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

We present a detailed overview of stimulated Brillouin scattering (SBS) in
 single-mode optical fibers. The review is divided into two parts. In the first part,
 we discuss the fundamentals of SBS. A particular emphasis is given to analytical
 calculation of the backreflected power and SBS threshold (SBST) in optical fibers
 with various index profiles. For this, we consider acousto-optic interaction in the
 guiding geometry and derive the modal overlap integral, which describes the
 dependence of the Brillouin gain on the refractive index profile of the optical
 fiber. We analyze Stokes backreflected power initiated by thermal phonons, compare
 values of the SBST calculated from different approximations, and discuss the SBST
 dependence on the fiber length. We also review an analytical approach to calculate
 the gain of Brillouin fiber amplifiers (BFAs) in the regime of pump depletion. In the
 high-gain regime, fiber loss is a nonnegligible effect and needs to be accounted for
 along with the pump depletion. We provide an accurate analytic expression for the BFA
 gain and show results of experimental validation. Finally, we review methods to
 suppress SBS including index-controlled acoustic guiding or segmented fiber links.
 The second part of the review deals with recent advances in fiber-optic applications
 where SBS is a relevant effect. In particular, we discuss the impact of SBS on the
 radio-over-fiber technology, enhancement of the SBS efficiency in Raman-pumped
 fibers, slow light due to SBS and SBS-based optical delay lines, Brillouin
 fiber-optic sensors, and SBS mitigation in high-power fiber lasers, as well as SBS in
 multimode and microstructured fibers. A detailed derivation of evolutional equations
 in the guided wave geometry as well as key physical relations are given in
 appendices.

Stimulated Brillouin scattering in optical fibers

Control over the dispersion of the refractive index is essential to the performance of most modern optical systems. These range from laboratory microscopes to optical fibres and even consumer products, such as photography cameras. Conventional methods of engineering optical dispersion are based on altering material composition, but this process is time-consuming and difficult, and the resulting optical performance is often limited to a certain bandwidth. Recent advances in nanofabrication have led to high-quality metasurfaces with the potential to perform at a level comparable to their state-of-the-art refractive counterparts. In this Review, we introduce the underlying physical principles of metasurface optical elements (with a focus on metalenses) and, drawing on various works in the literature, discuss how their constituent nanostructures can be designed with a highly customizable effective index of refraction that incorporates both phase and dispersion engineering. These metasurfaces can serve as an essential component for achromatic optics with unprecedented levels of performance across a broad bandwidth or provide highly customized, engineered chromatic behaviour in instruments such as miniature aberration-corrected spectrometers. We identify some key areas in which these achromatic or dispersion-engineered metasurface optical elements could be useful and highlight some future challenges, as well as promising ways to overcome them. Flat metasurface optics provides an emerging platform for combining semiconductor foundry methods of manufacturing and assembling with nanophotonics to produce high-end and multifunctional optical elements. This Review highlights the design of metasurfaces, recent advances in the field and initial promising applications.

Flat optics with dispersion-engineered metasurfaces

We show, using simulations, that a combination of orthogonal frequency division multiplexing (OFDM) and optical single sideband modulation can be used to compensate for chromatic dispersion in ultralong-haul wavelength-division multiplexed (WDM) systems. OFDM provides a high spectral efficiency, does not require a reverse feedback path for compensation, and has a better sensitivity than nonreturn to zero. This paper provides design rules for 800-4000-km optical-OFDM systems. The effects of WDM channel number and spacing, fiber dispersion, and input power per channel on the received Q are studied using extensive numerical simulations. These effects are summarized as a set of design rules

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Performance of Optical OFDM in Ultralong-Haul WDM Lightwave Systems

Dispersion Compensating Fibers

This paper reviews properties and use of conventional single-mode dispersion-compensating fibers (DCFs). The quality of the dispersion compensation expressed as residual dispersion after compensation is treated. Properties of actual DCFs for discrete compensation including loss and nonlinear effects are discussed. Fiber design with special emphasis on design tradeoffs is considered. The Raman properties of DCFs and their use as a discrete Raman amplifier are also discussed. Finally, DCF for use in dispersion-managed cables (DMCs) is addressed, including optimum fiber design and comparison of different configurations.

Dispersion-compensating fibers

The negative dispersion slope of dispersion-compensating fibers has been optimized by increasing the width of the depressed cladding. Simultaneous compensation and dispersion slope has been demonstrated on an actual link.

Design and manufacture of dispersion compensating fibre for simultaneous compensation of dispersion and dispersion slope

A new dispersion compensating fiber with extremely high negative dispersion slope is reported. Low insertion loss between 1530 and 1610 nm is demonstrated using a new splice technique.

New dispersion compensating fibres for simultaneous compensation of dispersion and dispersion slope of non-zero dispersion shifted fibres in the C or L band

Summary form only given. We report results of large volume production of more than 10000 km of dispersion-compensating fibers (DCF). This is equivalent to more than 1000 modules, which each can compensate 60 km of standard fiber. Reproducible large volume production of DCF is a difficult task. The design is very sensitive towards small variations in the index profile. For example, we find for our design that a 1% variation of either the core diameter or core index results in a change in dispersion of 5 and 2.5% respectively. Another challenge is to obtain low polarization-mode dispersion (PMD). DCF is more than one order of magnitude more sensitive to core ovalities than conventional telecommunication fibers due to the high core index used. Therefore extreme care has been taken to avoid core ovalities. At the same time we stimulate the mode coupling by introducing oscillatory twist into the fiber during draw. Enhanced mode coupling not only reduces the PMD, but also gives a more stable PMD value, for example during temperature cycling of DCF modules.

B. Edvold

Papers

Dispersion Compensating Fibers

Dispersion-compensating fibers

Design and manufacture of dispersion compensating fibre for simultaneous compensation of dispersion and dispersion slope

New dispersion compensating fibres for simultaneous compensation of dispersion and dispersion slope of non-zero dispersion shifted fibres in the C or L band

Large volume manufacturing of dispersion compensating fibers