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Numerical Methods in Photonics

Author: Andrei V. Lavrinenko

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 362

ISBN-13: 1466563893

Simulation and modeling using numerical methods is one of the key instruments in any scientific work. In the field of photonics, a wide range of numerical methods are used for studying both fundamental optics and applications such as design, development, and optimization of photonic components. Modeling is key for developing improved photonic devices and reducing development time and cost. Choosing the appropriate computational method for a photonics modeling problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods: FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green’s function, and FEM. After an introductory chapter outlining the basics of Maxwell’s equations, the book includes self-contained chapters that focus on each of the methods. Each method is accompanied by a review of the mathematical principles in which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATLAB® is used throughout the text. This book provides a solid basis to practice writing your own codes. The theoretical formulation is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.

Computational Photonics

Author: Marek S. Wartak

Publisher: Cambridge University Press

Published: 2013-01-10

Total Pages: 467

ISBN-13: 1139851403

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A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practising scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.

Mathematical and Computational Methods in Photonics and Phononics

Author: Habib Ammari

Publisher: American Mathematical Soc.

Published: 2018-10-15

Total Pages: 509

ISBN-13: 1470448009

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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.

Computational Photonics

Author: Salah Obayya

Publisher: John Wiley & Sons

Published: 2011-06-20

Total Pages: 268

ISBN-13: 1119957508

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This book explores the state-of-the art in computational modelling techniques for photonic devices In this book, the author provides a comprehensive coverage of modern numerical modelling techniques for designing photonic devices for use in modern optical telecommunications systems. In addition the book presents the state-of-the-art in computational photonics techniques, covering methods such as full-vectorial finite-element beam propagation, bidirectional beam propagation, complex-envelope alternative direction implicit finite difference time domain, multiresolution time domain, and finite volume time domain. The book guides the reader through the concepts of modelling, analysing, designing and optimising the performance of a wide range of photonic devices by building their own numerical code using these methods. Key Features: Provides a thorough presentation of the state-of-the art in computational modelling techniques for photonics Contains broad coverage of both frequency- and time-domain techniques to suit a wide range of photonic devices Reviews existing commercial software packages for photonics Presents the advantages and disadvantages of the different modelling techniques as well as their suitability for various photonic devices Shows the reader how to model, analyse, design and optimise the performance of a wide range of photonic devices by building their own numerical code using these methods Accompanying website contains the numerical examples representing the numerical techniques in this book, as well as several design examples (http://www.wiley.com/go/obayya_computational) This book will serve as an invaluable reference for researchers, optical telecommunications engineers, engineers in the photonics industry. PhD and MSc students undertaking courses in the areas of photonics and optical telecommunications will also find this book of interest.

Finite Element Modeling Methods for Photonics

Author: B. M. Azizur Rahman

Publisher: Artech House

Published: 2013-08-01

Total Pages: 265

ISBN-13: 1608075311

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The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astronomy, and sensing, to chemistry, imaging, and biomedical R&D. This book emphasizes practical, problem-solving applications and includes real-world examples to assist readers in understanding how mathematical concepts translate to computer code for finite element-based methods applicable to a range of photonic structures. In addition, this is the perfect support to anyone using the COMSOL Multiphysics© RF Module.

Numerical Methods in Photonics

Author: Andrei V. Lavrinenko

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 206

ISBN-13: 135183200X

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Integrated Photonics

Author: Clifford Pollock

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 374

ISBN-13: 1475755228

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From the beginning Integrated Photonics introduces numerical techniques for studying non-analytic structures. Most chapters have numerical problems designed for solution using a computational program such as Matlab or Mathematica. An entire chapter is devoted to one of the numeric simulation techniques being used in optoelectronic design (the Beam Propagation Method), and provides opportunity for students to explore some novel optical structures without too much effort. Small pieces of code are supplied where appropriate to get the reader started on the numeric work. Integrated Photonics is designed for the senior/first year graduate student, and requires a basic familiarity with electromagnetic waves, and the ability to solve differential equations with boundary conditions.

Numerical Methods for Metamaterial Design

Author: Kenneth Diest

Publisher: Springer Science & Business Media

Published: 2013-08-13

Total Pages: 226

ISBN-13: 9400766645

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This book describes a relatively new approach for the design of electromagnetic metamaterials. Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths. After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered. Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies. Additionally, new techniques for representing dielectric distributions in two dimensions, including level sets, are demonstrated as effective methods for gradient-based optimization. Each chapter begins with a rigorous review of the optimization strategy used, and is followed by numerous examples that combine the strategy with either electromagnetic simulations or analytical solutions of the scattering problem. Throughout the text, we address the strengths and limitations of each method, as well as which numerical methods are best suited for different types of metamaterial designs. This book is intended to provide a detailed enough treatment of the mathematical methods used, along with sufficient examples and additional references, that senior level undergraduates or graduate students who are new to the fields of plasmonics, metamaterials, or optimization methods; have an understanding of which approaches are best-suited for their work and how to implement the methods themselves.

Advanced Numerical Techniques for Photonic Crystals

Author: Didier Felbacq

Publisher: Morgan & Claypool Publishers

Published: 2016-12-07

Total Pages: 124

ISBN-13: 1681743027

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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.

Optical Properties of Photonic Crystals

Author: Kazuaki Sakoda

Publisher: Springer

Published: 2013-11-11

Total Pages: 230

ISBN-13: 3662143240

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Deals not only with the properties of the radiation modes inside the crystals but also with their peculiar optical response to external fields. A general theory of linear and nonlinear optical response is presented in a clear and detailed fashion using the Green’s function method. Important recent developments such as the enhancement of stimulated emission, second harmonic generation, quadrature-phase squeezing, and low-threshold lasing are likewise treated in detail and made understandable. Numerical methods are also emphasised. This book provides both introductory knowledge for graduate and undergraduate students and important ideas for researchers.