Copyrighted Material Wiley Series in Pure and Applied Opties.Glenn D.Boreman.Series Editor Ultrafast Optics ANDREW M.WEINER -8 0 ③WILEY Copyrighted Material
Copyright 2009 by John Wiley Sons,Inc.All rights reserved. Published by John Wiley Sons,Inc.,Hoboken,New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced,stored in a retrieval system,or transmitted in any form or by any means,electronic,mechanical,photocopying,recording,scanning,or otherwise,except as permitted under Section 107 or 108 of the 1976 United States Copyright Act,without either the prior written permission of the Publisher,or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center Inc.,222 Rosewood Drive,Danvers,MA 01923,(978)750-8400,fax (978)750-4470,or on the web at www.copyright.com.Requests to the Publisher for permission should be addressed to the Permissions Department,John Wiley Sons,Inc.,111 River Street,Hoboken,NJ 07030,(201)748-6011,fax (201) 748-6008,or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty:While the publisher and author have used their best efforts in preparing this book,they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose.No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation.You should consult with a professional where appropriate.Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages,including but not limited to special,incidental,consequential,or other damages. For general information on our other products and services or for technical support.please contact our Customer Care Department within the United States at (800)762-2974,outside the United States at (317)572-3993 or fax(317)572-4002. Wiley also publishes its books in a variety of electronic formats.Some content that appears in print may not be available in electronic formats.For more information about Wiley products,visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Weiner,Andrew Marc Ultrafast optics /Andrew M.Weiner. p.cm. Includes bibliographical references and index. ISBN978-0-471-41539-8(cloth) 1.Laser pulses,Ultrashort.2.Laser pulses,Ultrashort-Industrial applications. 3.Mode-locked lasers.4.Nonlinear optical spectroscopy.5.Nonlinear optics.I.Title QC689.5.L37W452009 621.366-dc22 2008052027 Printed in the United States of America 10987654321
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Weiner, Andrew Marc Ultrafast optics / Andrew M. Weiner. p. cm. Includes bibliographical references and index. ISBN 978-0-471-41539-8 (cloth) 1. Laser pulses, Ultrashort. 2. Laser pulses, Ultrashort–Industrial applications. 3. Mode-locked lasers. 4. Nonlinear optical spectroscopy. 5. Nonlinear optics. I. Title. QC689.5.L37W45 2009 621.36’6–dc22 2008052027 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
CONTENTS Preface xii 1 Introduction and Review 1.1 Introduction to Ultrashort Laser Pulses,1 1.2 Brief Review of Electromagnetics,4 1.2.1 Maxwell's Equations,4 1.2.2 The Wave Equation and Plane Waves,6 1.2.3 Poynting's Vector and Power Flow,8 1.3 Review of Laser Essentials,10 1.3.1 Steady-State Laser Operation,10 1.3.2 Gain and Gain Saturation in Four-Level Atoms,15 1.3.3 Gaussian Beams and Transverse Laser Modes,17 1.4 Introduction to Ultrashort Pulse Generation Through Mode-Locking.22 1.5 Fourier Series and Fourier Transforms,25 1.5.1 Analytical Aspects,25 1.5.2 Computational Aspects,28 Problems.30 2 Principles of Mode-Locking 32 2.1 Processes Involved in Mode-Locking,32 2.2 Active Mode-Locking,33 2.2.1 Time-Domain Treatment,34 2.2.2 Frequency-Domain Treatment,40 2.2.3 Variations of Active Mode-Locking.43 2.3 Passive Mode-Locking Using Saturable Absorbers,44 2.3.1 Saturation Model,47 2.3.2 Slow Saturable Absorber Mode-Locking,50 2.3.3 Fast Saturable Absorber Mode-Locking,54 vii
CONTENTS Preface xiii 1 Introduction and Review 1 1.1 Introduction to Ultrashort Laser Pulses, 1 1.2 Brief Review of Electromagnetics, 4 1.2.1 Maxwell’s Equations, 4 1.2.2 The Wave Equation and Plane Waves, 6 1.2.3 Poynting’s Vector and Power Flow, 8 1.3 Review of Laser Essentials, 10 1.3.1 Steady-State Laser Operation, 10 1.3.2 Gain and Gain Saturation in Four-Level Atoms, 15 1.3.3 Gaussian Beams and Transverse Laser Modes, 17 1.4 Introduction to Ultrashort Pulse Generation Through Mode-Locking, 22 1.5 Fourier Series and Fourier Transforms, 25 1.5.1 Analytical Aspects, 25 1.5.2 Computational Aspects, 28 Problems, 30 2 Principles of Mode-Locking 32 2.1 Processes Involved in Mode-Locking, 32 2.2 Active Mode-Locking, 33 2.2.1 Time-Domain Treatment, 34 2.2.2 Frequency-Domain Treatment, 40 2.2.3 Variations of Active Mode-Locking, 43 2.3 Passive Mode-Locking Using Saturable Absorbers, 44 2.3.1 Saturation Model, 47 2.3.2 Slow Saturable Absorber Mode-Locking, 50 2.3.3 Fast Saturable Absorber Mode-Locking, 54 vii
viii CONTENTS 2.4 Solid-State Laser Mode-Locking Using the Optical Kerr Effect,57 2.4.1 Nonlinear Refractive Index Changes,57 2.4.2 Self-Amplitude Modulation,Self-Phase Modulation,and Group Velocity Dispersion,58 2.4.3 Additive Pulse Mode-Locking,60 2.4.4 Kerr Lens Mode-Locking,64 2.4.5 Mode-Locking Solutions,75 2.4.6 Initiation of Mode-Locking,81 Problems,83 3 Ultrafast-pulse Measurement Methods 85 3.1 Terminology and Definitions,85 3.2 Electric Field Autocorrelation Measurements and the Power Spectrum,88 3.3 Electric Field Cross-Correlation Measurements and Spectral Interferometry,91 3.3.1 Electric Field Cross-Correlation.92 3.3.2 Spectral Interferometry,93 3.3.3 Application:Optical Coherence Tomography,96 3.4 Intensity Correlation Measurements,99 3.4.1 Correlation Measurements Using Second-Harmonic Generation,99 3.4.2 Experimental Procedures,108 3.4.3 Correlation Measurements Using Two-Photon absorption,110 3.4.4 Higher-Order Correlation Techniques,111 3.5 Chirped Pulses and Measurements in the Time-Frequency Domain,112 3.6 Frequency-Resolved Optical Gating,118 3.6.1 Polarization-Gating FROG.119 3.6.2 Self-Diffraction FROG.122 3.6.3 Second-Harmonic-Generation FROG,124 3.6.4 Frequency-Resolved Optical Gating Using Temporal Phase Modulation,125 3.6.5 Signal Recovery from FROG Traces,126 3.7 Pulse Measurements Based on Frequency Filtering.130 3.7.1 Single-Slit Approaches,131 3.7.2 Double-Slit Approach,134 3.8 Self-Referencing Interferometry,135 3.8.1 Time-Domain Interferometry of Chirped Pulses,135 3.8.2 Self-Referencing Spectral Interferometry,137 3.9 Characterization of Noise and Jitter,139 Problems,144 4 Dispersion and Dispersion Compensation 147 4.1 Group Velocity Dispersion,147 4.1.1 Group Velocity Definition and General Dispersion Relations,147 4.1.2 General Aspects of Material Dispersion,151 4.2 Temporal Dispersion Based on Angular Dispersion,155 4.2.1 Relation Between Angular and Temporal Dispersion,155 4.2.2 Angular Dispersion and Tilted Intensity Fronts,159 4.3 Dispersion of Grating Pairs,161
viii CONTENTS 2.4 Solid-State Laser Mode-Locking Using the Optical Kerr Effect, 57 2.4.1 Nonlinear Refractive Index Changes, 57 2.4.2 Self-Amplitude Modulation, Self-Phase Modulation, and Group Velocity Dispersion, 58 2.4.3 Additive Pulse Mode-Locking, 60 2.4.4 Kerr Lens Mode-Locking, 64 2.4.5 Mode-Locking Solutions, 75 2.4.6 Initiation of Mode-Locking, 81 Problems, 83 3 Ultrafast-pulse Measurement Methods 85 3.1 Terminology and Definitions, 85 3.2 Electric Field Autocorrelation Measurements and the Power Spectrum, 88 3.3 Electric Field Cross-Correlation Measurements and Spectral Interferometry, 91 3.3.1 Electric Field Cross-Correlation, 92 3.3.2 Spectral Interferometry, 93 3.3.3 Application: Optical Coherence Tomography, 96 3.4 Intensity Correlation Measurements, 99 3.4.1 Correlation Measurements Using Second-Harmonic Generation, 99 3.4.2 Experimental Procedures, 108 3.4.3 Correlation Measurements Using Two-Photon absorption, 110 3.4.4 Higher-Order Correlation Techniques, 111 3.5 Chirped Pulses and Measurements in the Time–Frequency Domain, 112 3.6 Frequency-Resolved Optical Gating, 118 3.6.1 Polarization-Gating FROG, 119 3.6.2 Self-Diffraction FROG, 122 3.6.3 Second-Harmonic-Generation FROG, 124 3.6.4 Frequency-Resolved Optical Gating Using Temporal Phase Modulation, 125 3.6.5 Signal Recovery from FROG Traces, 126 3.7 Pulse Measurements Based on Frequency Filtering, 130 3.7.1 Single-Slit Approaches, 131 3.7.2 Double-Slit Approach, 134 3.8 Self-Referencing Interferometry, 135 3.8.1 Time-Domain Interferometry of Chirped Pulses, 135 3.8.2 Self-Referencing Spectral Interferometry, 137 3.9 Characterization of Noise and Jitter, 139 Problems, 144 4 Dispersion and Dispersion Compensation 147 4.1 Group Velocity Dispersion, 147 4.1.1 Group Velocity Definition and General Dispersion Relations, 147 4.1.2 General Aspects of Material Dispersion, 151 4.2 Temporal Dispersion Based on Angular Dispersion, 155 4.2.1 Relation Between Angular and Temporal Dispersion, 155 4.2.2 Angular Dispersion and Tilted Intensity Fronts, 159 4.3 Dispersion of Grating Pairs, 161
CONTENTS 年 4.4 Dispersion of Prism Pairs,166 4.5 Dispersive Properties of Lenses.173 4.6 Dispersion of Mirror Structures,177 4.6.1 The Gires-Tournois Interferometer,178 4.6.2 Quarter-Wave Stack High Reflectors,180 4.6.3 Chirped Mirrors,182 4.7 Measurements of Group Velocity Dispersion,186 4.7.1 Interferometric Methods,187 4.7.2 Frequency-Domain Intracavity Dispersion Measurements,190 4.8 Appendix,191 4.8.1 Frequency-Dependent Phase Due to Propagation Through a Slab: Alternative Derivation,191 4.8.2 Impedance Method for Analysis of Dielectric Mirror Stacks,192 Problems,195 5 Ultrafast Nonlinear Optics:Second Order 198 5.1 Introduction to Nonlinear Optics,198 5.2 The Forced Wave Equation,201 5.2.1 Frequency-Domain Formulation,202 5.2.2 Time-Domain Formulation,203 5.3 Summary of Continuous-Wave Second-Harmonic Generation,204 5.3.1 Effect of Phase Matching,207 5.3.2 Phase Matching in Birefringent Media,209 5.3.3 Focusing Effects in Continuous-Wave SHG,215 5.4 Second-Harmonic Generation with Pulses,220 5.4.1 SHG in the Quasi-Continuous-Wave Limit,220 5.4.2 Ultrashort-Pulse SHG,221 5.4.3 Quasi-Phase Matching,228 5.4.4 Effect of Group Velocity Walk-off on SHG-Based Pulse Measurements.233 5.5 Three-Wave Interactions,237 5.5.1 Sum Frequency Generation,240 5.5.2 Difference Frequency Generation,244 5.5.3 Optical Parametric Amplification,245 5.6 Appendix,253 5.6.1 Spatial Walk-off and Pulse Fronts in Anisotropic Media,253 5.6.2 Velocity Matching in Broadband Noncollinear Three-Wave Mixing,254 Problems,256 6 Ultrafast Nonlinear Optics:Third Order 258 6.1 Propagation Equation for Nonlinear Refractive Index Media,258 6.1.1 Plane Waves in Uniform Media,260 6.1.2 Nonlinear Propagation in Waveguides,261 6.1.3 Optical Fiber Types,264 6.2 The Nonlinear Schrodinger Equation,266 6.3 Self-Phase Modulation,270 6.3.1 Dispersionless Self-Phase Modulation,270 6.3.2 Dispersionless Self-Phase Modulation with Loss,273
CONTENTS ix 4.4 Dispersion of Prism Pairs, 166 4.5 Dispersive Properties of Lenses, 173 4.6 Dispersion of Mirror Structures, 177 4.6.1 The Gires–Tournois Interferometer, 178 4.6.2 Quarter-Wave Stack High Reflectors, 180 4.6.3 Chirped Mirrors, 182 4.7 Measurements of Group Velocity Dispersion, 186 4.7.1 Interferometric Methods, 187 4.7.2 Frequency-Domain Intracavity Dispersion Measurements, 190 4.8 Appendix, 191 4.8.1 Frequency-Dependent Phase Due to Propagation Through a Slab: Alternative Derivation, 191 4.8.2 Impedance Method for Analysis of Dielectric Mirror Stacks, 192 Problems, 195 5 Ultrafast Nonlinear Optics: Second Order 198 5.1 Introduction to Nonlinear Optics, 198 5.2 The Forced Wave Equation, 201 5.2.1 Frequency-Domain Formulation, 202 5.2.2 Time-Domain Formulation, 203 5.3 Summary of Continuous-Wave Second-Harmonic Generation, 204 5.3.1 Effect of Phase Matching, 207 5.3.2 Phase Matching in Birefringent Media, 209 5.3.3 Focusing Effects in Continuous-Wave SHG, 215 5.4 Second-Harmonic Generation with Pulses, 220 5.4.1 SHG in the Quasi-Continuous-Wave Limit, 220 5.4.2 Ultrashort-Pulse SHG, 221 5.4.3 Quasi-Phase Matching, 228 5.4.4 Effect of Group Velocity Walk-off on SHG-Based Pulse Measurements, 233 5.5 Three-Wave Interactions, 237 5.5.1 Sum Frequency Generation, 240 5.5.2 Difference Frequency Generation, 244 5.5.3 Optical Parametric Amplification, 245 5.6 Appendix, 253 5.6.1 Spatial Walk-off and Pulse Fronts in Anisotropic Media, 253 5.6.2 Velocity Matching in Broadband Noncollinear Three-Wave Mixing, 254 Problems, 256 6 Ultrafast Nonlinear Optics: Third Order 258 6.1 Propagation Equation for Nonlinear Refractive Index Media, 258 6.1.1 Plane Waves in Uniform Media, 260 6.1.2 Nonlinear Propagation in Waveguides, 261 6.1.3 Optical Fiber Types, 264 6.2 The Nonlinear Schrodinger Equation, 266 ¨ 6.3 Self-Phase Modulation, 270 6.3.1 Dispersionless Self-Phase Modulation, 270 6.3.2 Dispersionless Self-Phase Modulation with Loss, 273