NONLINEAR OPTICS NELINEINAYA OPTIKA HEJH1HEHHAH OnTHKA
The Lebedev Physics Institute Series Editor: Academician D. V. Skobel'tsyn Director, P. N. Lebedev Physics Institute, Academy of Sciences of the USSR Volume 25 Volume 26 Volume 27 Volume 28 Volume 29 Volume 30 Volume 31 Volume 32 Volume 33 Volume 34 Volume 35 Volume 36 Volume 37 Volume 38 Volume 39 Volume 40 Volume 41 Volume 42 Volume 43 Optical Methods of Investigating Solid Bodies Cosmic Rays Research in Molecular Spectroscopy Radio Telescopes Quantum Field Theory and Hydrodynamics Physical Optics Quantum Electronics in Lasers and Masers Plasma Physics Studies of Nuclear Reactions Photomesonic and Photonuclear Processes Electronic and Vibrational Spectra of Molecules Photodisintegration of Nuclei in the Giant Resonance Region Electrical and Optical Properties of Semiconductors Wide band Cruciform Radio Telescope Research Optical Studies in Liquids and Solids Experimental Physics: Methods and Apparatus The Nucleon Compton Effect at Low and Medium Energies Electronics in Experimental Physics Nonlinear Optics In preparation Volume 44 Volume 45 Volume 46 Volume 47 Volume 48 Volume 49 Volume 50 Nuclear Physics and Interaction of Particles with Matter Experimental Physics: Programming and Computer Techniques Cosmic Rays and Interaction of High-Energy Particles Radio Astronomy Instruments and Observations Surface Properties of Semiconductors and Dynamics of Ionic Crystals Quantum Electronics and ParamagnetiC Resonance Electroluminescence
Proceedings (Trudy) of the P. N. Lebedev Physics Institute Volume 43 NONLINEAR OPTICS Edited by Academician D. V. Skobel'tsyn Director, P. N. Lebedev Physics Institute Academy of Sciences of the USSR, Moscow Translated from Russian by Frank L. Sinclair CONSULTANTS BUREAU NEW YORK-LONDON 1970
The Russian text was published by Nauka Press in Moscow in 1968 for the Academy of Sciences of the USSR as Volume 43 of the Proceedings (Trudy) of the P. N. Lebedev Physics Institute. The present translation is published under an agreement with Mezhdunarodnaya Kniga, the Soviet book export agency. TpY~hl Op~eHa ~ehhha (DH3HQeCKOrO UHCTHTYTa HM. IT. H. ~e6e~eba TOM XLIII Library of Congress Catalog Card Number 72-107530 SBN 306-10840-2 ISBN-13: 978-1-4615-7521-4 e-isbn-13: 978-1-4615-7519-1 DOl: 10.1007/978-1-4615-7519-1 1970 Consultants Bureau, New York A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N. Y. 10011 United Kingdom edition published by Consultants Bureau, London A Division of Plenum Publishing Company, Ltd. Donington House, 30 Norfolk Street, London, W.C. 2, England All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher
CONTENTS Some Questions of Gas Laser Theory S. G. Rautian.... 1 Introduction.............................................. 1 1. Optical Masers (Lasers)....................... 1 2. Content of Work..................................... 2 PART I: INTERACTION OF A QUANTUM SYSTEM AND AN ELECTROMAGNETIC FIELD Chapter 1. Induced Emission in a Strong Monochromatic Field.... 3. Basic Equations............................. 4. Kinetics of Induced Transitions.... 5. Induced Emission of Moving Atoms.... 6. Spatial Inhomogeneity of Medium Due to Saturation Effect.... Chapter 2. Spontaneous Emission with Induced Transitions Taken into Account.......................................... 24 7. General Theory...................................... 24 8. Spontaneous Emission of Stationary Atoms in an External Field...... 29 9. Spontaneous Emission of Moving Atoms...................... 32 Chapter 3. Induced Emission and Absorption of a "Weak" Field in the Presence of a "Strong" Field.......................... 40 10. Formulation of Problem................................ 40 11. Forced Emission and Absorption of Weak Field by Stationary Atoms in a Strong Monochromatic Field...................... 41 12. Induced Emission and Absorption of Weak Field by Moving Atoms... 43 Chapter 4. Effect of Atomic Collisions........................... 45 13. Classical Theory of Doppler Broadening of SpeGtral Lines with Collisions Taken into Account. General Theory.......... 45 14. Doppler Broadening... 49 15. Broadening Due to Interactions and Doppler Effect...,..... 56 16. On the Relaxation Terms in the Equation for the Density Matrix...... 62 17. The Saturation Effect with Collisions Taken into Account... 64 PART II. APPLICATION TO LASER THEORY 5 5 8 14 21 Chapter 5. Monochromatic Generation.... 18. Self-Consistent Problem...,.. 19. One-Dimensional Laser Model 75 75 77 v
vi CONTENTS 20. Stationary Atoms.................. 83 21. Moving Atoms................... 86 Chapter 6. Stability of Monochromatic Generation 90 22. Formulation of Problem. 90 23. General Formulas... 90 24. Stationary Atoms......... 92 25. Moving Atoms. Gas Losers.. 95 Appendix. Spectroscopic Applications of Gas Lasers. 97 Literature Cited...................... 100 Interaction of Electromagnetic Fields with Active Media T. 1. Kuznetsova......................... 105 Introduction......................... 105 Chapter 1. Calculation of Polarization of Medium 107 Chapter 2. One-Dimensional Laser Model. Monochromatic Generation. 115 Chapter 3. Some Properties of Two-Dimensional Active Resonators. 124 Chapter 4. Weak Fields in a Resonator Generating Monochromatic Radiation..................................... 130 Chapter 5. Nonlinear Interaction of Weak Fields in the Presence of a Strong Monochromatic Field in a Traveling-Wave Amplifier. 137 Summary.......................................... 142 Literature Cited..................................... 143 Electrodynamics of Lasers with an Open Resonator and Inhomogeneous Filling A. F. Suchkov..... 147 Literature Cited.... 153 Dynamics of a Q-Switched Laser V. S. Letokhov and A. F. Suchkov. Introduction............................. 1. Formulation of the Problem. Basic Equations. 2. Initial Conditions.... 3. Linear Development of Generation. Solution of Equations... 4. Field Distribution and Dependence on Initial Conditions. 5. Nonlinear Transverse Development of Generation.. 6. Numerical Integration of Equations.. Summary.... Literature Cited.... Nonlinear Interactions of Electromagnetic Waves in an Active Medium and Their Possible Application to the Development of New Types of Lasers B. P. Kirsanov.... Introduction...................................... 1. Derivation of Equations of Fields in "Resonance Parametic" and "Two-Photon" Lasers. Calculation of Nonlinear Polarization with Saturation Taken into Account.... 2. Two-Photon Laser.... 3. Generation of Submillimeter Waves by Two-Quantum Luminescence.. 4. Theory of the "Resonance Parametric" Laser in the Stable Phase Case.... 5. Theory of the "Resonance Parametric" Laser at the Random-Phase Limit.... 155 155 156 157 158 159 161 162 169 169 171 171 173 181 183 186 191
CONTENTS 6. Discussion of Results and Experimental Approach To Their Realization...................... Appendix 1. Quantum-Electrodynamic Description of Multiphoton Processes.... Appendix 2. Nonlinear Interactions with Random Phase. Comparison of Quantum and Semiclassicai Descriptions of Nonlinear Interactions Literature Cited.... vii 192 194 197 202