This book offers a comprehensive review of the state-of-the-art theoretical and experimental advances in linear and nonlinear parity-time-symmetric systems in various physical disciplines, and surveys the emerging applications of parity-time (PT) symmetry. PT symmetry originates from quantum mechanics, where if the Schrodinger operator satisfies the PT symmetry, then its spectrum can be all real. This concept was later introduced into optics, Bose-Einstein condensates, metamaterials, electric circuits, acoustics, mechanical systems and many other fields, where a judicious balancing of gain and loss constitutes a PT-symmetric system. Even though these systems are dissipative, they exhibit many signature properties of conservative systems, which make them mathematically and physically intriguing. Important PT-symmetry applications have also emerged. This book describes the latest advances of PT symmetry in a wide range of physical areas, with contributions from the leading experts. It is intended for researchers and graduate students to enter this research frontier, or use it as a reference book.

'The text is easy to read because the matter is clearly explained. Symmetries are a central component of physical laws, and the PT-symmetry proves to be very interesting and fruitful. The discussion of the matter is up-to-date and self-contained. The book is recommended to students of higher courses, PhD and researchers. It is also a basic read to those who wish to have an insight into this field.'Contemporary PhysicsOriginated by the author in 1998, the field of PT (parity-time) symmetry has become an extremely active and exciting area of research. PT-symmetric quantum and classical systems have theoretical, experimental, and commercial applications, and have been the subject of many journal articles, PhD theses, conferences, and symposia. Carl Bender's work has influenced major advances in physics and generations of students.This book is an accessible entry point to PT symmetry, ideal for students and scientists looking to begin their own research projects in this field.

This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.

To make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.

Artificial materials have been widely studied and used in photonics and microwaves in the last few decades. Recent research has proven that the introduction of specific higher symmetries in each cell of a periodic medium is an effective approach to obtain unprecedented exotic behaviors and to overcome the current limitations of these devices. For example, simple symmetries of a purely spatial type (glide or twist transformations) can have a huge impact on the properties of the resulting materials, thus defining wideband behaviors for flat lenses or large stop bands for novel EBG materials. This Special Issue opens with a novel discussion on the effect of time-reversal symmetries in antenna theory and presents new structures exploiting symmetries for antenna and microwave components, such as flat lenses, helix antennas, and gap-waveguides. Finally, new modeling methods are discussed for the study of wave propagation along glide surfaces and twist lines.

Metamaterials—artificially structured materials with engineered electromagnetic properties—have enabled unprecedented flexibility in manipulating electromagnetic waves and producing new functionalities. This book details recent advances in the study of optical metamaterials, ranging from fundamental aspects to up-to-date implementations, in one unified treatment. Important recent developments and applications such as superlens and cloaking devices are also treated in detail and made understandable. The planned monograph can serve as a very timely book for both newcomers and advanced researchers in this extremely rapid evolving field.

All-Dielectric Nanophotonics aims to review the underlying principles, advances and future directions of research in the field. The book reviews progress in all-dielectric metasurfaces and nanoantennas, new types of excitations, such as magnetic and toroidal modes and associated anapole states. Ultrahigh-Q resonant modes such as bound states in the continuum are covered and the promise of replacing conventional bulky optical elements with nanometer-scale structures with enhanced functionality is discussed. This book is suitable for new entrants to the field as an overview of this research area. Experienced researchers and professionals in the field may also find this book suitable as a reference. - Provides an overview of the fundamental principles, theories and calculation techniques underpinning all-dielectric nanophotonics research - Reviews current progress in the field, such as all-dielectric metasurfaces and nanoantennas, new types of excitations, associated anapole states, and more - Discusses emerging applications such as active nanophotonics with in-depth analysis

Edited and authored by leading experts from top institutions in Europe, the US and Asia, this comprehensive overview of micro- and nanophotonics covers the physical and chemical fundamentals, while clearly focusing on the technologies and applications in industrial R&D. As such, the book reports on the four main areas of telecommunications and display technologies; light conversion and energy generation; light-based fabrication of materials; and micro- and nanophotonic devices in metrology and control.

This book discusses the development of Fano-based techniques and reveals the characteristic properties of various wave processes by studying interference phenomena. It explains that the interaction of discrete (localized) states with a continuum of propagation modes leads to Fano interference effects in transmission, and explores novel coherent effects such as bound states in the continuum accompanied by collapse of Fano resonance. Originating in atomic physics, Fano resonances have become one of the most appealing phenomena of wave scattering in optics, microwaves, and terahertz techniques. The generation of extremely strong and confined fields at a deep subwavelength scale, far beyond the diffraction limit, plays a central role in modern plasmonics, magnonics, and in photonic and metamaterial structures. Fano resonance effects take advantage of the coupling of these bound states with a continuum of radiative electromagnetic waves. With their unique physical properties and unusual combination of classical and quantum structures, Fano resonances have an application potential in a wide range of fields, from telecommunication to ultrasensitive biosensing, medical instrumentation and data storage. Including contributions by international experts and covering the essential aspects of Fano-resonance effects, including theory, modeling and design, proven and potential applications in practical devices, fabrication, characterization and measurement, this book enables readers to acquire the multifaceted understanding required for these multidisciplinary challenges.

Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-oscillating systems. This book discusses as well the discontinuous self-oscillations of a symmetrical multi-vibrator neglecting anode reaction. The final chapter deals with the immense practical importance of the stability of physical systems containing energy sources particularly control systems. This book is a valuable resource for electrical engineers, scientists, physicists, and mathematicians.