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Library of Congress Cataloging-in-Publication Data

Paschotta, Rüdiger.

Field guide to laser pulse generation / Rudiger Paschotta.

p. cm. -- (SPIE field guides; FG 14)

Includes bibliographical references and index.

ISBN 978-0-8194-7248-9 (alk. paper)

1. Laser pulses, Ultrashort. 2. Pulse generators. 3.

Pulse techniques (Electronics) I. Title.

QC689.5.L37P37 2008



Published by


P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: + 1 360 676 3290

Fax: + 1 360 647 1445



The content of this book reflects the work and thought of the author. 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.


Introduction to the Series

Welcome to the SPIE Field Guides–a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.

Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in its coverage, the concise presentation might not be appropriate for those new to the field.

The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at

John E. Greivenkamp, Series Editor

Optical Sciences Center

The University of Arizona

The Field Guide Series

Keep information at your fingertips with all of the titles in the Field Guide series:

Field Guide to Geometrical Optics, John E. Greivenkamp (FG01)

Field Guide to Atmospheric Optics, Larry C. Andrews (FG02)

Field Guide to Adaptive Optics, Robert K. Tyson & Benjamin W. Frazier (FG03)

Field Guide to Visual and Ophthalmic Optics, Jim Schwiegerling (FG04)

Field Guide to Polarization, Edward Collett (FG05)

Field Guide to Optical Lithography, Chris A. Mack (FG06)

Field Guide to Optical Thin Films, Ronald R. Willey (FG07)

Field Guide to Spectroscopy, David W. Ball (FG08)

Field Guide to Infrared Systems, Arnold Daniels (FG09)

Field Guide to Interferometric Optical Testing, Eric P. Goodwin & James C. Wyant (FG10)

Field Guide to Illumination, Angelo V. Arecchi; Tahar Messadi; R. John Koshel (FG11)

Field Guide to Lasers, Rüdiger Paschotta (FG12)

Field Guide to Laser Pulse Generation

Lasers and related devices have an amazing potential for generating both very intense and extremely short light pulses. Within four decades, a wide range of techniques for pulse generation has been developed; these techniques can be applied to different laser types and span a huge parameter space in terms of pulse duration, peak power, and pulse repetition rate. It is therefore not surprising that laser pulses have found an extremely wide range of applications.

The primary objective of this Field Guide is to provide an overview of all essential methods of laser pulse generation, including Q switching, gain switching, mode locking, and also the amplification of ultrashort pulses to high energies. Some material on pulse characterization is also provided. Both the physical aspects involved and the various technical limitations are discussed in significant depth. This Field Guide should therefore be very useful for a wide audience, including practitioners in industry as well as researchers. Even those who only apply, but do not themselves develop, pulsed and ultrafast laser systems can learn, for example, about the potential of different pulse generation methods.

I am greatly indebted to my wife, Christine, who strongly supported the creation of this Field Guide by improving many of the figures.

Dr. Rüdiger Paschotta

RP Photonics Consulting GmbH

Zürich, Switzerland

Table of Contents

Glossary of Symbols x

Introduction to Optical Pulses 1

Optical Pulses in the Time Domain 2

Optical Pulses in the Frequency Domain 4

Bandwidth-Limited Pulses 5

Pulse Trains and Frequency Combs 6

Carrier–Envelope Offset 7

Overview of Laser Sources for Optical Pulses 9

Q Switching 10

Active and Passive Q Switching 11

Essentials of Laser Dynamics 12

Pumping the Gain Medium 13

Dynamics of Active Q Switching 14

Achievable Pulse Energy 15

Pulse Duration and Buildup Time 16

Influence of Pulse Repetition Rate 17

Dynamics of Passive Q Switching 18

Pulse Duration and Pulse Energy 20

Saturable Absorbers for Q Switching 21

Influence of Pump Fluctuations 22

Mode Beating in Multimode Lasers 23

Q-Switched Solid-State Bulk Lasers 24

Q-Switched Microchip Lasers 26

Q-Switched Fiber Lasers 27

Multiple Pulsing and Instabilities 28

Cavity Dumping 29

Gain Switching 30

Comparison with Other Techniques 32

Mode Locking 33

Active Mode Locking 34

Passive Mode Locking 36

Mode Locking with Fast Saturable Absorbers 37

Mode Locking with Slow Saturable Absorbers 38

Chromatic Dispersion 39

Dispersive Pulse Broadening 40

Effect of Dispersion in Mode-Locked Lasers 41

Dispersion Compensation 42

The Kerr Nonlinearity 44

Self-Phase Modulation 45

Self-Phase Modulation and Chromatic Dispersion 46

Optical Solitons 47

Quasi-Soliton Pulses in Laser Resonators 48

Semiconductor Saturable Absorbers 50

Other Saturable Absorbers for Mode Locking 54

Initiation of Mode Locking 55

Q-Switching Instabilities 56

Actively Mode-Locked Solid-State Bulk Lasers 58

Harmonic Mode Locking 59

Passively Mode-Locked Solid-State Bulk Lasers 60

Performance Figures of Mode-Locked Bulk Lasers 61

Choice of Solid-State Gain Media 62

Additive-Pulse Mode Locking 63

Kerr Lens Mode Locking 64

Generation of Few-Cycle Pulses 65

Mode-Locked High-Power Thin-Disk Lasers 67

Miniature Lasers with High Repetition Rates 69

Mode-Locked Fiber Lasers 70

Soliton Fiber Lasers 71

Limitations of Soliton Fiber Lasers 73

Stretched-Pulse Fiber Lasers 74

Similariton Fiber Lasers 75

Mode-Locked Diode Lasers 77

Mode-Locked VECSELs 79

Mode-Locked Dye Lasers 80

Instabilities of Mode-Locked Lasers 81

Cavity Dumping 83

Amplification of Ultrashort Pulses 84

Multipass Solid-State Bulk Amplifiers 86

Regenerative Amplifiers 87

Fiber Amplifiers 88

Chirped-Pulse Amplification 89

Optical Parametric Amplifiers 91

Pulse Characterization 92

Measurement of Pulse Energy and Peak Power 93

Autocorrelators 94

Pulse Characterization with FROG 97

Pulse Characterization with SPIDER 98

Measurement of Carrier–Envelope Offset 99

Timing Jitter of Mode-Locked Lasers 100

Measurement of Timing Jitter 101

Equation Summary 102

Bibliography 105

Index 117



electric field envelope function


velocity of light in vacuum


group delay dispersion


electric field strength


pulse energy


saturation energy (e.g., of a laser medium)


frequency (e.g., noise frequency)


modulation frequency


pulse repetition rate


gain coefficient


final gain coefficient


initial gain coefficient


gain coefficient in the steady state


power amplification factor [= exp(g)]


Planck’s constant


optical intensity (power per unit area)


saturation intensity (e.g., of a laser medium)


loss coefficient (e.g., for round-trip losses of a resonator)


refractive index


nonlinear index


optical power


average power


peak power


coefficient saturable loss


modulation depth of saturable absorber




round-trip time of a resonator


output coupler transmission


nonlinear coefficient


change of spectral phase




optical frequency


instantaneous frequency


carrier-envelope offset frequency


optical bandwidth


gain bandwidth


upper-state lifetime


pulse duration


angular frequency


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