This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.
This book begins with the history and fundamentals of optical fiber communications. Then, briefly introduces existing optical multiplexing techniques and finally focuses on spatial domain multiplexing (SDM), aka space division multiplexing, and orbital angular momentum of photon based multiplexing. These are two emerging multiplexing techniques that have added two new degrees of photon freedom to optical fibers.
Hyperbolic metamaterials were originally introduced to overcome the diffraction limit of optical imaging. Soon thereafter it was realized that hyperbolic metamaterials demonstrate a number of novel phenomena resulting from the broadband singular behavior of their density of photonic states. These novel phenomena and applications include super resolution imaging, new stealth technologies, enhanced quantum-electrodynamic effects, thermal hyperconductivity, superconductivity, and interesting gravitation theory analogs. Here I review typical material systems, which exhibit hyperbolic behavior and outline important new applications of hyperbolic metamaterials, such as imaging experiments with plasmonic hyperbolic metamaterials and novel VCSEL geometries, in which the Bragg mirrors may be engineered in such a way that they exhibit hyperbolic properties in the long wavelength infrared range, so that they may be used to efficiently remove excess heat from the laser cavity. I will also discuss potential applications of self-assembled photonic hypercrystals. This system bypasses 3D nanofabrication issues, which typically limit hyperbolic metamaterial applications. Photonic hypercrystals combine the most interesting features of hyperbolic metamaterials and photonic crystals.
In any linear system, the input and the output are connected by means of a linear operator. When the input can be notionally represented by a function that is null valued everywhere except at a specific location in spacetime, the corresponding output is called the Green function in field theories. Dyadic Green functions are commonplace in electromagnetics, because both the input and the output are vector functions of space and time. This book provides a survey of the state-of-the-art knowledge of infinite space dyadic Green functions.
This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers. Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.
The Only Source You Need for Understanding the Design and Applications of Photonic Crystal-Based Devices This book presents in detail the fundamental theoretical background necessary to understand the unique optical phenomena arising from the crystalline nature of photonic-crystal structures and their application across a range of disciplines. Organized to take readers from basic concepts to more advanced topics, the book covers: Preliminary concepts of electromagnetic waves and periodic media Numerical methods for analyzing photonic-crystal structures Devices and applications based on photonic bandgaps Engineering photonic-crystal dispersion properties Fabrication of two- and three-dimensional photonic crystals The authors assume an elementary knowledge of electromagnetism, vector calculus, Fourier analysis, and complex number analysis. Therefore, the book is appropriate for advanced undergraduate students in physics, applied physics, optics, electronics, and chemical and electrical engineering, as well as graduate students and researchers in these fields.
Presents the most recent theoretical developments and numerical/experimental validations of new metamaterials and phononic crystals for the broadband absorption of elastic waves and vibrations in structures. Coverage includes sound absorption, extraordinary transmission, wave broadband mitigation, wave steering, cloaking via the transformation method, and active acoustic metamaterials.
The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.
