Introduction to Laser Physics

223 Pages·1984·4.412 MB·English

by  Professor Koichi Shimoda (auth.)

Springer Series in Optical Sciences Volume44
Springer Series in Optical Sciences
Editorial Board: J.M. Enoch D.L. MacAdam A.L. Schawlow K. Shimoda T. Tamir
Volume 42 Principles of Phase Conjugation
By B. Ya. Zel'dovich, N. F. Pilipetsky, and V. V. Shkunov
Volume 43 X-Ray Microscopy
Editors: G. Schmahl and D. Rudolph
Volume 44 Introduction to Laser Physics
By K Shimoda
Volume 45 Scanning Electron Microscopy
By L. Reimer
Volume 46 Holography in Deformation Analysis
By W Schumann, J.-P. Zürcher, and D. Cuche
Volumes 1-41 are listed on the back inside cover
Koichi Shimoda
Introduction
to Laser Physics
With 87 Figures
Springer-Verlag
Berlin Heidelberg GmbH 1984
Professor Koichi Shimoda
Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohokuku,
Yokohama 223, Japan
Editorial Board ARTHUR L. SCHAWLOW, Ph. D.
Department of Physics,. Stanford University
Stanford, CA 94305, USA
JAY M. ENOCH, Ph. D. Professor KOICHI SHIMODA
School of Optometry, Faculty of Science and Technology,
University of California Keio University, 3-14-1 Hiyoshi, Kohoku-ku
Berkeley, CA 94720, USA Yokohama 223, Japan
DAVID L. MACADAM, Ph. D. THEODOR TAMIR, Ph. D.
68 Hamrnond Street, 981 East Lawn Drive,
Rochester, NY 14615, USA Teaneck, NJ 07666, USA
Revised translation of the original Japanese edition:
Reza
Koichi Shimoda: Butsuri Nyumon
© Koichi Shimoda 1983
Originally published in Japanese by Iwanami Shoten, Publishers, Tokyo (1983)
English translation by Munetada Yamamuro
ISBN 978-3-662-13550-1 ISBN 978-3-662-13548-8 (eBook)
DOI 10.1007/978-3-662-13548-8
Library of Congress Cataloging in Publication Data. Shimoda, Köichi. Introduction to laser physics.
(Springer series in optical sciences .; v. 44) Rev. translation of: Koichi Shimoda: Reza Butsuri Ny11mon.
1. Lasers. 1. Title. H. Series. QC688.S55 1984 535.5'8 84-5629
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concemed, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction
by photocopying machine or similar means, and storage in data banks. Under § 54 ofthe German Copyright
Law, where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort",
Munich.
© Springer-Verlag Berlin Heidelberg 1984
Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1984
Softcover reprint of the hardcover I st edition 1984
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence
of a specific statement, that such names are exempt from the relevant protective laws and regulations
and therefore free for general use.
Typesetting: Schwetzinger Verlagsdruckerei, 6830 Schwetzingen
2153/3130-543210
Preface
The laser has opened a new field of science and technology and its progress is
making great strides. Various types of lasers have developed to such an
extent that not only are they useful in industrial applications, they have also
brought about such innovations as the laser processing of microstructures of
semiconductor and other materials, the state selection of atoms and
molecules, single-atom detection and trapping, femtosecond measurements,
phase conjugation, and many others.
Accordingly, those who are engaged in laser engineering are often
required to understand and pursue the physical principles of the laser; this
goes without saying for scientists studying laser spectroscopy and quantum
optics.
Now, the purpose of this book is to provide an introductory course of
comprehensive laser physics for students with a background of electro
magnetic theory, basic quantum mechanics, and ca1culus. The text will afford
an effective understanding of the basic concepts, principles, and theoretical
treatments of the laser as weIl as laser-induced effects. However, laser phys
ics is still under development and it has not yet been fully established in any
accepted structure. The approach presented in this book is by an author who
has been involved in a substantial part of laser research from the·time before
the advent of the laser to the present.
Most of the mathematical treatments and physical ideas above an e1emen
tary level are explained in detail. The subject matter is treated with full
physical interpretation providing the reader with a concrete foundation in
laser physics. Discussing the orders of magnitude of physical quantities and
practical parameters is stressed, rather than theoretically ca1culating exact
values.
The first chapter is devoted to an overview of the state of the art of most
typicallasers. Modern optics relevant to lasers is described in the subsequent
chapters followed by the physical processes of emission and absorption of
light. Then, the principle of the laser and the concept of population inversion
are described and a rate-equation approach is used to present the output
characteristics of the laser. Atomic coherence and nonlinear polarization are
described in detail to provide the semic1assical theory of lasers, nonlinear
optics, and laser spectroscopy. Fully quantum-mechanical theories of the
laser are reviewed briefly. Each chapter is accompanied by problems, most of
which are not mere numerical ca1culations, but contain instructive and infor
mative material. Hints and short answers are given.
VI Preface
The author is very grateful to Prof. Munetada Yamamuro who translated
the Japanese edition. Without his efforts, this revised version in English
would not have been realized. Particular thanks should go to Dr. Helmut
Lotsch and Ms. Gillian Hayes of Springer-Verlag for their careful reading
and correction of the manuscript. They have furthermore supplied additional
reading and some references for the manuscript, and encouraged the author
to prepare the problems. Finally he thanks Mrs. Chitose Hikami for her
excellent typing of the manuscript and his students for their examination of
many derivations in the text and answers to the problems.
Yokohama, Japan, April, 1984 Koichi Shimoda
Contents
1. The Laser - An Unprecedented Light Source 1
1.1 The Properties of Laser Light 1
1.1.1 Directivity . . . . . . . . . . . 1
1.1.2 Monochromaticity . . . . . . . 2
1.1.3 Energy Density and Brightness . 3
1.1.4 Ultrashort Pulses . 4
1.2 Solid-State Lasers .. . 5
1.3 Gas Lasers ...... . 7
1.3.1 Atomic Gas Lasers 7
1.3.2 Molecular Lasers. 10
1.4 Dye Lasers . . . . . . . 13
1.5 Semiconductor Lasers . 14
1.6 Other Lasers and Laser Physics 18
Problems ...... . 19
2. The Coherence of Light 21
2.1 Young's Experiment 21
2.2 The Michelson Interferometer 23
2.3 Temporal Coherence and Spatial Coherence 25
2.4 Complex Representation of Light Field 28
2.5 Coherence Function 30
Problems ........... . 33
3. Electromagnetic Theory of Light 35
3.1 Maxwell's Equations .... 35
3.2 Reflection and Refraction of Light 39
3.3 Total Reflection ..... . 42
3.4 Fabry-Perot Resonator .. . 47
3.5 Fabry-Perot Interferometer 49
3.6 Planar Waveguide 53
3.7 Gaussian Beam . 59
Problems ...... . 64
4. Emission and Absorption of Light 66
4.1 Mode Density of Electromagnetic Waves 66
4.2 Planck's Law of Thermal Radiation ... 69
4.3 Spontaneous Emission and Stimulated Emission 72
VIII Contents
4.4 Dipole Radiation and Probability of Spontaneous Emission 75
4.5 Absorption of Light ............. 79
4.6 Complex Susceptibility and Refractive Index. 81
Problems . . . . . . 84
5. Principle of the Laser 87
5.1 Population Inversion 87
5.2 Population Inversion in a Three-Level Laser 89
5.3 Population Inversion in a Four-Level Laser 92
5.4 Laser Amplification ...... 94
5.5 Conditions for Laser Oscillation 95
5.6 Frequency of Laser Oscillation 100
Problems . . . . . . . . . . . . . 103
6. Output Characteristics ofthe Laser 106
6.1 Rate Equations of the Laser 106
6.2 Steady-State Output . 108
6.3 Oscillation Build-Up . 111
6.4 Relaxation Oscillation 113
6.5 Q-Switching 116
Problems . . . . . . 121
7. Coherent Interaction . . . . . . . . . . . . . . . . . . . . . .. 123
7.1 Interaction Between a Two-Level Atom and a Coherent Field 123
7.2 Induced Dipole Moment and Induced Emission Coefficient 127
7.3 Density Matrix . . . . . . . . . . . . . . . 129
7.4 Equations of Motion of the Density Matrix . 132
7.5 Optical Bloch Equations . . . . . . . . . . 136
7.5.1 Transformation to an Abstract Space 136
7.5.2 Representation in a Rotating Frame of Reference 138
7.5.3 Terms Representing Longitudinal Relaxation and
Transverse Relaxation 140
Problems . . . . . . . . . 141
8. Nonlinear Coherent EfTects 143
8.1 Saturation Effect . . . 143
8.2 Change in the Atomic Populations Due to Saturated
Absorption . . . . . . . . . . . . 147
8.3 Nonlinear Complex Susceptibility 150
8.4 Inhomogeneous Broadening . . . 152
8.4.1 Doppler Broadening . . . . 152
8.4.2 Nonlinear Susceptibility with Doppler Broadening . 154
8.5 Hole-Burning Effect . . . . . . 157
8.6 Coherent Transient Phenomena 160
8.6.1 Optical Nutation . . . . . 164
Contents IX
8.6.2 Free Induction Decay 165
8.6.3 Photon Echo . . . . . 166
8.6.4 Self-Induced Transparency . 168
Problems . . . . . . . . . 171
9. Theory ofLaser Oscillation 173
9.1 Fundamental Equations of the Semiclassical Theory 173
9.2 Single-Mode Oscillation . . . 177
9.2.1 Steady-State Oscillation 178
9.2.2 van der Pol Equation . . 180
9.3 Multimode OsciHation . . . . 182
9.3.1 Competition Between Two Modes of Oscillation . 182
9.3.2 Existence of Combination Frequencies . 186
9.4 Mode Locking . . . . . . . . . . . . . . . . . . . . . 188
9.5 Theory ofthe Gas Laser . . . . . . . . . . . . . . . . 191
9.5.1 Density Matrix of aGas of Molecules in a Standing-
Wave Field . . . . . . . . . . . . . . . . . 192
9.5.2 Approximate Solutions by Iteration . . . . 194
9.5.3 Output Characteristics in the Third-Order
Approximation (Lamb Dip) . . . . . . . 197
9.6 FuHy Quantum-Mechanical Theory of the Laser 199
Problems 201
References . . 205
Subject Index 207