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Spie Press Book

Coherent-Mode Representations in Optics
Author(s): Andrey S. Ostrovsky
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Book Description

This book provides you with a single source of information on the problem of coherent-mode representations in optics, including new perspectives on its potential applications. In particular, the "light string" and the "light capillary" beams may be advantageously used in communications, measurements, laser microtechnology, and microsurgery; application of the fast algorithm for bilinear transforms can significantly reduce the computer effort needed to simulate optical systems with partially coherent illumination.

Book Details

Date Published: 6 June 2006
Pages: 98
ISBN: 9780819463500
Volume: PM164

Table of Contents
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Preface ix
Chapter 1 Coherent-Mode Representation of Optical Fields and Sources 1
1.1 Introduction 1
1.2 Foundations of the Coherence Theory in the Space-Frequency Domain 1
1.3 Coherent-Mode Structure of the Field 5
1.4 Ensemble Representation of the Cross-Spectral Density Function 7
1.5 Effective Number of Coherent Modes 9
1.6 Coherent-Mode Representations of Some Model Sources 10
1.6.1 Gaussian Schell-model source 11
1.6.2 Gaussian Schell-model source 11
1.6.3 Bessel-correlated source 12
1.6.4 Lambertian source 13
1.7 Concluding Remarks 14
Chapter 2 Coherent-Mode Representation of Optical Systems 15
2.1 Introduction 15
2.2 Bilinear Systems in Optics 16
2.3 Coherent-Mode Representations of a Bilinear System 19
2.4 Fast Algorithm for Bilinear Transforms in Optics 22
2.5 Numerical Simulation 24
2.6 Concluding Remarks 28
Chapter 3 Coherent-Mode Representation of Propagation-Invariant Fields 31
3.1 Introduction 31
3.2 Propagation-Invariant Fields 32
3.3 Coherent-Mode Structure of the Propagation-Invariant Field 34
3.4 Special Classes of Propagation-Invariant Fields 37
3.4.1 Propagation-invariant fields of the first kind 37
3.4.2 Propagation-invariant fields of the second kind 38
3.4.3 Propagation-invariant fields of the third kind 40
3.5 Generation of Propagation-Invariant Fields 42
3.6 Physical Simulation 47
3.7 Concluding Remarks 50
Chapter 4 Coherent-Mode Representations in Radiometry 51
4.1 Introduction 51
4.2 Generalized Radiant Flux 53
4.3 Coherent-Mode Representation of Radiometric Quantities 55
4.4 Free-Space Propagation of Modal Radiance 58
4.5 Modal Radiometry of Gaussian Schell-Model Source 61
4.6 Concluding Remarks 63
Chapter 5 Alternative Coherent-Mode Representation of a Planar Source 65
5.1 Introduction 65
5.2 Alternative Source and its Coherent-Mode Structure 65
5.3 Choice of the Alternative Modal Basis 68
5.3.1 Hermitian basis 68
5.3.2 Bessel basis 69
5.4 Numerical Simulation 71
5.5 Concluding Remarks 72
References 75
Author index 84
Subject index 85


Everyone knows the fundamental role that the Fourier transform plays in optics, representing a monochromatic light field as a linear superposition of plane waves propagating in different directions. Perhaps, the coherent-mode representation of the optical field broached for the first time by H. Gamo in his Matrix Treatment of Partial Coherence (Progress in Optics III, E. Wolf, ed., North-Holland, Amsterdam, 1964), which was later developed by E. Wolf in his New theory of partial coherence in the space-frequency domain (J. Opt. Soc. Am. A, Vol. 72, No. 3, 1982, and Vol. 3, No. 1, 1986), plays a not less important role in contemporary optics. From a physical point of view, the coherent-mode representation describes an optical field of any state of coherence as a linear superposition of uncorrelated, completely coherent modes, a fact that gives new insight into the physics of generation, propagation, and transformation of optical radiation. From a mathematical standpoint, it expresses the cross-spectral density function of an optical field as a sum of terms that are separable in space, a fact that allows significant simplification of the analysis of statistical optical processes and systems. However, to my mind, the coherent-mode representation of optical fields, despite its power and attractiveness, has not yet found its due place in optical science and practice. This is affirmed, in particular, by a relatively small number of publications where the coherent-mode representation is treated. Even in a monumental treatise like Optical Coherence and Quantum Optics by L. Mandel and E.Wolf, less than two dozen pages are dedicated to this subject.

The present book represents a modest attempt to make up, to a certain extent, for a deficiency in possible applications of the coherent-mode representations in several areas of optics. This book is mainly based on the original results obtained by the author and his postgraduate students but, to ensure a thorough coverage of the total scope of the subject, it also contains some results of other authors, which are properly referenced. I tried to present this book in a brief recapitulative form, handy for both professionals and postgraduate students in physical optics. I hope that the book will be interesting for the reader and will stimulate the subsequent development of the coherent-mode representations in optics and their practical applications.

The main part of the writing was done at the Physics and Mathematics Department of the Autonomous University of Puebla, Mexico. I am grateful to M.Sc. E. Doger Guerrero, former Rector of the University, M.Sc. E. Aguera Ibanez, current Rector, Dr. P. H. Hernandez Tejeda, Vice-Rector, and Dr. C. Ramirez Romero, Head of the Department, for providing the excellent facilities for my work. Part of the text was prepared during my sabbatical leave at the National Institute of Astronomy, Optics, and Electronics, Mexico. I acknowledge my indebtedness to Dr. J. S. Guichard Romero, Director of the Institute, Dr. J. F. Soto Eguibar, Deputy Director, and G. Martinez Niconoff, former Coordinator of the Optical Division, for their hospitality and fruitful collaboration. The work on the book was partially supported by the National Council for Science and Technology (CONACYT) of Mexico under the projects 3644-E, 25841-E, and 36875-E; this is much appreciated.

Andrey S. Ostrovsky
April 2006

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