An Introduction to Hamiltonian Optics PDF Download
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Author: H. A. Buchdahl
Publisher: Courier Corporation
ISBN: 9780486675978
Category : Science
Languages : en
Pages : 392
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Book Description
Accessible study provides detailed account of the Hamiltonian treatment of aberration theory in geometrical optics. Many classes of optical systems defined in terms of their symmetries. Detailed solutions. 1970 edition.
Author: H. A. Buchdahl
Publisher: Courier Corporation
ISBN: 9780486675978
Category : Science
Languages : en
Pages : 392
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Book Description
Accessible study provides detailed account of the Hamiltonian treatment of aberration theory in geometrical optics. Many classes of optical systems defined in terms of their symmetries. Detailed solutions. 1970 edition.
Author: Christopher Gerry
Publisher: Cambridge University Press
ISBN: 9780521527354
Category : Science
Languages : en
Pages : 338
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Book Description
Publisher Description
Author: Gerardo F. Torres del Castillo
Publisher: Springer
ISBN: 3319952250
Category : Mathematics
Languages : en
Pages : 371
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Book Description
This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and well-chosen exercises. For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton–Jacobi equation, and the Liouville Theorem on solutions of the Hamilton–Jacobi equation. Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.
Author: Jin-Sheng Peng
Publisher: World Scientific
ISBN: 9789810234485
Category : Science
Languages : en
Pages : 584
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Book Description
This book discusses quantum optics and investigates the quantum properties of interactions between atoms and laser fields. It is divided into three parts. Part I introduces the elementary theory of the interaction between atoms and light. Part II provides a concentrated discussion on the quantum properties of light fields. Part III deals with the quantum dynamic properties of the atoms interacting with laser fields. This book can be used as a text for both graduate and undergraduate students; it will also benefit scientists who are interested in quantum optics and theoretical physics.
Author: Marlan O. Scully
Publisher: Cambridge University Press
ISBN: 9780521435956
Category : Science
Languages : en
Pages : 664
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Book Description
An in-depth and wide-ranging introduction to the field of quantum optics.
Author: Julio Chaves
Publisher: CRC Press
ISBN: 1482206749
Category : Science
Languages : en
Pages : 772
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Book Description
Introduction to Nonimaging Optics covers the theoretical foundations and design methods of nonimaging optics, as well as key concepts from related fields. This fully updated, revised, and expanded Second Edition: Features a new and intuitive introduction with a basic description of the advantages of nonimaging optics Adds new chapters on wavefronts for a prescribed output (irradiance or intensity), infinitesimal étendue optics (generalization of the aplanatic optics), and Köhler optics and color mixing Incorporates new material on the simultaneous multiple surface (SMS) design method in 3-D, integral invariants, and étendue 2-D Contains 21 chapters, 24 fully worked and several other examples, and 1,000+ illustrations, including photos of real devices Addresses applications ranging from solar energy concentration to illumination engineering Introduction to Nonimaging Optics, Second Edition invites newcomers to explore the growing field of nonimaging optics, while providing seasoned veterans with an extensive reference book.
Author: Gilbert Grynberg
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Covering a number of important subjects in quantum optics, this textbook is an excellent introduction for advanced undergraduate and beginning graduate students, familiarizing readers with the basic concepts and formalism as well as the most recent advances. The first part of the textbook covers the semi-classical approach where matter is quantized, but light is not. It describes significant phenomena in quantum optics, including the principles of lasers. The second part is devoted to the full quantum description of light and its interaction with matter, covering topics such as spontaneous emission, and classical and non-classical states of light. An overview of photon entanglement and applications to quantum information is also given. In the third part, non-linear optics and laser cooling of atoms are presented, where using both approaches allows for a comprehensive description. Each chapter describes basic concepts in detail, and more specific concepts and phenomena are presented in 'complements'.
Author: V. Lakshminarayanan
Publisher: Springer Science & Business Media
ISBN: 1461517117
Category : Science
Languages : en
Pages : 230
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Book Description
Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the current interest and activity in optical fibers and optical communication, analysis of light propagation in inhomogeneous media is dealt with in great detail. The past decade has witnessed great advances in adaptive optics and compensation for optical aberrations. The formalism described herein can be used to calculate aberrations ofoptical systems. Toward the end of the book, we present application of the formalism to current research problems. Of particular interest is the use of dynamic programming techniques which can be used to handle variational/extremum problems. This method has only recently been applied to opticalproblems.
Author: Dmitry Treschev
Publisher: Springer Science & Business Media
ISBN: 3642030289
Category : Mathematics
Languages : en
Pages : 221
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Book Description
This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
Author: Kurt Bernardo Wolf
Publisher: Springer Science & Business Media
ISBN: 9783540220398
Category : Science
Languages : en
Pages : 400
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Book Description
Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.
