N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

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

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

Real and Complex Analysis

Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

We present a novel comprehensive theory for the pump-to-probe interactions caused by the stimulated Raman scattering (SRS) in glass optical fibers. The developed theory applies to both the Raman gain with the undepleted pump assumption, and to the maximum loss induced by the Raman crosstalk (RXT loss). The latter is an effect that is the limiting propagation impairment in passive optical networks (PON). The main novelty of the paper is a rigorous mathematical analysis, describing the interaction of SRS with the polarization evolution due to polarization mode dispersion (PMD). The Raman gain (or the RXT loss) is modeled as a random process for which a comprehensive theory is developed, giving for the first time to our best knowledge, an exact closed-form expression for the mean and variance of the gain (or depletion), and a computationally efficient algorithm to numerically derive the gain probability density function. The developed theory is validated by the comparison with Monte Carlo analyses, based on the waveplate model for the optical fiber. The validation showed excellent agreement, confirming the validity of the developed theory. As an example of application, we used our theoretical results to analyze next-generation PON (NG-PON2) architectures, confirming that, in this scenario, RXT loss may be a limiting propagation effect.

/pdf/polarization-related-statistics-of-raman-crosstalk-in-single-1pmy78mef4.pdf

Polarization-Related Statistics of Raman Crosstalk in Single-Mode Optical Fibers

We measure the impulse response of cabled coupled- and uncoupled multi-core fibers over 100 nm in the C- and L-band. Our results provide insights to the properties of deployed SDM fibers for usage in applications such as transmission and distributed sensing.

Transfer Matrix Characterization of Field-Deployed MCFs

We generalize the concept of degree of polarization of single-mode fields to multi-mode fields by introducing a new parameter that we define degree of mutual coherence. The new definition enables characterizing by a single parameter the quality of the signal corrupted by various linear and nonlinear impairments at the output of an optical transmission system employing spatial division multiplexing. We propose two workable schemes based on standard optics to measure the degree of coherence, one valid for generic fields, another applying only to CW fields affected by ASE noise. We apply the notion of degree of mutual coherence to the characterization of the nonlinear mode coupling caused by two-pulse collisions in spatially multiplexed WDM systems. We show that a collision between pulses transmitted in different WDM channels produces nonlinear power transfer between degenerate spatial modes belonging to the same channel. Finally, we quantify the effect of multiple collisions in terms of reduction of the degree of mutual coherence under the assumption that uncorrelated messages are transmitted over different WDM channels.

Degree of Coherence in Space-Division Multiplexed Transmission

The adiabatic elimination of the polarization dynamics often invoked in treatments of pulse propagational and pulse interactions in semiconductor optical waveguides is critically investigated. By employing a systematic expansion of the polarization equation and staying within a third-order [(chi) (3 )] regime we are able to derive explicit corrections to the response function due to non-adiabatic effects. Several such effects are identified and analyzed. This provides a unified view of different results reported previously in the literature, but also identifies a new effect which apparently hasn't been analyzed so far. The effect relates to virtual excitation of the total carrier density, as opposed to the well-known adiabatic following effect of individual two-level systems, and we derive simple analytical expressions that relate this effect to the gain and index dispersion. We find it to give a sizable contribution to the well-known instantaneous effects of two-photon absorption and Kerr nonlinearity.

Non-adiabatic effects in semiconductor waveguides

We model the build-up of inter-channel nonlinear interference noise (NLIN) in wavelength division multiplexed systems by considering the pulse collision dynamics in the time domain. The fundamental interactions can be classified as two-pulse, three-pulse, or four-pulse collisions and they can be either complete, or incomplete. Each type of collision is shown to have its unique signature and the overall nature of NLIN is determined by the relative importance of the various classes of pulse collisions in a given WDM system. The pulse-collision picture provides qualitative and quantitative insight into the character of NLIN, offering a simple and intuitive explanation to all of the reported and previously unexplained phenomena. In particular, we show that the most important contributions to NLIN follow from two-pulse and four-pulse collisions. While the contribution of two-pulse collisions is in the form of phase-noise and polarization-state-rotation with strong dependence on modulation format, four-pulse collisions generate complex circular noise whose variance is independent of modulation format. In addition, two-pulse collisions are strongest when the collision is complete, whereas four-pulse collisions are strongest when the collision is incomplete. We show that two-pulse collisions dominate the formation of NLIN in short links with lumped amplification, or in links with distributed amplification extending over arbitrary length. In long links using lumped amplification the relative significance of four-pulse collisions increases, emphasizing the circularity of the NLIN while reducing its dependence on modulation format.

Antonio Mecozzi

Papers

Polarization-Related Statistics of Raman Crosstalk in Single-Mode Optical Fibers

Transfer Matrix Characterization of Field-Deployed MCFs

Degree of Coherence in Space-Division Multiplexed Transmission

Non-adiabatic effects in semiconductor waveguides

Pulse collision picture of inter-channel nonlinear interference noise in fiber-optic communications