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Photonic Crystals Mathematical Analysis And Numerical Approximation
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Book Synopsis Photonic Crystals: Mathematical Analysis and Numerical Approximation by : Willy Dörfler
Download or read book Photonic Crystals: Mathematical Analysis and Numerical Approximation written by Willy Dörfler and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers. In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of continuous and discrete spectrum, multiple scales in space and time, and the ill-posedness of these problems. This volume collects a series of lectures which introduce into the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical devices.
Book Synopsis Fundamentals of Photonic Crystal Guiding by : Maksim Skorobogatiy
Download or read book Fundamentals of Photonic Crystal Guiding written by Maksim Skorobogatiy and published by Cambridge University Press. This book was released on 2009 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic, rigorous, pedagogical introduction to the field of photonic crystals, ideal for researchers and graduate students.
Book Synopsis Mathematical Modeling in Optical Science by : Gang Bao
Download or read book Mathematical Modeling in Optical Science written by Gang Bao and published by SIAM. This book was released on 2001-01-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers. Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.
Book Synopsis Foundations Of Photonic Crystal Fibres (2nd Edition) by : Argyros Alexander
Download or read book Foundations Of Photonic Crystal Fibres (2nd Edition) written by Argyros Alexander and published by World Scientific Publishing Company. This book was released on 2012-06-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book lies at the meeting point of electromagnetic waveguides and photonic crystals. Although these are both widely studied topics, they have been kept apart until recently. The purpose of the first edition of this book was to give state-of-the-art theoretical and numerical viewpoints about exotic fibres which use “photonic crystal effects” and consequently exhibit some remarkable properties.Since that first edition, photonic crystal fibres have become an important and effective optical device. In this second edition, the description of the theoretical and numerical tools used to study these fibres is enhanced, whilst up-to-date information about the properties, applications and fabrication of these fibres is added./a
Book Synopsis Mathematical Results in Quantum Mechanics by : Pavel Exner
Download or read book Mathematical Results in Quantum Mechanics written by Pavel Exner and published by World Scientific. This book was released on 2014-11-13 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive overview on the state of the art of the quantum part of mathematical physics. In particular, it contains contributions to the spectral theory of Schrödinger and random operators, quantum field theory, relativistic quantum mechanics and interacting many-body systems. It also presents an overview on the achievements in mathematical physics since the last conference QMath11 held at Hradec Kralove, Czechia in 2010. Contents:Plenary Talks:A Bound for the Eigenvalue Counting Function for Higher-Order Krein Laplacians on Open Sets (F Gesztesy, M Mitrea, S Sukhtaiev and A Laptev)Trace Formulae for the Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian (T Lungenstrass and G D Raikov)On Long Range Behaviour of van der Waals Force (I Anapolitanos and I M Sigal)Quantum Spin Correlations and Random Loops (D Ueltschi)Equidistribution Estimates for Eigenfunctions and Eigenvalue Bounds for Random Operators (D Borisov, M Tautenhahn and I Veselić)Invited Section Talks:Vector Quantum Fields (J Dereziński)On the BCS Gap Equation for Superfluid Fermionic Gases (G Bräunlich, C Hainzl and R Seiringer)Improved Hardy Inequality in Twisted Tubes (H Kovařík)Microscopic Foundations of Ohm and Joule's Laws — The Relevance of Thermodynamics (J-B Bru and W de Siqueira Pedra)The Quantum Marginal Problem (C Schilling)Hartree-Fock Dynamics for Weakly Interacting Fermions (N Benedikter, M Porta and B Schlein)Contributed Talks:On the Ground State Energy of the Multipolaron in the Strong Coupling Limit (I Anapolitanos and B Landon)A Variation on Smilansky's Model (D Barseghyan and P Exner)Deriving the Gross-Pitaevskii Equation (N Benedikter)Boundary Triplets Approach for Dirac Operator (A A Boitsev)Bose-Einstein Condensation on Quantum Graphs (J Bolte and J Kerner)Description of Quantum and Classical Dynamics via Feynman Formulae (Ya A Butko)Asymptotic Observables, Propagation Estimates and the Problem of Asymptotic Completeness in Algebraic QFT (W Dybalski)Recent Probabilistic Results on Covariant Schrödinger Operators on Infinite Weighted Graphs (B Güneysu and O Milatovic)Resolvent Expansion for the Discrete One-Dimensional Schrödinger Operator (K Ito and A Jensen)Spectral Asymptotics for a δ′ Interaction Supported by an Infinite Curve (M Jex)Asymptotically Predefined Spectral Gaps for the Neumann Laplacian in Periodic Domains (A Khrabustovskyi)Graph Model for the Stokes Flow (M O Kovaleva and I Yu Popov)Point Contacts and Boundary Triples (V Lotoreichik, H Neidhardt and I Yu Popov)Trace Formulas for Singular and Additive Non-Selfadjoint Perturbations (M M Malamud and H Neidhardt)On δ′-Couplings at Graph Vertices (S S Manko)Stochastic Calculus and Non-Relativistic QED (B Güneysu, O Matte and J S Møller)Estimates for Numbers of Negative Eigenvalues of Laplacian for Y-Type Chain of Weakly Coupled Ball Resonators (A S Melikhova)On Thermodynamical Couplings of Quantum Mechanics and Macroscopic Systems (A Mielke)Almost Sure Purely Singular Continuous Spectrum for Quasicrystal Models (C Seifert)Adiabatic Theorems With and Without Spectral Gap Condition for Non-Semisimple Spectral Values (J Schmid)An Eigenvalue Counting Theorem with Applications to Random Schrödinger Operators (D Schmidt)System of Fermions with Zero-Range Interactions (A Teta) Readership: Graduate students, professionals and researchers in mathematical physics, quantum mechanics and field theory, quantum information, quantum chaos and physics of social systems. Key Features:Collection of state-of-the-art papers in mathematical physicsProminent contributorsShows the actual research topics in mathematical physicsKeywords:Schrödinger Operator;Spectral Theory;Random Operators;Quantum Field Theory;Relativistic Quantum Mechanics;Interacting Many-Body Systems
Book Synopsis Mathematical Modeling in Optical Science by : Gang Bao
Download or read book Mathematical Modeling in Optical Science written by Gang Bao and published by SIAM. This book was released on 2001-01-01 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
Download or read book The Holodeck written by Michael Cloran and published by Xlibris Corporation. This book was released on 2020-02-07 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about a requirements specification for a Holodeck at a proof of concept level. In it I introduce optical functions for a optical processor and describe how they map to a subset of the Risc-V open instruction set. I describe how parallelism could be achieved. I then describe a possible layered approach to an optical processor motherboard for the datacenter and for a personal Holodeck. I describe Volumetrics in brief and show how its evolution to Holodeck volumetrics could be done with bend light technology and the possibility of solidness to touch. I describe in detail the architecture of a Holodeck covering several approaches to Holodecks from static scene to scrolling scene to multi-user same complex to networked multi-user Holodecks.
Book Synopsis Photonic Crystals, Theory, Applications and Fabrication by : Dennis W Prather
Download or read book Photonic Crystals, Theory, Applications and Fabrication written by Dennis W Prather and published by John Wiley & Sons. This book was released on 2009-05-26 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Wave Phenomena written by Willy Dörfler and published by Springer Nature. This book was released on 2023-03-30 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.
Book Synopsis Electromagnetic Theory and Applications for Photonic Crystals by : Kiyotoshi Yasumoto
Download or read book Electromagnetic Theory and Applications for Photonic Crystals written by Kiyotoshi Yasumoto and published by CRC Press. This book was released on 2018-10-03 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Photonic technology promises much faster computing, massive parallel processing, and an evolutionary step in the digital age. The search continues for devices that will enable this paradigm, and these devices will be based on photonic crystals. Modeling is a key process in developing crystals with the desired characteristics and performance, and Electromagnetic Theory and Applications for Photonic Crystals provides the electromagnetic-theoretical models that can be effectively applied to modeling photonic crystals and related optical devices. The book supplies eight self-contained chapters that detail various analytical, numerical, and computational approaches to the modeling of scattering and guiding problems. For each model, the chapter begins with a brief introduction, detailed formulations of periodic structures and photonic crystals, and practical applications to photonic crystal devices. Expert contributors discuss the scattering matrix method, multipole theory of scattering and propagation, model of layered periodic arrays for photonic crystals, the multiple multipole program, the mode-matching method for periodic metallic structures, the method of lines, the finite-difference frequency-domain technique, and the finite-difference time-domain technique. Based on original research and application efforts, Electromagnetic Theory and Applications for Photonic Crystals supplies a broad array of practical tools for analyzing and designing devices that will form the basis for a new age in computing.
Book Synopsis Photonic Crystals by : Igor A. Sukhoivanov
Download or read book Photonic Crystals written by Igor A. Sukhoivanov and published by Springer. This book was released on 2009-09-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great interest in photonic crystals and their applications in the last 15 years is being expressed in the publishing of a large number of monographs, collections, textbooks and tutorials, where existing knowledge concerning - eration principles of photonic crystal devices and microstructured ?bers, their mathematicaldescription,well-knownandnovelapplicationsofsuchtechno- gies in photonics and optical communications are presented. They challenges authors of new books to cover the gaps still existing in the literature and highlight and popularize of already known material in a new and original manner. Authorsofthisbookbelievethatthenextsteptowardswideapplicationof photoniccrystalsisthesolutionofmanypracticalproblemsofdesignandc- putation of the speci?c photonic crystal-based devices aimed at the speci?c technicalapplication.Inordertomakethisstep,itisnecessarytoincreasethe number of practitioners who can solve such problems independently. The aim of this book is to extend the group of researchers, developers and students, who could practically use the knowledge on the physics of photonic crystals together with the knowledge and skills of independent calculation of basic characteristics of photonic crystals and modeling of various elements of - tegrated circuits and optical communication systems created on the basis of photonic crystals. The book is intended for quali?ed readers, specialists in the ?eld of optics and photonics, students of higher courses, master degree students and PhD students. As an introduction to the snopest, the book contains the basics of wave optics and radiation propagation in simple guiding media such as planar waveguides and step-index ?bers.
Book Synopsis Advances in Photonic Crystals by : Vittorio Passaro
Download or read book Advances in Photonic Crystals written by Vittorio Passaro and published by BoD – Books on Demand. This book was released on 2013-02-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects chapters on different theoretical and experimental aspects of photonics crystals for Nanophotonics applications. It is divided in two parts - a theoretical section and an experimental and applicative section. The first part includes chapters developing several numerical methods for analysis and design of photonic crystal devices, such as 2D ring resonators for filters, single and coupled nanobeam cavities, birefringence in photonic crystal cavities, threshold analysis in photonic crystal lasers, gap solitons in photonic crystals, novel photonic atolls, dynamic characteristics of photonic crystal filters. The second part focuses on some aspects of photonic crystals fabrication and relevant applications, such as nitrogen defect technology in diamond, silicon nitride free standing membranes, photonic crystals structures in silicon, photonic crystals for optical sensing.
Book Synopsis Photonic Crystals by : John D. Joannopoulos
Download or read book Photonic Crystals written by John D. Joannopoulos and published by Princeton University Press. This book was released on 2011-10-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Photonic Crystals by : Steven G. Johnson
Download or read book Photonic Crystals written by Steven G. Johnson and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Photonic Crystals: The Road from Theory to Practice explores the theoretical road leading to the practical application of photonic band gaps. These new optimal devices are based on symmetry and resonance and the benefits and limitations of hybrid "two dimensional" slab systems in three dimensions. The book also explains that they also signify a return to the ideal of an omnidirectional band gap in a structure inspired by and emulating the simplicity of two dimensions. Finally, the book takes a look at computational methods to solve the mathematical problems that underlie all undertakings in this field. Photonic Crystals: The Road from Theory to Practice should rapidly bring the optical professional and engineer up to speed on this intersection of electromagnetism and solid-state physics. It will also provide an excellent addition to any graduate course in optics.
Book Synopsis Photonic Crystals: Physics and Technology by : Concita Sibilia
Download or read book Photonic Crystals: Physics and Technology written by Concita Sibilia and published by Springer Science & Business Media. This book was released on 2009-02-03 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the work is give an overview of the activity in the field of Photonic Crystal developed in the frame of COST P11 action . The main objective of the COST P11 action was to unify and coordinate national efforts aimed at studying linear and nonlinear optical interactions with Photonic Crystals (PCs), without neglecting an important aspect related to the material research as idea and methods of realizations of 3D PC, together with the development and implementation of measurement techniques for the experimental evaluation of their potential applications in different area, as for example telecommunication with novel optical fibers, lasers, nonlinear multi-functionality, display devices, opto-electronics, sensors. The book contains contributions from authors who gave their lecture at the Cost P11 Training School.
Book Synopsis Mathematical Models and Numerical Methods for Full Wave Analysis of Prolate and Oblate Spheroidal Conformal Microwave Components by : Saif Al-Hasson
Download or read book Mathematical Models and Numerical Methods for Full Wave Analysis of Prolate and Oblate Spheroidal Conformal Microwave Components written by Saif Al-Hasson and published by Cuvillier Verlag. This book was released on 2014-08-29 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal components are used nowadays at higher rate than ever before. They can be found in curved mobile phones, communication, navigation, and imaging systems in land, water, air, and space vehicles. The integration of those components within the external structure became of significant importance for aerodynamic, electromagnetic, aesthetic, or physical reasons. As a result, many mathematical models were previously developed to analyze and optimize such conformed devices. In this thesis, we contributed to this field by developing various models for full wave analysis of spheroidal components. As a starting point, mathematical formulas for conforming antennas on oblate and prolate spheroids were obtained. Those conformation methods were validated by conforming many antennas on spheroidal surfaces. They were then used to formulate Method of Moments equations with spheroidally curved current functions for analyzing wire antennas of random shape conformed to spheroids in the frequency domain. The complete model was applied to a conformal Archimedean spiral antenna on an oblate spheroid and showed that the conformed spiral has similar current distribution as its planar counterpart but produces an unsymmetrical radiation pattern. The obtained model was then extended to spheroidal multi-layer structures by integrating the spheroidal dyadic Green’s Function within its mathematical derivation. However, due to a detected divergence in that function, the model couldn’t be implemented. On the side of time based analysis methods, a Finite Difference Time Domain method was developed for closed oblate and prolate spheroidal structures. Alternative formulas for the structure’s singularities and the condition of numerical stability were derived as well. The obtained model was then validated and used to characterize spheroidal cavities in the time and frequency domains. The method was extended later to unbounded spheroidal domain by deriving the Absorbing Boundary Conditions using the One Way Wave method. The whole model was then applied to characterize a patch antenna conformed to a prolate spheroid. Finally, an analytical solution for the transient fields in spherical multilayer media energized by spherical harmonics source and an algorithm for tracing back the path of all the reflected waves were obtained. The model was applied to different multilayer structures where the transient response was obtained and validated against a numerical solution.
Book Synopsis Computational Methods for Nanoscale Applications by : Igor Tsukerman
Download or read book Computational Methods for Nanoscale Applications written by Igor Tsukerman and published by Springer Science & Business Media. This book was released on 2007-12-24 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Positioning itself at the common boundaries of several disciplines, this work provides new perspectives on modern nanoscale problems where fundamental science meets technology and computer modeling. In addition to well-known computational techniques such as finite-difference schemes and Ewald summation, the book presents a new finite-difference calculus of Flexible Local Approximation Methods (FLAME) that qualitatively improves the numerical accuracy in a variety of problems.
