Geometric Optics On Phase Space

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Geometric Optics On Phase Space

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Author : Kurt Bernardo Wolf
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-07-21

Geometric Optics On Phase Space written by Kurt Bernardo Wolf 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 2004-07-21 with Science categories.

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.

Linear Ray And Wave Optics In Phase Space

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Author : Amalia Torre
language : en
Publisher: Elsevier
Release Date : 2005-11-11

Linear Ray And Wave Optics In Phase Space written by Amalia Torre and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-11 with Science categories.

Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner function based technique as the mathematical machinery to accommodate between the two opposite extremes of light representation: the localized ray of geometrical optics and the unlocalized wave function of wave optics.At a parallel level, the analogies with other branches of both classical and quantum physics, like classical and quantum mechanics, quantum optics, signal theory as well as magnetic optics, are evidenced by pertinent comments and/or rigorous mathematics. So, the Lie algebra and group methods are introduced and explained through the elementary optical systems within both the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a like manner, the Wigner function is introduced by following the original issue to individualize a phase space representation of quantum mechanics, which is mirrored by the issue to individualize a local frequency spectrum within the signal theory context. The basic analogy with the optics of charged particles inherently underlying the ray-optics picture in phase space is also evidenced within the wave-optics picture in the Wigner phase space.· amalgamation of a great deal of contributions having witnessed the phase space picture of optics over the past 30 years· introduces abstract concepts through concrete systems· hosts of figures and logical diagrams to favour intuition and to introduce mathematics· emphasis on the interrelations with quantum optics, signal theory and magnetic optics · feeds a feeling for genuine issues in higher mathematics and theoretical physics

Linear Ray And Wave Optics In Phase Space

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Author : Amalia Torre
language : en
Publisher: Elsevier
Release Date : 2020-06-01

Linear Ray And Wave Optics In Phase Space written by Amalia Torre and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-01 with Science categories.

Linear Ray and Wave Optics in Phase Space, Second Edition, is a comprehensive introduction to Wigner optics. The book connects ray and wave optics, offering the optical phase space as the ambience and the Wigner function based technique as the mathematical machinery to accommodate between the two opposite extremes of light representation: the localized ray of geometrical optics and the unlocalized wave function of wave optics. Analogies with other branches of classical and quantum physics—such as classical and quantum mechanics, quantum optics, signal theory and magnetic optics—are evidenced by pertinent comments and/or rigorous mathematics. Lie algebra and group methods are introduced and explained through the elementary optical systems within the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a similar manner, the Wigner function is introduced by following the original issue to individualize a phase space representation of quantum mechanics, which is mirrored by the issue to individualize a local frequency spectrum within the signal theory context. The basic analogy with the optics of charged particles inherently underlying the ray-optics picture in phase space is also evidenced within the wave-optics picture in the Wigner phase space. This second edition contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics. All chapters are fully revised and updated. All topics have been developed to a deeper level than in the previous edition and are now supported with Mathematica and Mathcad codes. Provides powerful tools to solve problems in quantum mechanics, quantum optics and signal theory Includes numerous examples supporting a gradual and comprehensive introduction to Wigner optics Treats both ray and wave optics, resorting to Lie-algebra based methods Connects the subject with other fields, such as quantum optics, quantum mechanics, signal theory and optics of charged particles Introduces abstract concepts through concrete examples Includes logical diagrams to introduce mathematics in an intuitive way Contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics Supported with Mathematica and Mathcad codes

Phase In Optics

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Author : Vlasta Pe?inov 
language : en
Publisher: World Scientific
Release Date : 1998

Phase In Optics written by Vlasta Pe?inov  and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.

The history of the quantum phase problem, characterized by renewed interest in the solution to the problem, is included and brought up to date.

Lagrangian Optics

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Author : V. Lakshminarayanan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002

Lagrangian Optics written by V. Lakshminarayanan 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 2002 with Mathematics categories.

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.

Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition

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Author : Darryl D Holm
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-07-13

Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition written by Darryl D Holm and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-13 with Mathematics categories.

See also GEOMETRIC MECHANICS — Part II: Rotating, Translating and Rolling (2nd Edition) This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. It treats the fundamental problems of dynamical systems from the viewpoint of Lie group symmetry in variational principles. The only prerequisites are linear algebra, calculus and some familiarity with Hamilton's principle and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie-Poisson Hamiltonian formulations and momentum maps in physical applications.The many Exercises and Worked Answers in the text enable the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly.The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. In particular, the role of Noether's theorem about the implications of Lie group symmetries for conservation laws of dynamical systems has been emphasised throughout, with many applications./a

Group Theoretical Methods In Physics Proceedings Of The Yamada Conference Xl And Xx International Colloquium

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Author : Tohru Eguchi
language : en
Publisher: World Scientific
Release Date : 1995-05-11

Group Theoretical Methods In Physics Proceedings Of The Yamada Conference Xl And Xx International Colloquium written by Tohru Eguchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05-11 with categories.

The topics discussed in this volume are: Symmetry and Foundations in Classical and Quantum Mechanics; Geometry, Topology and Quantum Field Theory; Quantum Groups and Infinite-Dimensional Lie Algebras; Algebraic Approach to Nuclear Structure; Integrable Statistical Systems and Theory of Critical Phenomena Supersymmetry; Atomic and Molecular Physics; Condensed Matter Physics; Other Applications of Group Theory to Physics.

The Geometry Of Heisenberg Groups

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Author : Ernst Binz
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

The Geometry Of Heisenberg Groups written by Ernst Binz 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 2008 with Mathematics categories.

"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.

Geometric Mechanics

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Author : Darryl D. Holm
language : en
Publisher: World Scientific
Release Date : 2008

Geometric Mechanics written by Darryl D. Holm and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Physics Of Light And Optics Black White

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Author : Michael Ware
language : en
Publisher: Lulu.com
Release Date : 2015

Physics Of Light And Optics Black White written by Michael Ware and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Electromagnetic waves categories.