Mathematical Theory Of Diffraction
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Mathematical Theory Of Diffraction
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Author : Arnold Sommerfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Theory Of Diffraction written by Arnold Sommerfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Arnold Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. The body of Sommerfeld's work is devoted to the systematic development of a method for deriving solutions of the wave equation on Riemann surfaces, a fascinating but perhaps underappreciated topic in mathematical physics.
Mathematical Theory Of Diffraction
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Author : Arnold Sommerfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
Mathematical Theory Of Diffraction written by Arnold Sommerfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
A. Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work.
The Mathematical Theory Of Huygens Principle
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Author : Bevan B. Baker
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Mathematical Theory Of Huygens Principle written by Bevan B. Baker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Baker and Copson originally set themselves the task of writing a definitive text on partial differential equations in mathematical physics. However, at the time, the subject was changing rapidly and greatly, particularly via the developments coming from quantum mechanics. Instead, the authors chose to focus on a particular area of the broad theory, producing a monograph complete in itself. The resulting book deals with Huygens' principle in optics and its application to the theory of diffraction. Baker and Copson concern themselves with the general theory of the solution of the PDEs governing the propagation of light. Extensive use is made of Green's method. A chapter is dedicated to Sommerfeld's theory of diffraction, including diffraction of polarized light by a perfectly reflecting half-plane and by a black half-plane. New material was added for subsequent editions, notably Rayleigh's method of integral equations to the problem of diffraction by a planar screen. Some of the simpler diffraction problems are discussed as examples. Baker and Copson's book quickly became the standard reference on the subject of Huygens' principle. It remains so today.
Equations Of Mathematical Diffraction Theory
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Author : Mezhlum A. Sumbatyan
language : en
Publisher: CRC Press
Release Date : 2004-09-29
Equations Of Mathematical Diffraction Theory written by Mezhlum A. Sumbatyan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-29 with Science categories.
Equations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case. Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications.
Scattering Theory For Diffraction Gratings
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Author : Calvin H. Wilcox
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Scattering Theory For Diffraction Gratings written by Calvin H. Wilcox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The scattering of acoustic and electromagnetic waves by periodic sur faces plays a role in many areas of applied physics and engineering. Opti cal diffraction gratings date from the nineteenth century and are still widely used by spectroscopists. More recently, diffraction gratings have been used as coupling devices for optical waveguides. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound. Similarly, the surface of a crystal acts as a diffraction grating for the scattering of atomic beams. This list of natural and artificial diffraction gratings could easily be extended. The purpose of this monograph is to develop from first principles a theory of the scattering of acoustic and electromagnetic waves by periodic surfaces. In physical terms, the scattering of both time-harmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for the Helmholtz and d'Alembert wave equations in plane domains bounded by periodic curves. In the formal ism adopted here these problems are intimately related to the spectral analysis of the Laplace operator, acting in a Hilbert space of functions defined in the domain adjacent to the grating.
Geometrical Theory Of Diffraction
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Author : Vladimir Andreevich Borovikov
language : en
Publisher: IET
Release Date : 1994
Geometrical Theory Of Diffraction written by Vladimir Andreevich Borovikov and has been published by IET this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book details the ideas underlying geometrical theory of diffraction (GTD) along with its relationships with other EM theories.
Advanced Studies In The Mathematical Theory Of Scattering Volume 3
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Author : Jean-Michel L. Bernard
language : en
Publisher: John Wiley & Sons
Release Date : 2024-10-11
Advanced Studies In The Mathematical Theory Of Scattering Volume 3 written by Jean-Michel L. Bernard and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-11 with Science categories.
This book presents a collection of independent mathematical studies, describing the analytical reduction of complex generic problems in the theory of scattering and propagation of electromagnetic waves in the presence of imperfectly conducting objects. Their subjects include: a global method for scattering by a multimode plane; diffraction by an impedance curved wedge; scattering by impedance polygons; advanced properties of spectral functions in frequency and time domains; bianisotropic media and related coupling expressions; and exact and asymptotic reductions of surface radiation integrals. The methods developed here can be qualified as analytical when they lead to exact explicit expressions, or semi-analytical when they drastically reduce the mathematical complexity of studied problems. Therefore, they can be used in mathematical physics and engineering to analyse and model, but also in applied mathematics to calculate the scattered fields in electromagnetism for a low computational cost.
Fundamentals Of The Physical Theory Of Diffraction
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Author : Pyotr Ya. Ufimtsev
language : en
Publisher: John Wiley & Sons
Release Date : 2007-02-09
Fundamentals Of The Physical Theory Of Diffraction written by Pyotr Ya. Ufimtsev and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-09 with Science categories.
This book is the first complete and comprehensive description of the modern Physical Theory of Diffraction (PTD) based on the concept of elementary edge waves (EEWs). The theory is demonstrated with the example of the diffraction of acoustic and electromagnetic waves at perfectly reflecting objects. The derived analytic expressions clearly explain the physical structure of the scattered field and describe in detail all of the reflected and diffracted rays and beams, as well as the fields in the vicinity of caustics and foci. Shadow radiation, a new fundamental component of the field, is introduced and proven to contain half of the total scattered power.
Diffraction Effects In Semiclassical Scattering
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Author : H. M. Nussenzveig
language : en
Publisher: Cambridge University Press
Release Date : 1992-07-23
Diffraction Effects In Semiclassical Scattering written by H. M. Nussenzveig and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-07-23 with Science categories.
This book deals with the theory of critical effects in semiclassical scattering, in which the standard approximations break down. Such critical effects are responsible for phenomena such as rainbows and glories.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.