A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation in photonic crystal fiber

This paper reviews the fundamental concepts and basic theory of polarization mode dispersion (PMD) in optical fibers. It introduces a unified notation and methodology to link the various views and concepts in Jones space and Stokes space. The discussion includes the relation between Jones vectors and Stokes vectors, rotation matrices, the definition and representation of PMD vectors, the laws of infinitesimal rotation, and the rules for PMD vector concatenation.

https://www.pnas.org/content/pnas/97/9/4541.full.pdf

PMD fundamentals: Polarization mode dispersion in optical fibers

In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

https://iopscience.iop.org/article/10.1088/1464-4266/7/5/R02/pdf

Spatiotemporal optical solitons

An analytical characterization of polarization dispersion measurements is presented. The authors report the solution of Poole's stochastic dynamical equation for the evolution of the polarization dispersion vector with fiber length. The authors extend this to a more complete description by considering small, second-order dispersion effects through the frequency derivative of the dispersion vector. The complete analytical solution is seen to accord with what were originally empirically derived features of the joint probability distribution of the polarization dispersion vector and its frequency derivatives. Among the analytically determined properties are the Gaussian probability densities of the three components of the dispersion vector, and the hyperbolic secant (soliton shaped) probability densities of the components of the derivative of the dispersion vector. >

Statistical theory of polarization dispersion in single mode fibers

Polarization mode dispersion and the polarization decorrelation and diffusion lengths are calculated in fibers with randomly varying birefringence. Two different physical models in which the birefringence orientation varies arbitrarily are studied and are shown to yield nearly identical results. These models are appropriate for communication fibers. We show that both the length scales for polarization mode dispersion and polarization decorrelation measured with respect to the local axes of birefringence are equal to the fiber autocorrelation length. We also show that the coupled nonlinear Schrodinger equation which describes wave evolution over long length along a communication fiber can be reduced to the Manakov equation. The appropriate averaging length for the linear polarization mode dispersion is just the fiber autocorrelation length but the appropriate averaging length for the nonlinear terms is the diffusion length in the azimuthal direction along the Poincare sphere which can be different, The implications for the nonlinear evolution are discussed.

Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence

Optical Fiber Propagation Optical Amplifiers Optical Transmission Systems Soliton Optical Communications Repeaterless Systems Long Distance TDM Transmission WDM Optically Amplified Systems Transmission in All-Optical Networks Appendices Index

Nonlinear Optical Communication Networks

A simple relationship is found for the evolution of the principal states of polarization (PSPs) and their differential group delay in fiber links. A simple expression is found, using the relationship, for the probability of the differential group delay (DGD), considering the evolution of the PSPs as a Brownian motion. The theory has been verified experimentally on an optical cable composed of 12 single-mode, shifted-dispersion fibers 2.2-km long. The results show that the DGD grows as the square root of the length when the length of the fiber is far larger than the correlation length of the perturbation. The measured value of DGD can vary substantially in two fibers belonging to the same ensemble, and in the same fiber, considering two frequencies differing by more than 5 nm. >

Statistical treatment of the evolution of the principal states of polarization in single-mode fibers

Periodically spaced amplifiers along a transoceanic cable provide the phase-matching condition for a four-wave mixing process owing to Kerr nonlinearity. A new kind of sideband instability, shows up in both positive and negative dispersion regimes that is similar to modulation instability. A comparison with the sideband instability that was recently discovered for solitons is carried out.

Sideband instability induced by periodic power variation in long-distance fiber links

We report some results of measurements of the frequency dependence of the state of polarization at the end of a low-birefringence long-cabled (50-km) optical fiber. The principal states of polarization and their group-delay difference were determined by making use of the Poincare sphere representation.

Measurement of the group-delay difference between the principal states of polarization on a low-birefringence terrestrial fiber cable.

This paper reports the main results obtained in the framework of the COST239 project on the implementation of transparent optical network schemes to connect main European cities. The investigation on transmission limitations has shown that transmission systems, for which 1662:5 Gbit/s WDM systems are used due to traf®c reasons, have a maximum range shorter than 1000 km. This condition does not allow a completely transparent network. Two solutions, the partitioned and the gridconnected network architecture, are proposed, described, and compared in the paper.

F. Matera

Papers

Nonlinear Optical Communication Networks

Statistical treatment of the evolution of the principal states of polarization in single-mode fibers

Sideband instability induced by periodic power variation in long-distance fiber links

Measurement of the group-delay difference between the principal states of polarization on a low-birefringence terrestrial fiber cable.

Study on the Implementation of Optical Transparent Transport Networks in the European Environment—Results of the Research Project COST 239