Linear Ray And Wave Optics In Phase Space

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Author: Amalia Torre
Publisher: Elsevier
ISBN: 9780080535531
Size: 10.85 MB
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Linear Ray And Wave Optics In Phase Space by Amalia Torre

Original Title: Linear Ray And Wave Optics In Phase Space

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

Phase Space Optics Fundamentals And Applications

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Author: Markus Testorf
Publisher: McGraw Hill Professional
ISBN: 0071597999
Size: 28.95 MB
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Phase Space Optics Fundamentals And Applications by Markus Testorf

Original Title: Phase Space Optics Fundamentals And Applications

A comprehensive cross section of phase-space optics This definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cutting-edge phase-space techniques. Phase-Space Optics: Fundamentals and Applications details theoretical concepts of phase space as well as novel engineering applications in specific disciplines. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phase-space interpretation of ultrafast optics. Work with Wigner optics, analyze phase-space equations, develop wave propagation models, and gain a new understanding of optical sources and systems. Discover how to: Describe optical phenomena using Wigner and ambiguity functions Perform phase-space rotations using ray transformation matrices Influence the trade-off between pupil size and depth of field Analyze and design optical signals using the Radon-Wigner transform Accomplish superresolution by squeezing phase space Interpret the intimate relationship between radiometry and coherence Use basic algebra to discover self-imaging, Fresnel diffraction, and the Talbot effect Develop discrete models, sampling criteria, and interpolation formulae Work with ultrafast processes and complex space-time structures

Geometric Optics On Phase Space

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Author: Kurt Bernardo Wolf
Publisher: Springer Science & Business Media
ISBN: 9783540220398
Size: 43.73 MB
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Geometric Optics On Phase Space by Kurt Bernardo Wolf

Original Title: Geometric Optics On Phase Space

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.

The Fractional Fourier Transform

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Author: M. Alper Kutay
Publisher: John Wiley & Sons Incorporated
ISBN: 9780471963462
Size: 28.62 MB
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The Fractional Fourier Transform by M. Alper Kutay

Original Title: The Fractional Fourier Transform

The discovery of the Fractional Fourier Transform and its role in optics and data management provides an elegant mathematical framework within which to discuss diffraction and other fundamental aspects of optical systems. This book explains how the fractional Fourier transform has allowed the generalization of the Fourier transform and the notion of the frequency transform. It will serve as the standard reference on Fourier transforms for many years to come.

Mathematical Optics

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Author: Vasudevan Lakshminarayanan
Publisher: CRC Press
ISBN: 1439869618
Size: 59.89 MB
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Mathematical Optics by Vasudevan Lakshminarayanan

Original Title: Mathematical Optics

Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at

Atom Optics

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Author: Pierre Meystre
Publisher: Springer Science & Business Media
ISBN: 9780387952741
Size: 48.39 MB
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Atom Optics by Pierre Meystre

Original Title: Atom Optics

One of the most profound revolutions brought about by quantum mechanics is that it does away with the distinction between waves and particles: atoms, in particular, can exhibit all the properties that we associate with wave phenomena, such as diffraction and interference; it has recently even become possible to prepare collections of atoms in coherent states, like those of photons in a laser beam. These developments are at the core of the rapidly expanding field of atom optics. ||Atom Optics gradually leads the reader from elementary concepts to the frontiers of the field. It is organized in three parts, linear, nonlinear, and quantum atom optics. After a review of light forces on atoms and of laser cooling, the first part discusses the application of light forces to atom optical elements such as gratings, mirrors and lenses, matter-wave diffraction, and atomic traps and resonators. The discussion of nonlinear atom optics starts with a review of collisions from a viewpoint that clearly demonstrates its profound analogy with nonlinear optics. The last part, quantum atom optics, first recalls key results of many-body theory in a formulation geared specifically toward atom optics. This is followed by a discussion of atomic Bose-Einstein condensation and "atom lasers." The final chapters treat such applications as atomic solitons, four-wave mixing, superradiance, and conclude with the coherent amplification of matter waves. ||An online web component to the book, a gateway to atom optics, contains links to the leading references and journals in the field, to research sites, and to updates for the contents of the book. FROM THE REVIEWS: ¿Atom optics today has reached maturity: It has become both wave (coherent) and nonlinear atom optics. Of course that expansion required generalization in a new book. Pierre Meystre has taken just such a generalist approach in his timely ATOM OPTICS. His were the pioneering works in atom optics; to get information from the first explorer is always most valuable to the reader ¿ Recommend[ed] to all strata of the physics community.¿ ¿PHYSICS TODAY

Lie Methods In Optics Ii

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Author: Kurt Bernardo Wolf
Publisher: Springer
ISBN: 9783540521235
Size: 53.10 MB
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Lie Methods In Optics Ii by Kurt Bernardo Wolf

Original Title: Lie Methods In Optics Ii

Recent developments in Lie methods applied to various problems in optics and computer design are surveyed in this volume, based on lectures given and work done at the 1988 workshop held in Cocoyoc, Mexico. Topics discussed include perturbation expansions, the mathematical foundations of coherent optical computing, holographic image and interferometry, neural architecture for pattern recognition, recent progress in symbolic calculations with Lie structures together with applications, the operations of convolution and correlation of signals performed by optical means, wide-angle optics based on the Euclidean group of motions and its relation to the Heisenberg-Weyl approach to canonical quantization. Applications discussed include computer design, particle optics in the Superconducting Supercollider, and neural networks. Computational techniques are emphasized. This volume is an excellent introduction to a rather active field of research and can be recommended to graduate students as well as to researchers.

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