evolution equation for the probability distribution of the polarization state was derived previously [ Physica D55, 166 ( 1992)]. Comparisons between this distribution and Monte Carlo simulations are presented that demonstrate the validity of the analytical results. The simulations also show that the polarization state of a pulse is completely randomized on the longer soliton-period length scale. This provides justification for the assumption of a uniformly distributed polarization state used in previous analyses of this problem [ Opt. Lett.16, 1231 ( 1991); J. Lightwave Technol.10, 28 ( 1992)]. Furthermore, the higher-order effects of group birefringence are assessed. In particular, the polarization-state fluctuations induced by the randomness are shown to reduce significantly the effects of pulse splitting and dispersive radiation loss caused by group-velocity birefringence.

Generalized nonlinear coupled mode equations for ultrashort pulse propagation in optical fibers

Abstract A generalized model to describe the ultrashort pulse propagation in optical fibers with arbitrary modes present by taking advantage of the coupled mode approach is proposed. First the generalized nonlinear coupled mode equations in the frequency domain are derived exactly. Then the simplified forms for the weakly guiding optical fibers are obtained both in the frequency domain and in the time domain. Finally we discuss the particular forms in two special cases, i.e., ideal single-mode fibers and birefringent single-mode fibers.

Inverse-scattering approach to femtosecond solitons in monomode optical fibers.

Using the inverse-scattering transform with 3×3 U-V matrix representation and fully exploiting the symmetry properties of the scattering matrix elements, we found the one-parameter single-soliton, the four-parameter breather soliton, and the general N-soliton solutions of a perturbed nonlinear Schrodinger equation which describes the femtosecond pulse propagation in optical fibers. The threshold power below which the one-parameter single soliton cannot be formed was given. The main characteristic of the general single-soliton solution of the perturbed nonlinear Schrodinger equation is that it presents an arbitrary number of ‘‘humps’’ (local maxima of the amplitude) of different heights.

Soliton solutions for a perturbed nonlinear Schrodinger equation

Using the inverse scattering transform the authors found one-parameter and the breather-like four-parameter soliton solutions of a perturbed nonlinear Schrodinger equation which describes the pulse propagation in optical fibres in the femtosecond regime

Wave-breaking-free pulses in nonlinear-optical fibers

A qualitative as well as quantitative investigation is made of the conditions for avoiding wave breaking during pulse propagation in optical fibers. In particular, it is shown that pulses having a parabolic intensity variation are approximate wave-breaking-free solutions of the nonlinear Schrodinger equation in the high-intensity limit. A simple expression for the compression factor of a fiber-grating compressor based on parabolic pulses is also derived.

Analytic method for solving the nonlinear Schrodinger equation describing pulse propagation in dispersive optic fibres

The authors give a method for obtaining new exact solutions of the nonlinear Schrodinger equation describing pulse propagation in optical fibres for both the anomalous and the normal dispersion regime. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system whose solution determines the exact solutions of the nonlinear Schrodinger equation. By using the phase diagrams associated with the corresponding nonlinear differential equations they classify all the obtained solutions into one of the following categories: bright or dark solitary waves, bright or dark soliton solutions, rational (algebraic) bright or dark solitons, regular or singular periodic waves and stationary solutions. They give a set of particular solutions which describe the periodic wave patterns that are generated by the temporal self-phase modulation instability, the periodic evolution of bright solitons on a continuous wave background and the collision of two dark waves with equal amplitudes.

Pulse propagation in optical fibers near the zero dispersion point.

The problem of nonlinear pulse propagation in optical fibers near the zero dispersion point is investigated. It is shown, both analytically and numerically, that stable double-humped solitary-wave solutions potentially can be used for transmission. The results clarify previous problems with the existence of single-humped localized solitary waves, i.e., fundamental solitons, which are forbidden in the strict mathematical sense.

Stationary Solution of Nonlinear Propagation of Femtosecond Optical Pulse by Circuit Model

A nonlinear wave equation including dispersion over a wide range of the spectrum, is theoretically analyzed, and a stationary solution is found for a femtosecond optical pulse propagation in optical fiber. Soliton theory for the nonlinear propagation of optical pulse was proposed by Hasegawa in 1973. The soliton solution is obtained as the stationary eigensolution of the nonlinear Schroedinger equation (NLS). However, for short pulses it becomes invalid over a long distance because of the higher-order effects. In this paper, i) a new wave equation is introduced which includes the higher-order dispersion by an electrical circuit model and the higher-order shock effect, and ii) the stationary eigensolution of this equation is derived. The eigenwaveform has the pulse width of 13.8 fs with a fixed amplitude, and the chirping in the peak corresponds to experimental results in previous studies.

Self-steepening of optical pulses in dispersive media

We describe an analytical solution of the modified nonlinear Schrödinger equation with the inclusion of the self-steepening term. The results are applied, in particular, to the case of pulse propagation in optical fibers; the role of anomalous dispersion is analyzed, and asymmetric temporal behavior is seen.

Exact solutions of the nonlinear Schrödinger equation for the normal-dispersion regime in optical fibers.

We describe a method for obtaining exact solutions of the nonlinear Schrodinger equation for describing pulse propagation in optical fibers in the normal-group-velocity-dispersion regime. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system whose solutions determine the exact solutions of the nonlinear Schrodinger equation.

Prolongation structures of a higher-order nonlinear Schrodinger equation

A higher-order Schrodinger equation containing parameters, which is used to describe pulse propagation in optical fibres, is shown to admit an infinite-dimensional prolongation structure for exactly four combinations of the parameters, besides the classical NLS equation. For each of these cases, the structure of the resulting prolongation algebra is determined explicitly. For the first three cases the prolongation algebra is essentially a sub-algebra of A1(1), the fourth case turns out to be sub-algebra of the twisted Kac-Moody algebra A2(2). Using vector-field representations, related systems of differential equations for the (pseudo-) potential functions are given for each of the cases. The cases found here correspond exactly to the derived NLS equations I and II, the Hirota equation and the equation recently considered by Sasa and Satsuma (1991). The result of this paper strongly indicates that the considered higher-order NLS equation is completely integrable for precisely these four cases.

Invariant of motion method for nonlinear pulse propagation in optical fibers.

Invariant of motion method for nonlinear pulse propagation in optical fibers.

Approximate analytical approaches to nonlinear pulse propagation in optical fibers: A comparison.

A comparison is made of two recently suggested approximate analytical methods for the investigation of nonlinear pulse propagation in optical fibers, as described by the nonlinear Schr\odinger (NLS) equation. One approach is based on a variational procedure involving Ritz's optimization while the other makes use of invariants of the NLS equation. Despite their different character the approximation schemes are shown to lead to identical results for the evolution of the pulse amplitude and pulse width.

Generation and stabilization of short soliton pulses in the amplified nonlinear Schrödinger equation

The nonlinear Schrodinger equation (NLS), with its modified forms, is the central equation for the description of nonlinear pulse propagation in optical fibers. There are a number of different physical situations in which coupling between waves leads to energy transfer. In such systems, ultrashort pulses have been observed to form during propagation. In this paper we show that much of this behavior can be understood by considering the effects of gain in the NLS. We also show that perturbations of the NLS do not destroy these results, provided that the modified equation possesses solitary-wave solutions.

Femtosecond pulse propagation in optical fibers: higher order effects

Higher-order effects in femtosecond-pulse propagation in optical fibers are examined. In particular, the specific contributions to nonlinear chirping in the fiber by the higher-order cubic dispersion term and by the shock term are investigated. The effects on the output spectrum of fiber input pulses having an initial chirp and an initial asymmetric pulse shape are also investigated. By comparison to a global description, it is shown that, for optical pulses having reasonable power levels, dispersion effects can be accurately approximated by a Taylor series expansion in the nonlinear Schrodinger equation even for pulses containing two optical cycles. >

General formalism for the study of nonlinear pulse propagation in optical fibres

A general formalism for the study of nonlinear pulse propagation in optical fibres is presented. It is then applied to study the time evolution of a Gaussian laser pulse in a fibre with cubic and fifth-order nonlinearity in the index of refraction. The results are presented and discussed.