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

Differential-phase-shift keying (DPSK) has recently been used to reach record distances in long-haul lightwave communication systems. This paper will review theoretical, as well as implementation, aspects of DPSK, and discuss experimental results.

Optical phase-shift-keyed transmission

An applications-oriented review of optical parametric amplifiers in fiber communications is presented. The emphasis is on parametric amplifiers in general and single pumped parametric amplifiers in particular. While a theoretical framework based on highly efficient four-photon mixing is provided, the focus is on the intriguing applications enabled by the parametric gain, such as all-optical signal sampling, time-demultiplexing, pulse generation, and wavelength conversion. As these amplifiers offer high gain and low noise at arbitrary wavelengths with proper fiber design and pump wavelength allocation, they are also candidate enablers to increase overall wavelength-division-multiplexing system capacities similar to the more well-known Raman amplifiers. Similarities and distinctions between Raman and parametric amplifiers are also addressed. Since the first fiber-based parametric amplifier experiments providing net continuous-wave gain in the for the optical fiber communication applications interesting 1.5-/spl mu/m region were only conducted about two years ago, there is reason to believe that substantial progress may be made in the future, perhaps involving "holey fibers" to further enhance the nonlinearity and thus the gain. This together with the emergence of practical and inexpensive high-power pump lasers may in many cases prove fiber-based parametric amplifiers to be a desired implementation in optical communication systems.

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Fiber-based optical parametric amplifiers and their applications

We analyze the scalability of diffraction-limited fiber lasers considering thermal, non-linear, damage and pump coupling limits as well as fiber mode field diameter (MFD) restrictions. We derive new general relationships based upon practical considerations. Our analysis shows that if the fiber's MFD could be increased arbitrarily, 36 kW of power could be obtained with diffraction-limited quality from a fiber laser or amplifier. This power limit is determined by thermal and non-linear limits that combine to prevent further power scaling, irrespective of increases in mode size. However, limits to the scaling of the MFD may restrict fiber lasers to lower output powers.

Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power

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

Dispersion Compensating Fibers

We evaluate numerically and experimentally the stimulated Brillouin scattering (SBS) threshold increase for a short, highly nonlinear GeO/sub 2/-doped fiber by applying different temperature distributions along the fiber. The temperature coefficient for the Brillouin frequency downshift is measured to 1.2 MHz//spl deg/C. A threefold SBS threshold increase is obtained for a 100-m long highly nonlinear fiber with a 140/spl deg/C temperature gradient. The proposed scheme is implemented in a wavelength converter based on fiber optical four-wave mixing (FWM). The SBS suppression scheme shows negligible influence on the FWM efficiency as well as the wavelength conversion bandwidth. The temperature coefficient for the zero dispersion wavelength is measured to 0.062 nm//spl deg/C.

Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution

In this letter, we report on up to 300-Gb/s real-time all-fiber-based optical eye-diagram measurements with 1.6-ps temporal resolution and 5-Hz refresh rate by all-optical sampling using parametric amplification in a short (50 m) highly nonlinear fiber. This represents, to the best of our knowledge, the highest bit-rate eye-diagram measurement so far, as well as the first demonstration of a fiber-based eye analyzer. The sensitivity and operational optical bandwidth is comparable to previously reported state-of-the-art nonlinear crystal-based sampling systems. We believe our results show that fiber-based optical sampling is indeed a potential candidate for characterization of future ultrahigh bit-rate optical communication systems.

300-Gb/s eye-diagram measurement by optical sampling using fiber-based parametric amplification

A transparent continuous wave-pumped highly nonlinear fibre wavelength converter (WC) with a conversion bandwidth of 61 nm and a pump wavelength tuning range of 24 nm, the largest ever reported for fibre-based WCs, is demonstrated. The conversion quality is confirmed by bit error rate measurements showing < 1.4 dB power penalty at 10 Gbit/s data transmission.

Transparent wavelength conversion in fibre with 24 nm pump tuning range

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.

S.N. Knudsen

Papers

Dispersion Compensating Fibers

Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution

300-Gb/s eye-diagram measurement by optical sampling using fiber-based parametric amplification

Transparent wavelength conversion in fibre with 24 nm pump tuning range

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