Instabilities and Chaos in Quantum Optics II PDF
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Instabilities and Chaos in Quantum Optics" NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics New York and London C Mathematical Kluwer Academic Publishers and Physical Sciences Dordrecht, Boston, and London o Behavioral and Social Sciences E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris, and Tokyo Recent Volumes in this Series Volume 170-Physics and Applications of Quantum Wells and Superlattices edited by E. E. Mendez and K. von Klitzing Volume 171-Atomic and Molecular Processes with Short Intense Laser Pulses edited by Andre D. Bandrauk Volume 172-Chemical Physics of Intercalation edited by A. P. Legrand and S. Flandrois Volume 173-Particle Physics: Cargese 1987 edited by Maurice Levy, Jean-Louis Basdevant, Maurice Jacob, David Speiser, Jacques Weyers, and Raymond Gastmans Volume 174-Physicochemical Hydrodynamics: Interfacial Phenomena edited by Manuel G. Velarde Volume 175-Superstrings edited by Peter G. o. Freund and K. T. Mahanthappa Volume 176-Nonlinear Evolution and Chaotic Phenomena edited by Giovanni Gallavotti and Paul F. Zweifel Volume 177-lnstabilities and Chaos in Quantum Optics II edited by N. B. Abraham, F. T. Arecchi, and L. A. Lugiato Series B: Physics I nstabi I ities and Chaos in Quantum Optics II Edited by N. B. Abraham Bryn Mawr College Bryn Mawr, Pennsylvania F. T. Arecchi University of Florence and National Institute of Optics Florence, Italy and L. A. Lugiato Turin Polytechnic Turin, Italy Springer Science+Business Media, LLC Proceedings of a NATO Advanced Study Institute on Instabilities and Chaos in Quantum Optics, held June 28-July 7, 1987, in II Ciocco, Italy Library of Congress Cataloging in Publication Data NATO Advanced Study Institute on Instabilities and Chaos in Quantum Optics (1987: II Ciocco, Italy) Instabilities and chaos in quantum optics II. (NATO ASI series. Series B, Physics; v. 177) Proceedings of a NATO Advanced Study Institute on Instabilities and Chaos in Quantum Optics, held in II Ciocco, Italy, June 28-July 7,1987. "Published in cooperation with NATO Scientific Affairs Division." Includes bibliographical references and index. 1. Quantum optics—Congresses. 2. Lasers—Congresses. 3. Masers—Con- gresses. 4. Chaotic behavior in systems—Congresses. 5. Nonlinear opt ics - Congresses. I. Abraham, N. B. (Neal B.) II. Arecchi, F. T. III. Lugiato, L. A. (Luigi A.), 1944- . IV. North Atlantic Treaty Organization. Scientific Affairs Division. V. Title. VI. Series. QC46.15.N35 1987 535 8-12479 ISBN 978-1-4899-2550-3 ISBN 978-1-4899-2548-0 (eBook) DOI 10.1007/978-1-4899-2548-0 © Springer Science+Business Media New York 1988 Originally published by Plenum Press, New York in 1988 Softcover reprint of the hardcover 1st edition 1988 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher PREFACE This volume contains tutorial papers from the lectures and seminars presented at the NATO Advanced Study Institute on "Instabilities and Chaos in Quantum Optics", held at the "Il Ciocco" Conference Center, Castelvecchio Pascoli, Lucca, Italy, June 28-July 7, 1987. The title of the volume is designated Instabilities and Chaos in Quantum Optics II, because of the nearly coincident publication of a collection of articles on research in this field edited by F.T. Arecchi and R.G. Harrison [Instabilities and Chaos in Quantum Optics, (Springer, Berlin, 1987) 1. That volume provides more detailed information about some of these topics. Together they will serve as a comprehensive and tutorial pair of companion volumes. This school was directed by Prof. Massimo Inguscio, of the Department of Physics, University of Naples, Naples, Italy to whom we express our gratitude on behalf of all lecturers and students. The Scientific Advisory Committee consisted of N.B. Abraham of Bryn Mawr College; F.T. Arecchi of the National Institute of Optics in Florence and the University of Florence, and L.A. Lugiato of the Politechnic Institute of Torino. The school continues the long tradition of Europhysics Summer Schools in Quantum Electronics which have provided instruction and training for young researchers and advanced students working in this field for almost twenty years. In addition to the support from the NATO ASI program, support was also received from the following organizations: u.S. National Science Foundation Consiglio Nazionale delle Ricerche, Italy Settore di Fisica Atomica e Molecolare del GNSM Universita di Napoli Universita degli Studi di Pisa Istituto Nazionale di Ottica Bryn Mawr College Lambda-Physik, Gmbh, Gottingen European Office of the U.S. Office of Naval Research (for a special session on transverse effects in optical bistability and instabilities) dB Electronic, Milan Officine Galileo, Firenze European Physical Society (Quantum Electronics Division) IBM (Italy) Ente Nazionale Energie Alternative (ENEA, Italy) Coherent, Inc. Laser Optronics S.R.L. (Italy) Elicam S.R.L. (Italy) MicroControle-Nachet (Italy) v We are grateful for the expert administrative help of Giovanna Inguscio, Iva Arecchi, and Anna Chiara Arecchi in the management of the meeting. We wish to thank all of the lecturers fo·r the clarity of their presentations and to especially thank the contributors to this volume who have helped to enhance its tutorial value and the speed of its production. The school was followed by an International Workshop on Instabilities, Dynamics and Chaos of Nonlinear Optical Systems which welcomed over 120 experts in the field to an intense three-day presentation of their latest research results. The participants in the school who had been prepared by their ten days of study received the added benefit of presentations from and interaction with many other scholars who are contributing to the rapid growth of the field. We are pleased to be able to supplement the tutorial section of this volume with a report of the presentations at the workshop which includes mention of many of their latest results, descriptions of new areas of study, and suggestions of areas where further progress is needed and/or expected. The "Meeting Report" includes many references to where these new results can be found in the research literature. N.B. Abraham F.T. Arecchi L.A. Lugiato December, 1987 vi CONTENTS Laser (and Maser) Instabi~ities 25 YEARS OF LASER INSTABILITIES 1 L.A. Lugiato, L.M. Narducci, J.R. Tredicce, and D.K. Bandy SHIL'NIKOV CHAOS IN LASERS ... 27 F.T. Arecchi INSTABILITIES IN FIR LASERS . . . . . . . . • . . . . . . . . . . . .. 41 C.O. Weiss ANALYSIS OF INSTABILITY AND CHAOS IN OPTICALLY PUMPED THREE LEVEL LASERS . . . 53 R.G. Harrison, J.V. Moloney, J.S. Uppal and W. Forysiak THEORY AND EXPERIMENTS IN THE LASER WITH SATURABLE ABSORBER 69 E. Arimondo GAS LASER INSTABILITIES AND THEIR INTERPRETATION . . . . . . . . . .. 83 L .. W. Casperson EXPERIMENTAL STUDIES OF INSTABILITIES AND CHAOS IN SINGLE-MODE, INHOMOGENEOUSLY BROADENED GAS LASERS ••. 99 N.B. Abraham, M.F.H. Tarroja and R.S. Gioggia MULTISTABILITY AND CHAOS IN A TWO-PHOTON MICROSCOPIC MASER 123 L. Davidovich, J.M. Raimond, M. Brune and S. Haroche BISTABLE BEHAVIOR OF A RELATIVISTIC ELECTRON BEAM IN A MAGNETIC STRUCTURE (WIGGLER). . . . . . . . . . . . . . . . . . . 139 R. Bonifacio and L. De Salvo Souza C~assica~ and Quantum Noise PUMP NOISE EFFECTS IN DYE LASERS . . . . . . . . . . • 147 M. San Miguel QUANTUM CHAOS IN QUANTUM OPTICS: LECTURES ON THE QUANTUM DYNAMICS OF CLASSICALLY CHAOTIC SYSTEMS . . . . • . 163 R. Graham vii Transverse Effects TRANSVERSE EFFECTS IN NONLINEAR OPTICS 193 J.V. Moloney SPATIAL CHAOS IN BISTABLE OPTICAL ARRAYS . • • . . . . . . . . . • . . . 219 W.J. Firth INSTABILITIES IN PASSIVE OPTICAL SYSTEMS: TEMPORAL AND SPATIAL PATTERNS . ...•. . • . . 231 L.A. Lugiato, L.M. Narducci, R. Lefever, and C. Oldano Dynamics in Optical Bistability and Nonlinear Optical Media IKEDA DELAYED-FEEDBACK INSTABILITIES 247 H.M. Gibbs, D.L. Kaplan, F.A. Hopf, M. LeBerre, E. Ressayre and A. Tallet EXPERIMENTAL INVESTIGATION OF THE SINGLE-MODE INSTABILITY IN OPTICAL BISTABILITY . . • 257 A.T. Rosenberger, L.A. Orozco and H.J. Kimble DYNAMICS OF OPTICAL BISTABILITY IN SODIUM AND TRANSIENT BIMODALITY . . . 265 W. Lange OPTICAL BISTABILITY: INTRODUCTION TO NONLINEAR ETALONS GaAs ETALONS AND WAVEGUIDES; REGENERATIVE PULSATIONS ............... 281 H.M. Gibbs SPATIAL AND TEMPORAL INSTABILITIES IN SEMICONDUCTORS • . . • . . . . . . 297 I. Galbraith and H. Haug FOUR-WAVE MIXING AND DYNAMICS 311 W.J. Firth Methods of Analysis in Nonlinear Dynamics BIFURCATION PROBLEMS IN NONLINEAR OPTICS . . . . . . . . . . • . • . . . 321 P. Mandel STRANGE ATTRACTORS: ESTIMATING THE COMPLEXITY OF CHAOTIC SIGNALS • • • 335 R. Badii and A. Politi METHODS OF ADIABATIC ELIMINATION OF VARIABLES IN SIMPLE LASER MODELS . . 363 G.L. Oppo and A. Politi Meeting report: INSTABILITIES, DYNAMICS AND CHAOS IN NONLINEAR OPTICAL SYSTEMS . . . . . 375 N.B. Abraham, E. Arimondo, and R.W. Boyd Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 393 Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 viii 25 YEARS OF LASER INSTABILITIES L.A. Lugiato Dipartimento di Fisica, Politecnico di Torino, Torino, Italy L.M. Narducci, J.R. Tredicce Physics Departtnent, Drexel University, Philadelphia, Pa. 19104 and D.K.Bandy Physics Departtnent, Oklahoma State University, Stillwater, Ok. 74078 The purpose of these lectures is to provide an introduction to the field of laser instabilities and an overview of one of the most popular theoretical models: the homogeneously broadened, unidirectional ring laser system. We discuss both multimode and single-mode operation, the possible steady states and their stability properties. In the process, we identify some valuable features of the plane-wave Maxwell-Bloch equations and single out some of their shortcomings. We conclude this survey with an outline of current attempts at removing the remaining open problems with an extension of the plane-wave theory and the inclusion of transverse effects. 1. Introduction Contrary to what the title of these lectures may suggest, the laser is much older than just 25 years. As I learned in the well known textbook by O. Sveltol (the reader may wish to confmn this with his or her own eyes), the fIrst recorded mention of the laser dates back almost 2000 years ago in the writing of Pliny the Elder (Gaius Plinius Secundus ) who reported that .. Laser. .. inter eximia naturae dona numeratum plurimus compositionibus inseritur .. (The laser is numbered among the most remarkable gifts of nature, and lends itself to a variety of applications; from Historiae Naturalis). The laser was a plant that used to grow on the shores of modem day Lybia. It was a popular ingredient in Roman cuisine, a celebrated tonic and a powerful aid to cure the wounds of enemy arrows and to remove the sting of poisonous insects. With the advance of the Sahara desert to the shores of the Mediterranean sea, the laser became extinct. It was discovered again in 1960. Its modem version is not well known for its culinary virtues, although, under appropriate conditions, it does find medical applications. What makes it interesting from our point of view, however, is its unusual propensity for producing radiation that varies in intensity even under steady or nearly steady pumping conditions. This feature, in fact, caught people's attention from the very early days of the modem era of the laser. The appearance of spiking action, as this pulsing phenomenon is usually called, was observed in maser systems even before the discove(Y of the laser2, but it became a virtually universal feature of solid state optical devices:;. Random spiking, for example, is almost a signature of ruby and neodymium lasers, while beautifully re~ular undamped oscillations have been produced with neodymium lasers in clad optical fibers . It would be only natural to expect that a c.w. pumped laser should produce a steady output, and indeed many lasers can be made to operate in a very stable way. Often,
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