This book is devoted to the investigations of non-stationary electromagnetic processes. The investigations are undertaken analytically mainly using the Volterra integral equations approach. The book contains a systematic statement of this approach for the investigations of electrodynamics phenomena in the time domain and new results and applications in microwave techniques and photonics. Particular consideration is given to electromagnetic transients in time-varying media and their potential applications. The approach is formulated and electromagnetic phenomena are investigated in detail for a hollow metal waveguide, which contains moving dielectric or plasma-bounded medium, and dielectric waveguides with time-varying medium inside a core.
Table of Contents
Basic Relations for an Electromagnetic Field in a Medium with Time-Varying Parameters and/or Moving Boundaries. Generalized Wave Equation for an Electromagnetic Field in a Time-Varying Medium. Fundamental Solutions to Maxwell’s Equations (Green’s Functions). Causal Time-Spatial Interpretation of Electromagnetic Field Interaction with Time-Varying Objects. The Resolvent Method for Solving the Integral Equation. Transformation of an Electromagnetic Field in an Unbounded Medium with Time-Varying Parameters. Transformation of an Electromagnetic Wave in a Non-Dispersive Time-Varying Medium. Evolution of a Harmonic Wave in a Medium Modulated by Repetitive Identical Pulses. Wave Chaotic Behavior Generated by Linear Time-Varying Systems. Electromagnetic Wave in Isotropic Plasma with Step-Wise Change of Plasma Density. Plane Wave in Gyrotropic Plasma with “Switching On” of a Magnetizing Field. Influence of Medium Plane Boundaries on Electromagnetic Transients. A Resolvent for an Initial-Boundary-Value 1D Problem in a Dielectric. Electromagnetic Field in a Half-Restricted Time-Varying Medium. Jump Changes of Plasma Density in a Plasma Half-Space with a Plane Boundary. The Evolution of an Electromagnetic Field in the Dielectric Layer after Its Creation. Electromagnetic Field in a Layer with Non-Linear and Time-Varying Medium. Triple Asymmetry in Time-Spatial Structure of an Airy Pulse in Non-Stationary Environment. 3D+T Problems with Electromagnetic Transients. The 3D Resolvent for a Problem with a Plane Boundary of a Dielectric Half-Space. Fresnel's Formulas in Time-Domain for a Plane Interface between Two Dielectrics. Inclined Incidence of a Plane Wave on a Plane Boundary of the Time-Varying Medium. Refocusing of Point Source Radiation by the Plane Boundary of a Time-Varying Dielectric. Formation of Point Source Image by Time Change of Plasma. Frequency Change of Partial Spherical Waves Induced By Time Change of Medium Permittivity. Evolution of Waves after Plasma Ignition in a Sphere. Non-Stationarity of Electromagnetic Waves Caused by the Movement of a Medium Boundary. Transformation of an Electromagnetic Wave by a Uniformly Moving Boundary of a Medium. Evolution of an Electromagnetic Wave after the Beginning of Medium Boundary Movement. Relativistic Uniform Accelerated Movement of a Medium Boundary. Electromagnetic Field Energy Accumulation in a Collapsing Dielectric Layer. An Electromagnetic Field in a Metallic Waveguide with a Moving Medium. Expansion of an Electromagnetic Field by Non-Stationary Eigen-Functions of a Waveguide. Equations for a Field in the Waveguide with a Non-Stationary Insertion. Vibration of a Boundary of a Plane Dielectric Resonator. Uniform Movement of a Dielectric Layer in the Presence of Waveguide Dispersion. Penetration of an Electromagnetic Wave through Plasma Boundary after Its Start in a Waveguide. Interaction of an Electromagnetic Wave with a Plasma Bunch Moving in a Metallic Waveguide. Frequency Multiplication and Amplitude Amplification. Resonance Effects in a Stratified Plasma Cluster Moving in a Waveguide. Non-Stationary Electromagnetic Processes in Time-Varying Dielectric Waveguides. Wave Equations for Longitudinal and Transverse Components in Generalized Functions. Volterra Integral Equations for Non-Stationary Electromagnetic Processes in Time-Varying Dielectric Waveguides. Solution for the Problem with a Time Jump Change in the Waveguide Core Permittivity. Harmonic Wave Transformation Caused by a Permittivity Change in the Waveguide Core. Transformation of a Wave in a Non-Linear Dielectric Waveguide. Two Ways for Calculation of Field Evolution in Dielectric Waveguide: via Brillouin- or Eigen-Waves.
Alexander Nerukh is professor and head of the Department of Higher Mathematics, Kharkov National University of Radioelectronics, Ukraine. His main scientific interests are in radiophysics, transient and non-linear electrodynamics, nanophotonics, and dynamical chaos. He has published more than 330 journal/conference papers and four books. Prof. Nerukh is a senior member of the IEEE and a member of the European Microwave Association and the Optical Society.
Trevor Benson is professor of optoelectronics and a member of the George Green Institute for Electromagnetics Research at the University of Nottingham, UK. His research interests include experimental and numerical studies of electromagnetic fields and waves, mid-infrared photonics, lasers and amplifiers, and the electromagnetic resilience of aircraft. He is the author or coauthor of more than 800 journal and conference papers.
"This book presents advanced analytical models based on Volterra integral equations for electromagnetic wave phenomena in dynamically changing environments in a complete, mathematically rigorous but still very clear way. The analyzed problems are presented hierarchically in a very logical structure, and their analytic solutions are suitably illustrated with highly instructive graphs and drawings. The book may serve indisputably as an indispensable reference for academicians, researchers, and students studying electromagnetic wave phenomena in a variety of wavelength ranges, including optical, terahertz, microwave, and other radiations."
—Prof. Marian Marciniak, National Institute of Telecommunications, Poland
"This book comes as a most timely contribution, bringing the collected and systematized knowledge on non-stationary electromagnetic processes in plasma, waveguides, and moving media to the tables of experts working on time-modulated platforms for microwave, photonic, and acoustic devices."
—Prof. Sergei A. Tretyakov, Aalto University, Finland
"This book deals with a modern subject in electromagnetics and ably presents a generalized theory of non-stationary electromagnetics. The theory is validated by applying it to several particular cases of time-varying media problems solved earlier by the authors of the book as well as other researchers. The generalization of the theory should lead to the solution of a large range of problems of this developing field."
—Prof. Dikshitulu Kalluri, University of Massachusetts Lowell, USA