Chapter 2 - Variational methods in nonlinear fiber optics and related fields

Publisher Summary The pseudo–linear transmission is a method for the transmission of high-speed time-division multiplexed (TDM) signals where fast variations of each channel waveform with cumulative dispersion allows important averaging of the intrachannel effects of fiber nonlinearity. The pseudo–linear transmission involves complex optimization of modulation format, dispersion mapping, and nonlinearity. These transmissions occupy a space somewhere between dispersion-mapped linear transmission and nonlinear soliton transmission. The pseudo-linear regime of transmission is characterized by a rapid pulse broadening, which results in a dramatic reduction of the solitonic effect on each pulse. As a result, full dispersion compensation can be used in this regime. Extensive analysis of pseudo-linear transmission and reviews of the TDM transmission experiments at 40 and 160 Gb/s have been provided in the chapter. Two new forms of nonlinear interactions between rapidly dispersing pulses namely intrachannel cross–phase modulation (IXPM) and intrachannel four–wave mixing (IFWM) are also presented. These two intrachannel effects are the most important nonlinear interactions in pseudo-linear transmission and determine the dispersion mapping even for the wavelength–division multiplexed (WDM) systems. Further, the chapter describes the semiconductor–based technologies that enable the development of stable and reliable high–speed transmitters and receivers.

Pseudo-Linear Transmission of High-Speed TDM Signals: 40 and 160 Gb/s

Soliton dynamics in the discrete nonlinear Schrödinger equation

https://math.arizona.edu/~gabitov/papers/1997_OC_GST.pdf

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.

Full length article Optical pulse dynamics in fiber links with dispersion compensation

An analytical investigation is made of the asymptotic propagation properties of pulses evolving from nonsoliton initial conditions in an optical-fiber communication system. Explicit analytical results are obtained for the characteristic parameters of the asymptotically emerging soliton as well as of the accompanying decaying nonsoliton part. The importance of the dispersively decaying part of the pulse for a soliton-based optical-fiber communication system is especially emphasized.

Asymptotic propagation properties of pulses in a soliton-based optical-fiber communication system

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.

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

We demonstrate that the amount of self-phase modulation in a coherent optical transmission system grows more slowly for a phase-modulated than for an amplitude-modulated signal. Signal degradation is discussed in terms of variations in the spectral contents of the amplitude and phase modulations, and explicit analytical expressions are given for the linear modulation indices of phase and amplitude of phase-shift keying coherent transmission systems.

T. Reichel

Papers

Asymptotic propagation properties of pulses in a soliton-based optical-fiber communication system

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

Importance of self-phase modulation for amplitude- and phase-modulated coherent optical transmission systems: a comparison.