We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

Capacity Limits of Optical Fiber Networks

In the 2015 review paper 'Petawatt Class Lasers Worldwide' a comprehensive overview of the current status of highpower facilities of >200 TW was presented. This was largely based on facility specifications, with some description of their uses, for instance in fundamental ultra-high-intensity interactions, secondary source generation, and inertial confinement fusion (ICF). With the 2018 Nobel Prize in Physics being awarded to Professors Donna Strickland and Gerard Mourou for the development of the technique of chirped pulse amplification (CPA), which made these lasers possible, we celebrate by providing a comprehensive update of the current status of ultra-high-power lasers and demonstrate how the technology has developed. We are now in the era of multi-petawatt facilities coming online, with 100 PW lasers being proposed and even under construction. In addition to this there is a pull towards development of industrial and multidisciplinary applications, which demands much higher repetition rates, delivering high-average powers with higher efficiencies and the use of alternative wavelengths: mid-IR facilities. So apart from a comprehensive update of the current global status, we want to look at what technologies are to be deployed to get to these new regimes, and some of the critical issues facing their development.

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Petawatt and exawatt class lasers worldwide

The investigation of nonlinear wave phenomena has been one of the main direc tions of research in optics for the last few decades. Soliton concepts applied to the description of intense electromagnetic beams and ultrashort pulse propagation in various media have contributed much to this field. The notion of solitons has proved to be very useful in describing wave processes in hydrodynamics, plasma physics and condensed matter physics. Moreover, it is also of great importance in optics for ultrafast information transmission and storage, radiation propagation in resonant media, etc. In 1973, Hasegawa and Tappert made a significant contribution to optical soliton physics when they predicted the existence of an envelope soliton in the regime of short pulses in optical fibres. In 1980, Mollenauer et al. conducted ex periments to elucidate this phenomenon. Since then the theory of optical solitons as well as their experimental investigation has progressed rapidly. The effects of inhomogeneities of the medium and energy pumping on optical solitons, the interaction between optical solitons and their generation in fibres, etc. have all been investigated and reported. Logical devices using optical solitons have been developed; new types of optical solitons in media with Kerr-type nonlinearity and in resonant media have been described.

Optical Solitons

Dispersion-managed solitons in fibre systems and lasers

Fiber-optic distributed sensing, employing the Brillouin effect, is already a commercially available measurement technique for the accurate estimation of the static strain/temperature fields along tens of kilometers with a spatial resolution of the order of a meter. Furthermore, relentless research efforts are paving the way to even much wider usability of the technique through recently achieved enhanced performance in each of its critical dimensions: measurement range has been extended to hundreds of kilometers; spatial resolution is of the order of a centimeter or less, signal to noise ratio has been significantly improved; fast dynamic events can be captured at kHz’s sampling rates; and a much better understanding of the underlying physics has been obtained, along with the formulation of figures of merit, and the preparation and early adoption of appropriate standards and guidelines. This paper describes the basics, as well as the state of the art, of the leading Brillouin interrogation methods, with emphasis on the significant progress made in the last 3 years. It also includes a short introduction to coding, which has proven instrumental in many of the recently obtained performance records.

[INVITED] State of the art of Brillouin fiber-optic distributed sensing

Introduction Stimulated Raman Scattering in Optical Fibers Raman Pumping in Optical Fiber Communications Distributed Raman amplification along the transmission span Discrete Raman amplifiers Impairments and Limitations to Raman Amplification.

Raman amplification in fiber optical communication systems

Coupled nonlinear equations that describe the nonlinear process of stimulated Raman scattering in optical fibers are derived. These equations account in a unified manner for the Raman amplification, the Stokes generation, the induced self-frequency shift, and the interpulse stimulated Raman-scattering-induced cross-frequency shift. The equations reduce to a well-known form for relatively wide picosecond pump pulses. Using these equations, we show theoretically that the effects of cross-phase modulation, self-frequency shift, and cross-frequency shift cause two optical pulses copropagating in the anomalous dispersion regime of the fiber to shed some of their energy and evolve into a narrower soliton, which has a higher frequency shift than a single propagating soliton. It is also shown that the self-frequency shift of femtosecond pulses is detrimental to Raman generation. As the input pulse width is reduced, the spectrum of the pulse shifts by an amount comparable with the Raman shift. The shift increases continuously with propagation at such a rapid rate that the Stokes pulse has no time to build up from noise to significant energy levels.

Unified description of ultrafast stimulated Raman scattering in optical fibers

The generalized nonlinear Schr\"odinger equation governs wave propagation in nonlinear dispersive media by including the effects of group-velocity dispersion, self-phase-modulation, stimulated Raman scattering, and self-steepening. This equation is shown to have solitary-wave solutions that correspond to an optical shock front moving at the group velocity. The properties of such kink-type solitary waves are discussed.

Kink solitons and optical shocks in dispersive nonlinear media.

A novel technique that can lead to simultaneous amplification and compression of picosecond optical pulses is proposed. It consists of copropagating a weak signal pulse with an intense pump pulse in an optical fiber whose minimum-dispersion wavelength is chosen such that it falls between the pump and the signal wavelengths. The pump pulse amplifies the signal pulse through stimulated Raman scattering and at the same time imposes a nearly linear frequency chirp on it through cross-phase modulation. The chirped signal pulse is simultaneously compressed in the anomalous-dispersion regime of the optical fiber as it becomes amplified. Numerical simulations are used to predict the extent of amplification and compression under realistic practical conditions. The signal pulse can be compressed by more than a factor of 10 while it is amplified by 40–50 dB.

Clifford Headley

Papers

Raman amplification in fiber optical communication systems

Unified description of ultrafast stimulated Raman scattering in optical fibers

Kink solitons and optical shocks in dispersive nonlinear media.

Simultaneous amplification and compression of picosecond optical pulses during Raman amplification in optical fibers