Validation of the variational approach for chirped pulses in fibers with periodic dispersion (original) (raw)
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On the theory of chirped optical solitons in fiber lines with varying dispersion
1998
Abstract We study a soliton solution of a path-averaged (in the spectral domain) propagation equation governing the transmission of a chirped breather pulse in the fiber lines with dispersion compensation. We demonstrate that the averaged Hamiltonian model correctly describes features of the chirped soliton observed in numerical simulations and experiments.
Physical review, 1993
The propagation of a soliton in a nonlinear optical fiber with a periodically modulated but signpreserving dispersion coefficient is analyzed by means of the variational approximation. The dynamics are reduced to a second-order evolution equation for the width of the soliton that oscillates in an effective potential well in the presence of a periodic forcing induced by the imhomogeneity. This equation of motion is considered analytically and numerically. Resonances between the oscillations in the potential well and the external forcing are analyzed in detail. It is demonstrated that regular forced oscillations take place only at very small values of the amplitude of the inhomogeneity; the oscillations become chaotic as the inhomogeneity becomes stronger and, when the dimensionless amplitude attains a threshold value which is typically less than 4, the soliton is completely destroyed by the periodic inhomogeneity.
Optical pulse propagation in fibers with random dispersion
2004
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 fourth-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 perturbation theory based on the inverse scattering transform (IST). A good agreement between these two approaches is found. Possible ways of compensation of the radiative decay of solitons using the linear and nonlinear amplification are explored. The corresponding mean field equation coincides with the complex Swift-Hohenberg equation. The condition for the autosolitonic regime in propagation of optical pulses along a fiber line with fluctuating dispersion is derived and the existence of autosoliton (dissipative soliton) is confirmed by direct numerical simulation of the stochastic NLSE. The dynamics of solitons in optical communication systems with random dispersion-management is further studied applying the variational principle to the mean field NLSE, which results in a system of ODEs for soliton parameters. Extensive numerical simulations of the stochastic NLSE, mean field equation and corresponding set of ODEs are performed to verify the predictions of the developed theory.
Regular and chaotic dynamics of periodically amplified picosecond solitons
Journal of The Optical Society of America B-optical Physics, 2002
Chirped-pulse propagation under periodic amplification is considered on the basis of the variational method, and the resulting pulse-shape chaotic oscillations are studied. The system of equations governing the evolution of the parameter functions is nonintegrable and is solved by the canonical perturbation method and the construction of local approximate invariants embracing all the essential features of the phase-space dynamics. The latter provide useful guidelines for choosing the appropriate launching-pulse width and chirp for stable propagation for each specific transmission-link configuration. This fact is supported by comparison of the analytic results with the respective numerical ones of the exact dynamical system obtained by the variational method and by the direct integration of the nonlinear Schrödinger equation as well. The structure of the chaotic layer between the two distinct modes of behavior of a propagating pulse, namely, breathing and spreading/decaying, is also investigated qualitatively by utilizing Melnikov's method. Examples from technologically realistic configurations are given for 4-14-ps pulses and for amplification periods of 40-100 km.
Nonlinear pulse propagation in optical fiber
Optics Letters, 1978
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.
Periodic waves and solitons in a nonlinear fibre with resonant impurities
Journal of Modern Optics, 2002
We shall consider a coupled nonlinear SchroÈ dinger equation± Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical ®bre. By making use of the integrability of the dynamic equations, we shall apply the ®nite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.
Dispersion-managed solitons in a periodically and randomly inhomogeneous birefringent optical fiber
Journal of the Optical Society of America B, 2000
The propagation of dispersion-managed vector solitons in optical fibers with periodic and random birefringence is studied. With the help of a variational approach, the equations that describe the evolution of pulse parameters are derived. Numerical modeling is performed for variational equations and for fully coupled periodic and stochastic nonlinear Schrödinger equations. It is shown that variational equations can be effectively used to describe the averaged dynamics of dispersion-managed vector solitons with stochastic perturbations. It is shown, analytically and numerically, that dispersion-managed (DM) solitons have the same resistance to random birefringence as do ordinary solitons. The dependence of the mean decay length of a DM vector soliton on the strength of random birefringence and on the energy of the initial pulse is found.
Modern Physics Letters B, 2020
In this article, we investigate the optical soiltons and other solutions to Kudryashov’s equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as [Formula: see text]-model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The...
Nonlinear pulse propagation in optical fibers (A)
1987
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.