There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Exploiting the interplay between gain, loss and the coupling strength between different optical components creates a variety of new opportunities in photonics to generate, control and transmit light. Inspired by the discovery of real eigenfrequencies for non-Hermitian Hamiltonians obeying parity–time (PT) symmetry, many counterintuitive aspects are being explored, particularly close to the associated degeneracies also known as ‘exceptional points’. This Review explains the underlying physical principles and discusses the progress in the experimental investigation of PT-symmetric photonic systems. We highlight the role of PT symmetry and non-Hermitian dynamics for synthesizing and controlling the flow of light in optical structures and provide a roadmap for future studies and potential applications. This Review discusses recent developments in the area of non-Hermitian physics, and more specifically the special case of non-Hermitian optical systems with parity–time symmetry.

Parity-time symmetry and exceptional points in photonics.

The increasing capability for manufacturing a wide variety of optoelectronic devices from polymer and polymer–silicon hybrids, including transmission fibre, modulators, detectors and light sources, suggests that organic photonics has a promising future in communications and other applications.

Organic photonics for communications

Polarization-maintaining fibers and their applications are reviewed. The classification of high-birefringent fibers and low-birefringent fibers and their fabrication methods and characteristics are discussed in Section II. Analytical methods and numerical methods for fiber design on the birefringence are presented in Section III. Degradation factors of polarization maintenance expressed as crosstalk or mode-coupling parameters caused by internal origins such as structural imperfections, wavelength, and nonlinear effects, and by external origins such as temperature fluctuations, mechanical perturbations, and electromagnetic effects, are discussed in Section IV. Characterization methods on beat length, mode coupling, stress distribution, and mechanical strength are presented in Section V. Applications to the fiber devices and nonlinear effects, and splicing methods for the polarization-maintaining fibers are described in Sections VI and VII.

Polarization-maintaining fibers and their applications

A Bragg grating in a single-mode polymer optical fiber (POF) has been created. The novel grating has a length of 1 cm with a reflectivity of 80% and a linewidth of about 0.5 nm. The wavelength tunability of the POF grating by stretching was investigated and a wavelength tunable range of 20 nm has been achieved. Based on the properties of the polymer, we believe that this kind of grating has a wavelength tuning potential of more than 100 nm.

Highly tunable Bragg gratings in single-mode polymer optical fibers

Photosensitivity and Gratings in Dye-Doped Polymer Optical Fibers

Static soliton states in twin-core nonlinear optical fibers are examined using an improved variational approximation: the soliton's width is an additional varying parameter, together with the ratio of the energies in, and the phase difference between, the two cores. For the symmetric coupler, results agree well with numerical ones; in particular, the bifurcation between symmetric and asymmetric solitons is shown to be slightly subcritical. For the asymmetric coupler, the control parameters are the difference between the cores' dispersion coefficients and the phase velocity mismatch. Soliton states in the asymmetric coupler show a strong and easily controlled bistability. The soliton exists for some energies even when one of the cores has normal dispersion. \textcopyright{} 1996 The American Physical Society.

Symmetric and asymmetric solitons in twin-core nonlinear optical fibers.

The propagation and the switching of solitons in nonlinear optical fiber couplers have been investigated with a variational method within the framework of the Lagrangian density formulation. Simple analytical solutions have been found to the coupled nonlinear Schrodinger equations that govern the soliton propagation in a nonlinear fiber coupler. It is shown that the soliton propagation and switching behavior predicted by the present analytical method agrees well with results from numerical analysis. In particular, we found that the present analysis is accurate in predicting soliton switching from one core to the other. In addition, our analysis leads us to the discovery of new soliton eigenstates and to the determination of the bifurcation behavior of solitons in nonlinear fiber couplers.

Soliton switching and propagation in nonlinear fiber couplers: analytical results

A method of measuring the stresses, residual or applied, in an optical fiber or preform is presented. It is shown that the stress profiles can be obtained from the Abel transform of the derivative of the retardation. The axial stress profile is shown to bear the same shape as the refractive-index profile. Measurement results indicate that the applied tension during the fiber drawing process is frozen into the fiber, consequently affecting the intrinsic strength of the fiber. The method of estimating the fiber drawing tension from the fiber stress profile is also given.

Pak Lim Chu

Papers

Highly tunable Bragg gratings in single-mode polymer optical fibers

Photosensitivity and Gratings in Dye-Doped Polymer Optical Fibers

Symmetric and asymmetric solitons in twin-core nonlinear optical fibers.

Soliton switching and propagation in nonlinear fiber couplers: analytical results

Measurement of stresses in optical fiber and preform