Bellingham, Washington USA Library of Congress Cataloging-in-Publication Data Ostrovsky, Andrey S. Coherent-mode representations in optics / Andrey S. Ostrovsky. p. cm. -- (SPIE monograph ; pm 164) Includes bibliographical references and index. ISBN 0-8194-6350-7 1. Coherence (Optics). 2. Physical optics. I. Title. II. Series. QC476.C6O77 2006 535'.2--dc22 2006011409 Published by SPIE—The International Society for Optical Engineering P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1 360 676 3290 Fax: +1 360 647 1445 Email: [email protected] Web: http://spie.org Copyright © 2006 The Society of Photo-Optical Instrumentation Engineers All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher. The content of this book reflects the work and thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. Printed in the United States of America. Tothememoryofmymother,AllaBurjinskayaOstrovskaya, andmyfather,SergeyOstrovsky. Contents Preface ix Chapter1 Coherent-ModeRepresentationofOpticalFieldsand Sources 1 1.1 Introduction 1 1.2 FoundationsoftheCoherenceTheoryintheSpace-FrequencyDomain 1 1.3 Coherent-ModeStructureoftheField 5 1.4 EnsembleRepresentationoftheCross-SpectralDensityFunction 7 1.5 EffectiveNumberofCoherentModes 9 1.6 Coherent-ModeRepresentationsofSomeModelSources 10 1.6.1 GaussianSchell-modelsource 11 1.6.2 Bessel-correlatedsource 12 1.6.3 Lambertiansource 13 1.7 ConcludingRemarks 14 Chapter2 Coherent-ModeRepresentationofOpticalSystems 15 2.1 Introduction 15 2.2 BilinearSystemsinOptics 16 2.3 Coherent-ModeRepresentationsofaBilinearSystem 19 2.4 FastAlgorithmforBilinearTransformsinOptics 22 2.5 NumericalSimulation 24 2.6 ConcludingRemarks 28 Chapter3 Coherent-ModeRepresentationofPropagation-Invariant Fields 31 3.1 Introduction 31 3.2 Propagation-InvariantFields 32 3.3 Coherent-ModeStructureofthePropagation-InvariantField 34 3.4 SpecialClassesofPropagation-InvariantFields 37 3.4.1 Propagation-invariantfieldsofthefirstkind 37 3.4.2 Propagation-invariantfieldsofthesecondkind 38 3.4.3 Propagation-invariantfieldsofthethirdkind 40 3.5 GenerationofPropagation-InvariantFields 42 3.6 PhysicalSimulation 47 3.7 ConcludingRemarks 50 Chapter4 Coherent-ModeRepresentationsinRadiometry 51 4.1 Introduction 51 4.2 GeneralizedRadiantFlux 53 4.3 Coherent-ModeRepresentationofRadiometricQuantities 55 vii viii Coherent-ModeRepresentationsinOptics 4.4 Free-SpacePropagationofModalRadiance 58 4.5 ModalRadiometryofGaussianSchell-ModelSource 61 4.6 ConcludingRemarks 63 Chapter5 AlternativeCoherent-ModeRepresentationofaPlanar Source 65 5.1 Introduction 65 5.2 AlternativeSourceanditsCoherent-ModeStructure 65 5.3 ChoiceoftheAlternativeModalBasis 68 5.3.1 Hermitianbasis 68 5.3.2 Besselbasis 69 5.4 NumericalSimulation 71 5.5 ConcludingRemarks 72 References 75 IndextoReferencedAuthors 84 Subjectindex 85 Preface 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 ofPartialCoherence(ProgressinOpticsIII,E.Wolf,ed.,North-Holland,Amster- dam, 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.Fromaphysicalpointofview,thecoherent-moderepresentationdescribes anopticalfieldofanystateofcoherenceasalinearsuperpositionofuncorrelated, completely coherent modes, a fact that gives new insight into the physics of gen- eration,propagation,andtransformationofopticalradiation.Fromamathematical 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 simplifica- tion of the analysis of statistical optical processes and systems. However, to my mind,thecoherent-moderepresentationofopticalfields,despiteitspowerandat- tractiveness, 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 Opti- calCoherenceandQuantumOpticsbyL.MandelandE.Wolf,lessthantwodozen pagesarededicatedtothissubject. 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 thetotalscopeofthesubject,italsocontainssomeresultsofotherauthors,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 developmentofthecoherent-moderepresentationsinopticsandtheirpracticalap- plications. There are many people to whom I owe a special word of thanks for their help with the creation of this book. First of all, I consider it my pleasant duty to mention here the scientists whose publications had a decisive influence on the results presented in the book. Listed in alphabetical order, they are: G. S. Agar- wal, W. Carter, J. Durnin, J. Duvernoy, J. T. Foley, A. T. Friberg, H. Gamo, ix