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

The silicon chip has been the mainstay of the electronics industry for the last 40 years and has revolutionized the way the world operates. Today, a silicon chip the size of a fingernail contains nearly 1 billion transistors and has the computing power that only a decade ago would take up an entire room of servers. As the relentless pursuit of Moore's law continues, and Internet-based communication continues to grow, the bandwidth demands needed to feed these devices will continue to increase and push the limits of copper-based signaling technologies. These signaling limitations will necessitate optical-based solutions. However, any optical solution must be based on low-cost technologies if it is to be applied to the mass market. Silicon photonics, mainly based on SOI technology, has recently attracted a great deal of attention. Recent advances and breakthroughs in silicon photonic device performance have shown that silicon can be considered a material onto which one can build optical devices. While significant efforts are needed to improve device performance and commercialize these technologies, progress is moving at a rapid rate. More research in the area of integration, both photonic and electronic, is needed. The future is looking bright. Silicon photonics could provide low-cost opto-electronic solutions for applications ranging from telecommunications down to chip-to-chip interconnects, as well as emerging areas such as optical sensing technology and biomedical applications. The ability to utilize existing CMOS infrastructure and manufacture these silicon photonic devices in the same facilities that today produce electronics could enable low-cost optical devices, and in the future, revolutionize optical communications

http://ieeexplore.ieee.org/iel5/6668/34347/01638290.pdf

Silicon photonics

The very broad bandwidth of low-loss optical transmission in a single-mode fiber and the recent improvements in single-frequency tunable lasers have stimulated significant advances in dense wavelength division multiplexed optical networks This technology, including wavelength-sensitive optical switching and routing elements and passive optical elements, has made it possible to consider the use of wavelength as another dimension, in addition to time and space, in network and switch design The independence of optical signals at different wavelengths makes this a natural choice for multiple-access networks, for applications which benefit from shared transmission media, and for networks in which very large throughputs are required Recent progress in multiwavelength networks are reviewed, some of the limitations which affect the performance of such networks are discussed, and examples of several network and switch proposals based on these ideas are presented Discussed also are critical technologies that are essential to progress in this field >

Dense wavelength division multiplexing networks: principles and applications

BACKGROUND Singularities are critical points for which the behavior of a mathematical model governing a physical system is of a fundamentally different nature compared to the neighboring points. Exceptional points are spectral singularities in the parameter space of a system in which two or more eigenvalues, and their corresponding eigenvectors, simultaneously coalesce. Such degeneracies are peculiar features of nonconservative systems that exchange energy with their surrounding environment. In the past two decades, there has been a growing interest in investigating such nonconservative systems, particularly in connection with the quantum mechanics notions of parity-time symmetry, after the realization that some non-Hermitian Hamiltonians exhibit entirely real spectra. Lately, non-Hermitian systems have raised considerable attention in photonics, given that optical gain and loss can be integrated as nonconservative ingredients to create artificial materials and structures with altogether new optical properties. ADVANCES As we introduce gain and loss in a nanophotonic system, the emergence of exceptional point singularities dramatically alters the overall response, leading to a range of exotic functionalities associated with abrupt phase transitions in the eigenvalue spectrum. Even though such a peculiar effect has been known theoretically for several years, its controllable realization has not been made possible until recently and with advances in exploiting gain and loss in guided-wave photonic systems. As shown in a range of recent theoretical and experimental works, this property creates opportunities for ultrasensitive measurements and for manipulating the modal content of multimode lasers. In addition, adiabatic parametric evolution around exceptional points provides interesting schemes for topological energy transfer and designing mode and polarization converters in photonics. Lately, non-Hermitian degeneracies have also been exploited for the design of laser systems, new nonlinear optics phenomena, and exotic scattering features in open systems. OUTLOOK Thus far, non-Hermitian systems have been largely disregarded owing to the dominance of the Hermitian theories in most areas of physics. Recent advances in the theory of non-Hermitian systems in connection with exceptional point singularities has revolutionized our understanding of such complex systems. In the context of optics and photonics, in particular, this topic is highly important because of the ubiquity of nonconservative elements of gain and loss. In this regard, the theoretical developments in the field of non-Hermitian physics have allowed us to revisit some of the well-established platforms with a new angle of utilizing gain and loss as new degrees of freedom, in stark contrast with the traditional approach of avoiding these elements. On the experimental front, progress in fabrication technologies has allowed for harnessing gain and loss in chip-scale photonic systems. These theoretical and experimental developments have put forward new schemes for controlling the functionality of micro- and nanophotonic devices. This is mainly based on the anomalous parameter dependence in the response of non-Hermitian systems when operating around exceptional point singularities. Such effects can have important ramifications in controlling light in new nanophotonic device designs, which are fundamentally based on engineering the interplay of coupling and dissipation and amplification mechanisms in multimode systems. Potential applications of such designs reside in coupled-cavity laser sources with better coherence properties, coupled nonlinear resonators with engineered dispersion, compact polarization and spatial mode converters, and highly efficient reconfigurable diffraction surfaces. In addition, the notion of the exceptional point provides opportunities to take advantage of the inevitable dissipation in environments such as plasmonic and semiconductor materials, which play a key role in optoelectronics. Finally, emerging platforms such as optomechanical cavities provide opportunities to investigate exceptional points and their associated phenomena in multiphysics systems.

Exceptional points in optics and photonics.

Amplification of ultrashort optical pulses in semiconductor laser amplifiers is shown to result in considerable spectral broadening and distortion as a result of the nonlinear phenomenon of self-phase modulation (SPM). The physical mechanism behind SPM is gain saturation, which leads to intensity-dependent changes in the refractive index in response to variations in the carrier density. The effect of the shape and the initial frequency chirp of input pulses on the shape and the spectrum of amplified pulses is discussed in detail. Particular attention is paid to the case in which the input pulsewidth is comparable to the carrier lifetime so that the saturated gain has time to recover partially before the trailing edge of the pulse arrives. The experimental results, performed by using picosecond input pulses from a 1.52- mu m mode-locked semiconductor laser, are in agreement with the theory. When the amplified pulse is passed through a fiber, it is initially compressed because of the frequency chirp imposed on it by the amplifier. This feature can be used to compensate for fiber dispersion in optical communication systems. >

Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers

Fiber-optic communication systems using semiconductor laser amplifiers are investigated theoretically and experimentally. The noise and bit-error-rate characteristics of lightwave systems with optical amplifiers are calculated and the dependence of system performance on amplifier characteristics such as optical bandwidth, noise figure, gain, etc., is shown. Experimental results for both a 4-Gb/s optical preamplifier as well as coherent and direct detection systems with four inline amplifiers are presented. >

Lightwave systems with optical amplifiers

We report a new mechanism of direct frequency modulation, the cavity‐mode enhanced frequency modulation (CME‐FM), using the newly developed cleaved‐coupled‐cavity (C3) semiconductor laser. In this operation, one of the diode of the C3 laser was operated as a laser, while the other diode was operated as a frequency modulator. It was shown that a very large frequency excursion of 150 A and frequency tuning rate of 10 A/mA have been obtained with a C3 GaInAsP crescent laser operating at 1.3 μm. Time‐resolved spectral and spectral‐resolved pulse response measurements also showed that such C3 lasers operated in highly stable single‐longitudinal mode at all times even under high‐speed direct frequency modulation. In addition to the important application as the optical source in FM optical communication systems, the present CME‐FM C3 laser can also be used as the optical source in wavelength‐division multiplexing systems. Further, it opens the possibility of ultrahigh capacity multilevel optical FM information t...

High‐speed direct single‐frequency modulation with large tuning rate and frequency excursion in cleaved‐coupled‐cavity semiconductor lasers

Vertical-cavity electrically pumped surface-emitting microlasers
are formed on GaAs substrates at densities greater than two million per
square centimeter. Two wafers were grown with ln0.2Ga0.8As active material
composing three 80 ? thick quantum wells in one and a single
quantum well (SQW) 100 ? thick in the other. Lasing was seen in devices
as small as 1 .5 ?m diameter with <0.05 ?m3 active material. SQW microlasers
5 x 5 ?m square had room-temperature cw current thresholds as
low as 1.5 mA with 983 nm output wavelength. 10 x 10 ?m square SQW
microlasers were modulated by a pseudorandom bit generator at 1 Gb/s
with less than 10-10 bit error rate. Pulsed output >170 mW was obtained
from a 100?m square device. The laser output passes through the nominally
transparent substrate and out its back side, a configuration well
suited for micro-optic integration and photonic switching and interchip
connections.

/pdf/surface-emitting-microlasers-for-photonic-switching-and-n9rwu431bg.pdf

Surface-Emitting Microlasers for Photonic Switching and Interchip Connections

An analysis and the device performance of an integrated optical 4-channel multi/demultiplexer based on Mach-Zehnder interferometers elements are presented. The channel spacing is 77 AA. Single-mode channel waveguides are made from P-doped SiO/sub 2/ core layers. Waveguide losses as low as 0.05 dB/cm and fiber-to-waveguide butt coupling as low as 0.5 dB for lambda =1.5 mu m have been obtained. The multiplexer transfers power from four input channels into a common output channel with an average fiber-to-fiber loss of 2.6 dB per channel. The average crosstalk of the demultiplexer is -16 dB. >

N.A. Olsson

Papers

Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers

Lightwave systems with optical amplifiers

High‐speed direct single‐frequency modulation with large tuning rate and frequency excursion in cleaved‐coupled‐cavity semiconductor lasers

Surface-Emitting Microlasers for Photonic Switching and Interchip Connections

Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO/sub 2/ waveguides on Si