Elena G. Shapiro

Optical pulse dynamics in fiber links with dispersion compensation

We examine optical pulse propagation in a transmission system with periodical pulse amplification and dispersion compensation both numerically and by a variational method. We confirm by direct numerical simulations the validity of the concept of a “breathing” soliton, which we previously proposed. We demonstrate that the sign of the residual dispersion is responsible for the stability of the pulse stream.

Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed.

Variational approach to optical pulse propagation in dispersion compensated transmission systems

Within the area of optical pulse propagation in long-haul transmission systems various designs for dispersion compensation are investigated. On the basis of variational procedures with collective coordinates, a very effective method is presented which allows to determine quite accurately the possible operation points. We have obtained an analytical formula for the soliton power enhancement. This analytical expression is in good agreement with numerical results, in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. The procedure is suitable to analyze the proper design of dispersion compensating elements. The results allow also to describe the shape of the dispersion-managed soliton. We discuss also a qualitative physical explanation of the possibility to transmit a soliton at zero or normal average dispersion. Analytical predictions are confirmed by direct numerical simulations.

Symmetrical dispersion compensation for standard monomode-fiber-based communication systems with large amplifier spacing

Optical 10-Gbit / s return-to-zero pulse transmission in cascaded communication systems using dispersion compensation of the standard monomode fiber with large amplifier spacing is examined. It is shown that pulse distortions that are due to Kerr nonlinearity are significantly diminished by symmetrical ordering of the compensation sections when the total number of precompensation and postcompensation sections is equal. Repositioning of these sections is not critical.

THEORY OF GUIDING-CENTER BREATHING SOLITON PROPAGATION IN OPTICAL COMMUNICATION SYSTEMS WITH STRONG DISPERSION MANAGEMENT

We present a theory of chirped breathing pulse propagation in optical transmission systems with strong dispersion management. Fast changes of pulse width and chirp over one period are given by a simple model that is verified by direct numerical simulations. An average pulse evolution in the leading order is described by the nonlinear Schrödinger equation, with additional parabolic potential that can be a trapping (when a grating is used) or a nontrapping (without a grating) type.

Nonlinear solitary waves with Gaussian tails

Abstract We study analytically and numerically the stationary localized solutions of the nonlinear Schrodinger equation (NLSE) with an additional parabolic potential. Such a model occurs in a wide range of physical applications, including plasma physics and nonlinear optics. Bound states with Gaussian tails (these tails appear due to the parabolic linear potential) play an important role in the dynamics of the systems modelled by this equation. We prove the existence of the bound states and describe their properties.

DYNAMICS OF A NONLINEAR DIPOLE VORTEX

A localized stationary dipole solution to the Euler equations with a relationship between the vorticity and streamfunction given as ω=−ψ+ψ3 is presented. By numerical integration of the Euler equations this dipole is shown to be unstable. However, the initially unstable dipole reorganizes itself into a new nonlinear dipole, which is found to be stable. This new structure has a functional relationship given as ω=αψ+βψ3−γψ5. Such dipoles are stable to head‐on collisions and they are capable of creating tripolar structures when colliding off axis. The effects of increasing Newtonian viscosity on the nonlinear dipole is studied revealing that even though the nonlinearity is weakening, the dipole does not relax towards a Lamb dipole.

Reduction of nonlinear intrachannel effects by channel asymmetry in transmission lines with strong bit overlapping

We have examined the statistics of simulated bit-error rates in optical transmission systems with strong patterning effects and have found strong correlation between the probability of marks in a pseudorandom pattern and the error-free transmission distance. We discuss how a reduced density of marks can be achieved by preencoding optical data.

Novel approaches to numerical modeling of periodic dispersion-managed fiber communication systems

We present two approaches to numerical modeling of periodic dispersion-managed (DM) fiberoptic communication systems. The first approach is a path-average mapping method giving analytical expression for the transfer function (over a system period) for arbitrary cascaded DM system with different periods of the amplification and dispersion compensation. The second method is an expansion of the signal in periodic DM transmission lines in the complete basis of Gauss-Hermite functions with the leading Gaussian zero mode. Theoretical results are verified by direct numerical simulations.

Dispersion-managed soliton in fiber links with in-line filtering presented in the basis of chirped Gauss–Hermite functions

Applying the complete basis of chirped Gauss–Hermite functions, we present a theory of dispersion-managed (DM) solitons in communication systems with in-line filtering. In specific practical example we show that a DM soliton can be well described by a few modes in such an expansion (with the zero Gaussian mode), justifying the use of a Gaussian trial function in the previously developed variational approach. The method presented here is a regular way to estimate the accuracy of the approximate variational approach. An analytical formula to describe the dependence of excess gain on filter bandwidth and map parameters is derived. It is shown that use of the filters additionally increases the peak power of a DM soliton compared with that of a DM system without in-line filtering. The suggested expansion also presents a systematic method to account for the effect of practical perturbations. Theoretical results are verified by numerical simulations.