Lasers and Electro-optics

Transcription

1 Lasers and Electro-optics Covering a broad range of topics in modern optical physics and engineering, this textbook is invaluable for undergraduate students studying laser physics, optoelectronics, photonics, applied optics, and optical engineering. This new edition has been re-organized, so that it now covers many new topics such as the optics of stratified media, quantum-well lasers and modulators, free-electron lasers, diode-pumped solid-state and gas lasers, imaging and non-imaging optical systems, squeezed light, periodic poling in nonlinear media, very-short-pulse lasers, and new applications of lasers. The textbook gives a detailed introduction to the basic physics and engineering of lasers, as well as covering the design and operational principles of a wide range of optical systems and electro-optic devices. It features full details of important derivations and results, and provides many practical examples of the design, construction, and performance characteristics of different types of lasers and electro-optic devices. is Minta Martin Professor of Engineering and Professor of Electrical and Computer Engineering at the University of Maryland. He is co-author of the best-selling text Building Scientific Apparatus (fourth edition, Cambridge University Press, 2009).

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3 Lasers and Electro-optics Second Edition CHRISTOPHER C. DAVIS University of Maryland

4 University Printing House, Cambridge CB2 8BS, United Kingdom Published in the United States of America by Cambridge University Press, New York Cambridge University Press is part of the University of Cambridge. It furthers the University s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. Information on this title: / C. Davis 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2014 Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall A catalog record for this publication is available from the British Library Library of Congress Cataloging-in-Publication Data Davis, Christopher C., Lasers and electro-optics /, University of Maryland. Second edition. pages cm Includes bibliographical references and index. ISBN (hardback) 1. Lasers. 2. Electrooptics. I. Title. TA1675.D dc ISBN Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

5 Preface to the Second Edition page xv 1 Electromagnetic waves, light, and lasers The laser Light and electromagnetic waves Some basic electromagnetic theory The polarization state of an electromagnetic wave Electromagnetic waves and their propagation through matter Spontaneous and stimulated transitions Lasers as oscillators The energy levels of atoms, molecules, and condensed matter Amplification at optical frequencies The relation between energy density and intensity The intensity of a beam of electromagnetic radiation in terms of photon flux Black-body radiation The relation between the Einstein A and B coefficients The effect of level degeneracy The ratio of spontaneous and stimulated transitions Problems 30 Further reading 31 References 31 2 Optical frequency amplifiers Introduction Homogeneous line broadening Inhomogeneous broadening Optical frequency amplification Optical frequency oscillation saturation The power output from a laser amplifier The electron oscillator model of a radiative transition The classical oscillator explanation for stimulated emission Problems 69 References 70 v

6 vi 3 An introduction to two practical laser systems Introduction Three- and four-level lasers The ruby laser The helium neon laser 79 References 84 4 Optical resonators containing amplifying media Introduction Optical resonators containing amplifying media The oscillation frequency Multimode laser oscillation Mode-beating The power output of a laser Optimum coupling Problems 107 References Laser radiation Introduction Diffraction Babinet s principle Two parallel narrow slits A single slit Two-dimensional apertures Laser modes Beam divergence The linewidth of laser radiation Coherence properties Interference Problems 130 References Control of laser oscillators Introduction Multimode operation Single-longitudinal-mode operation Mode-locking Methods of mode-locking Pulse compression Attosecond pulses 149 References Optically pumped solid-state lasers Introduction 153

7 vii 7.2 Optical pumping in three- and four-level lasers Pulsed versus continuous-wave operation Threshold population inversion and the stimulated-emission cross-section Paramagnetic-ion solid-state lasers The Nd:YAG laser Continuous-wave operation of the Nd:YAG laser The Nd 3+ glass laser Geometrical arrangements for optical pumping High-power pulsed solid-state lasers Diode-pumped solid-state lasers Fiber lasers Relaxation oscillations (spiking) Rate equations for relaxation oscillation Undamped relaxation oscillations Giant-pulse (Q-switched) lasers A theoretical description of the Q-switching process Problem 203 References Gaslasers Introduction Excitation schemes The argon-ion laser Pumping saturation in gas-laser systems Pulsed gas lasers Continuous-wave ion lasers Metal -vapor ion lasers Gas discharges for exciting gas lasers Rate equations for gas-discharge lasers Problem 228 References Molecular gas lasers I Introduction The energy levels of molecules Vibrations of a polyatomic molecule Rotational energy states Rotational populations The overall energy state of a molecule The carbon dioxide laser The carbon monoxide laser Other gas-discharge molecular lasers 251 References 251

8 viii 10 Molecular gas lasers II Introduction Gas transport lasers Gas dynamic lasers High-pressure pulsed gas lasers Ultraviolet molecular gas lasers Photodissociation lasers Chemical lasers Far-infrared lasers Problem 274 References Tunable lasers Introduction The titanium sapphire laser Organic dye lasers Calculation of threshold pump power in dye lasers Inorganic liquid lasers Free-electron lasers Problems 298 References Semiconductor lasers Introduction Semiconductor physics background Carrier concentrations Intrinsic and extrinsic semiconductors The p n junction Recombination and luminescence Heterojunctions Semiconductor lasers The gain coefficient of a semiconductor laser Threshold current and power voltage characteristics Longitudinal and transverse modes Quantum-well lasers Semiconductor laser structures Surface-emitting lasers Laser diode arrays and broad-area lasers Blue green lasers Quantum cascade lasers Silicon lasers Modulation of semiconductor lasers Problems 356

9 ix Further reading 357 References Passive optical systems Introduction The propagation of rays and waves through isotropic media Simple reflection and refraction analysis Paraxial-ray analysis Non-imaging light collectors Generalized imaging systems The numerical aperture Apertures, stops, and pupils Vignetting Exact ray tracing and aberrations Chromatic aberrations Geometrical aberrations Spot diagram The modulation transfer function The use of impedances in optics Problems 406 References Periodic optical systems, resonators, and inhomogeneous media Introduction Plane waves in media with complex refractive indices Negative-refractive-index materials Structures with periodically varying dielectric properties The transfer matrix for a single slab The etalon A thin metal film A stratified medium of multiple slabs Fiber Bragg gratings Analysis of multi-layer structures by impedance techniques Photonic crystals Periodic lens sequences The identical-thin-lens waveguide The propagation of rays in mirror resonators The propagation of rays in isotropic media with refractive-index gradients Media with a Gaussian radial index variation The propagation of spherical waves Problems 436 References The optics of Gaussian beams Introduction 438

10 x 15.2 Beam-wave solutions of the wave equation Higher-order modes Transformation of Gaussian beams by general optical systems The transformation of a Gaussian beam by a lens Gaussian beams in lens waveguides The propagation of a Gaussian beam in a medium with a quadratic refractive-index profile The propagation of Gaussian beams in media with spatial gain or absorption variations Propagation in a medium with a parabolic gain profile Gaussian beams in plane and spherical mirror resonators Symmetrical resonators Examples of resonator design Diffraction losses Unstable resonators Other beam waves Problems 478 References Optical fibers and waveguides Introduction Ray theory of cylindrical optical fibers Ray theory of a dielectric-slab guide The Goos Hänchen shift Wave theory of the dielectric-slab guide P waves in the slab guide Dispersion curves and field distributions in a slab waveguide S waves in the slab guide Practical slab guide geometries Cylindrical dielectric waveguides Modes and field patterns The weakly guiding approximation Mode patterns Cutoff frequencies Multimode fibers Fabrication of optical fibers Dispersion in optical fibers Holey fibers Solitons Erbium-doped fiber amplifiers Coupling optical sources and detectors to fibers Problems 535 References 536

11 xi 17 The optics of anisotropic media Introduction The dielectric tensor Stored electromagnetic energy in anisotropic media Propagation of monochromatic plane waves in anisotropic media The two possible directions of D for a given wave vector are orthogonal Angular relationships involving D, E, H, k, and the Poynting vector S The indicatrix Uniaxial crystals Index surfaces Other surfaces related to the uniaxial indicatrix Huygenian constructions Retardation Biaxial crystals Intensity transmission through polarizer/waveplate/polarizer combinations The Jones calculus Mueller calculus Problems 578 References The electro-optic and acousto-optic effects and modulation of light beams Introduction to the electro-optic effect The linear electro-optic effect The quadratic electro-optic effect Longitudinal electro-optic modulation Transverse electro-optic modulation Electro-optic amplitude modulation Electro-optic phase modulation High-frequency waveguide electro-optic modulators Other high-frequency electro-optic devices Electro-absorption modulators Electro-optic beam deflectors Acousto-optic modulators Applications of acousto-optic modulators Construction and materials for acousto-optic modulators Problem 620 References Introduction to nonlinear processes Introduction Anharmonic potentials and nonlinear polarization Nonlinear susceptibilities and mixing coefficients Second-harmonic generation 629

12 xii 19.5 The linear electro-optic effect Parametric and other nonlinear processes Macroscopic and microscopic susceptibilities Problem 638 References Wave propagation in nonlinear media Introduction Electromagnetic waves and nonlinear polarization Second-harmonic generation The effective nonlinear coefficient d eff Phase matching Beam walk-off and 90 phase matching Second-harmonic generation with Gaussian beams Up-conversion and difference-frequency generation Optical parametric amplification Parametric oscillators Parametric-oscillator tuning Phase conjugation Optical bistability Practical details of the use of crystals for nonlinear applications Problems 680 References Detection of optical radiation Introduction Noise Detector performance parameters Practical characteristics of optical detectors Thermal detectors Detection limits for optical detector systems Coherent detection The bit-error rate Problems 733 References Coherence theory Introduction Square-law detectors The analytic signal Correlation functions Temporal coherence Spatial coherence Spatial coherence with an extended source 751

13 xiii 22.8 Propagation laws of partial coherence Propagation from a finite plane surface The van Cittert Zernike theorem The spatial coherence of a quasi-monochromatic, uniform, spatially incoherent circular source Intensity-correlation interferometry Intensity fluctuations Photon statistics The Hanbury Brown Twiss interferometer The Hanbury Brown Twiss experiment with photon-count correlations Squeezed light 780 References Laser applications Optical communication systems Optical amplification and wavelength-division multiplexing Holography Medical applications of lasers Laser weapons Laser isotope separation Laser plasma generation and fusion 813 References 816 Appendix 1 Optical terminology 821 Appendix 2 The δ-function 824 Appendix 3 Black-body radiation formulas 826 Appendix 4 RLC circuits 828 Appendix 5 Storage and transport of energy by electromagnetic fields 831 Appendix 6 The reflection and refraction of a plane electromagnetic wave at a boundary between two isotropic media of different refractive indices 834 Appendix 7 The vector differential equation for light rays 837 Appendix 8 Symmetry properties of crystals and the 32 crystal classes 841 Appendix 9 Tensors 845 Appendix 10 Bessel-function relations 848 Appendix 11 Green s functions 849 Appendix 12 Recommended values of some physical constants 852 Index 853

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15 Preface to the Second Edition xv The author of a text generally feels obligated to explain the reasons for his or her writing. This is a matter of tradition as it provides an opportunity for explaining the development and philosophy of the text, its subject matter and intended audience, and acknowledges the help that the author has received. In the case of a second edition of a text, as is the case here, a new preface provides an opportunity for the author to explain the revisions of the second edition and to further acknowledge help from colleagues. I hope to accomplish these tasks briefly here. The first edition of this text grew over many years out of notes that I had developed for courses at the senior undergraduate and beginning graduate student level at the University of Manchester, Cornell University, and the University of Maryland, College Park. These courses covered many aspects of laser physics and engineering, the practical aspects of optics that pertain to an understanding of these subjects, and a discussion of related phenomena and devices whose importance has grown from the invention of the laser in These include nonlinear optics, electro-optics, acousto-optics, and the devices that take practical advantage of these phenomena. The names given to the fields that encompass such subject matter have included laser physics, optical electronics, optoelectronics, photonics, and quantum electronics. The fundamentals of these subjects have not changed significantly in the years that have intervened since the publication of the first edition. However, there have been important technological advances that need discussion, as well as new laser applications. A few important new topic areas now included are fiber lasers, aberrations in optical systems, stratified media, photonic crystals, periodic poling for phase matching, and new methods for obtaining laser pulses of very short duration. Expanded discussion is provided about diode-pumped solid-state lasers, free-electron lasers, semiconductor physics, semiconductor lasers, photon statistics, squeezed light, and analysis of polarized light. This is a textbook, not a research monograph, although I have attempted to provide enough detail to help researchers obtain the background necessary for exploration of more specialized literature. After teaching this material for over 40 years I hope that I have found helpful ways to make the subject understandable to students. I have certainly benefited greatly from their feedback, which has contributed to the changes in this second edition. Although a comprehensive understanding of the laser and associated phenomena requires a quantum-mechanical treatment, almost all aspects of laser operation and important related phenomena can be explained well classically. Therefore, this text requires no knowledge of quantum mechanics, although a background in electromagnetic theory at the undergraduate level is desirable for a greater understanding. Most electrical engineering majors do not take a course in quantum mechanics until they reach graduate level, and many physics majors will not have acquired sufficient quantum mechanics knowledge at

16 xvi Preface to the Second Edition the undergraduate level for this to make a meaningful contribution to better understanding in a study of lasers and electro-optics. For all the above reasons this text should be suitable for senior undergraduate and beginning graduate students in electrical engineering or physics. It should also prove useful to other engineers or chemists who use lasers and electro-optic devices. The text is broken up into two principal parts. Chapters 1 12 discuss the basic physics and engineering of lasers of all kinds, beginning with a discussion of the fundamental physics of the stimulated emission process and laser amplifiers. This is followed by chapters on laser resonators and the characteristics of laser radiation and methods for controlling it. There are succeeding chapters that cover optically pumped insulating crystal lasers, atomic gas lasers, and molecular gas lasers of various kinds including gas transport, gas dynamics and chemically pumped varieties, and tunable lasers. The first section of the book concludes with a chapter on semiconductor lasers that begins with a review of the basic physics necessary for their understanding. The second part of the text covers various issues of relevance to lasers and electrooptics, including optical analysis and design techniques, the optics of Gaussian beams, laser resonators, and anisotropic crystalline materials. There are chapters on optical fibers, electro-optic and acousto-optic devices, the fundamentals of nonlinear optics, and application of nonlinear optics in harmonic generation, parametric processes, phase conjugation, and optical bistability. The text concludes with chapters on optical detectors and the detection process, coherence theory, and applications of lasers. I have found that Chapters 1 12 provide sufficient material for a one semester course on lasers, with some applications from Chapter 23 included. Chapters 5 and 13 18, together with Chapter 22, form the basis of a one-semester course on optical design, electrooptic devices, and optical detectors. I draw on the somewhat more difficult material in Chapters as reference material in both the one-semester courses just mentioned, and also as adjunct material in more advanced graduate courses. I have been an experimentalist in the optics and laser business for over four decades. I have always found the laser itself a fascinating device that provides a teaching vehicle for discussing many fundamental physics concepts as well as practical aspects of optical design. I have always tried to introduce practical details of real lasers into my classes as early as a treatment of some of the associated fundamentals permits. This should be apparent in the current text where I digress in Chapter 3 into a fairly detailed practical discussion of two historically important lasers, even though contextually a fuller discussion of these devices could be left until later. I believe that this makes pedagogical sense as students get a glimpse of where they are headed. Throughout the text I have attempted to provide full details of important derivations, and provide practical examples from the literature on the design, construction, and performance characteristics of lasers and electrooptic devices. In developing a sound approach to teaching the material in this text to many students over more than four decades I have drawn inevitably on the work of many others. There have been many other books that cover material that is shared in common with the current one. What is different between this and related texts is not so much the analytic treatment of common subject matter, but the specific choice of material presentation sequence, and

17 xvii Preface to the Second Edition assorted explanations. As it is said, there is nothing new under the sun, so it is not the intent of this author to claim that the treatment of particular topics in the current text is necessarily unique. Different authors impart their own slant to the same subject matter: sometimes their treatments converge, particularly when there is one especially good way of explanation that is valid. I have attempted in every case to provide references to the original literature from which I have benefited in my writing, and I apologize for any inadvertent omissions. There is a vast literature on the subjects covered and would be it impossible to list all the important published work that has added to our knowledge. I have attemped to list key early work in each area covered, since use of the Science Citations Index 1 will in this way provide links to almost all the work in an area. Over the course of many years I have learned much from my contacts in the classroom, office, and research laboratory, and at conferences. I am indebted to numerous past and present colleagues and students for their intellectual stimulation, collaboration in research, advice, provision of material, and feedback on early versions of the current text that have contributed greatly to the finished product. I would like to thank especially my past and present faculty colleagues Quirino Balzano, Kyuman Cho, Mario Dagenais, Julius Goldhar, Ping-Tong Ho, the late Urs Hochuli, Terry King, Chi Lee, Ross McFarlane, Stuart Milner, Ian Smith, Igor Smolyaninov; and finally George Wolga who gave me valuable help at the very beginning of this work. I am especially grateful to Professor Thomas Murphy for his helpful comments on how to treat the topic of semiconductor lasers, which just on its own could fill many volumes. My graduate students and post-doctoral research associates have over several years provided help and advice that have helped me greatly. I am particularly grateful to Navik Agrawal, David Coleman, Mohammed Eslami, Ehren Hwang, Jonathan Ko, Jaime Llorca, Billy Nelson, John Rzasa, Tommy Shen, and Chensheng Wu, for their current help with my research that has provided the time to finish this new edition. I am most grateful to Joan Hamilton and Nono Kusuma for drawing many of the diagrams and to Dave Mazzoni and Sarah Fish for help with additional diagrams. I appreciate the patience of several editors at Cambridge University Press in waiting for completion of this second edition, and for accepting ongoing excuses as to why it was not completed earlier. I am most grateful to Patricia Keehn for her expert and careful computer typesetting work using TEX over enormous numbers of revisions of the first edition. 2 Most of all, I am indebted to my family, especially my wife Mary, for their unfailing love and support over the course of my career. College Park, Maryland November Part of the Web of Science, a subscription data base that is widely available: web-of-science/ 2 In most cases where curves showing the parametric variation of phenomena discussed in the text are given these have been calculated from scratch using Mathcad ( Mathsoft, Inc.) The entire text has been typeset using Donald Knuth s TEX: The TEXbook, Addison-Wesley, Reading, MA, TEX is a trademark of the American Mathematical Society.