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 show that the interplay between spatial mode dispersion (SMD) and the modulation format has a substantial impact on cross-phase modulation (XPM) in space-division multiplexed systems with strongly coupled modes. We propose a simple formula to account for SMD in the modulation-format-dependent XPM contribution.

Modulation-Format Dependent Impact of Modal Dispersion on Cross-Phase Modulation in SDM Transmission

We present a unified model for modal dispersion and mode-dependent loss in fibers for space-division multiplexed transmission. The proposed model, based on a generalized Stokes-space representation of multi-modal fields, is validated by comparison with experimental data.

Generalized Stokes-space analysis of modal dispersion in fibers for space-division multiplexing with mode-dependent loss

The oceans present a major gap in geophysical instrumentation, hindering fundamental research on submarine earthquakes and the Earth&#8217;s interior structure, as well as effective earthquake and tsunami warning for offshore events. Emerging fiber-optic sensing technologies that can leverage submarine telecommunication cables present an new opportunity in filling the data gap. Marra et al. (2018) turned a 96 km long submarine cable into a sensitive seismic sensor using ultra-stable laser interferometry of a round-tripped signal. Another technology, Distributed Acoustic Sensing (DAS), interrogates intrinsic Rayleigh backscattering and converts tens of kilometers of dedicated fiber into thousands of seismic strainmeters on the seafloor (e.g., Lindsey et al., 2019; Sladen et al., 2019; Williams et al., 2019; Spica et al., 2020). Zhan et al. (2021) successfully sensed seismic and water waves over a 10,000 km long submarine cable connecting Los Angeles and Valparaiso, by monitoring the polarization of regular optical telecommunication channels. However, these new technologies have substantially different levels of sensitivity, coverage, spatial resolution, and scalability. In this talk, we advocate that strategic combinations of the different sensing techniques (including conventional geophysical networks) are necessary to provide the broadest coverage of the seafloor while making high-fidelity, physically interpretable measurements. Strategic collaborations between the geophysics community and telecommunication community without burdening the telecomm operation (e.g., by multiplexing or using regular telecom signals) will be critical to the long term success.&#160;Marra, G., C. Clivati, R. Luckett, A. Tampellini, J. Kronj&#228;ger, L. Wright, A. Mura, F. Levi, S. Robinson, A. Xuereb, B. Baptie, D. Calonico, 2018. Ultrastable laser interferometry for earthquake detection with terrestrial and submarine cables. Science, eaat4458.Lindsey, N.J., T. C. Dawe, J. B. Ajo-Franklin, 2019. Illuminating seafloor faults and ocean dynamics with dark fiber distributed acoustic sensing. Science. 366, 1103&#8211;1107.Sladen, A., D. Rivet, J. P. Ampuero, L. De Barros, Y. Hello, G. Calbris, P. Lamare, 2019. Distributed sensing of earthquakes and ocean-solid Earth interactions on seafloor telecom cables. Nat Commun. 10, 5777.Spica, Z.J., Nishida, K., Akuhara, T., P&#233;tr&#233;lis, F., Shinohara, M. and Yamada, T., 2020. Marine Sediment Characterized by Ocean&#8208;Bottom Fiber&#8208;Optic Seismology. Geophysical Research Letters, 47(16), p.e2020GL088360.Williams, E.F., M. R. Fern&#225;ndez-Ruiz, R. Magalhaes, R. Vanthillo, Z. Zhan, M. Gonz&#225;lez-Herr&#225;ez, H. F. Martins, 2019. Distributed sensing of microseisms and teleseisms with submarine dark fibers. Nat Commun. 10, 5778.Zhan, Z., M. Cantono, V. Kamalov, A. Mecozzi, R. Muller, S. Yin, J.C. Castellanos, 2021. Optical polarization-based seismic and water wave sensing on transoceanic cables. Science, in press.

Towards multi-method geophysical sensing on submarine cables

We report transmission results in cabled coupled-core multicore fibers (CC-MCFs), investigated by using off-line digital signal processing techniques and long term real-time measurements in an urban environment. The results confirm that transmission over coupled-core multicore fibers is a technically viable approach.

Transmission over Coupled-Core Multicore Fibers

We consider a line with noise in the simplest case. Loss does not add noise. Amplification via phase insensitive amplifiers do add noise. A lower bound of this capacity is the quantum analog to the Shannon capacity of a linear channel with additive white Gaussian noise, namely the difference of the Von Neumann entropy of the signal plus noise at the output of the line and the entropy of the noise alone. We show that this expression is indeed the capacity for the case of an amplifier with infinitesimal gain $G = 1+\epsilon$, and for a cascade of an amplifier with arbitrary gain and a large loss, such that the overall gain of the cascade is infinitesimal.

Antonio Mecozzi

Papers

Modulation-Format Dependent Impact of Modal Dispersion on Cross-Phase Modulation in SDM Transmission

Generalized Stokes-space analysis of modal dispersion in fibers for space-division multiplexing with mode-dependent loss

Towards multi-method geophysical sensing on submarine cables

Transmission over Coupled-Core Multicore Fibers

Classical capacity of the noisy bosonic channel and the bosonic minimum output entropy conjecture