GasLasersEndo& Walter/GasLasers DK553X_C000 FinalProof page i 17.11.2006 4:29pmEndo&Walter/GasLasers DK553X_C000 FinalProof page ii 17.11.2006 4:29pmOPTICAL SCIENCE AND ENGINEERINGFounding EditorBrian J. ThompsonUniversity of RochesterRochester, NewYork1. Electron and Ion Microscopy and Microanalysis: Principles and Applications,Lawrence E. Murr2. Acousto-Optic Signal Processing: Theory and Implementation, edited by Norman J. Berg and John N. Lee3. Electro-Optic and Acousto-Optic Scanning and Deflection, Milton Gottlieb, Clive L. M. Ireland, and John Martin Ley4. Single-Mode Fiber Optics:Principles and Applications, Luc B. Jeunhomme5. Pulse Code Formats for Fiber Optical Data Communication: Basic Principlesand Applications, David J. Morris6. Optical Materials:An Introduction to Selection and Application, Solomon Musikant7. Infrared Methods for Gaseous Measurements: Theory and Practice, edited byJoda Wormhoudt8. Laser Beam Scanning:Opto-Mechanical Devices, Systems, and Data StorageOptics, edited by Gerald F. Marshall9. Opto-Mechanical Systems Design, Paul R. Yoder, Jr.10. Optical Fiber Splices and Connectors:Theory and Methods, Calvin M. Millerwith Stephen C. Mettler and Ian A. White11. Laser Spectroscopy and Its Applications, edited by Leon J. Radziemski, Richard W. Solarz, and Jeffrey A. Paisner12. Infrared Optoelectronics:Devices and Applications, William Nunley and J. Scott Bechtel13. Integrated Optical Circuits and Components:Design and Applications, edited by Lynn D. Hutcheson14. Handbook of Molecular Lasers, edited by Peter K. Cheo15. Handbook of Optical Fibers and Cables, Hiroshi Murata16. Acousto-Optics, Adrian Korpel17. Procedures in Applied Optics, John Strong18. Handbook of Solid-State Lasers,edited by Peter K. Cheo19. Optical Computing:Digital and Symbolic, edited by Raymond Arrathoon20. Laser Applications in Physical Chemistry, edited by D. K. Evans21. Laser-Induced Plasmas and Applications, edited by Leon J. Radziemski and David A. Cremers22. Infrared Technology Fundamentals, Irving J. Spiro and Monroe Schlessinger23. Single-Mode Fiber Optics:Principles and Applications, Second Edition,Revised and Expanded, Luc B. Jeunhomme24. Image Analysis Applications, edited by Rangachar Kasturi and Mohan M. Trivedi25. Photoconductivity:Art, Science, and Technology, N. V. Joshi26. Principles of Optical Circuit Engineering, Mark A. Mentzer27. Lens Design, Milton LaikinEndo&Walter/GasLasers DK553X_C000 FinalProof page iii 17.11.2006 4:29pm28. Optical Components, Systems, and Measurement Techniques, Rajpal S. Sirohiand M. P. Kothiyal29. Electron and Ion Microscopy and Microanalysis: Principles and Applications,Second Edition, Revised and Expanded, Lawrence E. Murr30. Handbook of Infrared Optical Materials, edited by Paul Klocek31. Optical Scanning, edited by Gerald F. Marshall32. Polymers for Lightwave and Integrated Optics: Technology and Applications,edited by Lawrence A. Hornak33. Electro-Optical Displays, edited by Mohammad A. Karim34. Mathematical Morphology in Image Processing, edited by Edward R. Dougherty35. Opto-Mechanical Systems Design: Second Edition, Revised and Expanded,Paul R. Yoder, Jr.36. Polarized Light: Fundamentals and Applications, Edward Collett37. Rare Earth Doped Fiber Lasers and Amplifiers, edited by Michel J. F. Digonnet38. Speckle Metrology, edited by Rajpal S. Sirohi39. Organic Photoreceptors for Imaging Systems, Paul M. Borsenberger and David S. Weiss40. Photonic Switching and Interconnects, edited by Abdellatif Marrakchi41. Design and Fabrication of Acousto-Optic Devices, edited by Akis P. Goutzoulisand Dennis R. Pape42. Digital Image Processing Methods, edited by Edward R. Dougherty43. Visual Science and Engineering: Models and Applications, edited by D. H. Kelly44. Handbook of Lens Design, Daniel Malacara and Zacarias Malacara45. Photonic Devices and Systems, edited by Robert G. Hunsberger46. Infrared Technology Fundamentals: Second Edition, Revised and Expanded,edited by Monroe Schlessinger47. Spatial Light Modulator Technology: Materials, Devices, and Applications, edited by Uzi Efron48. Lens Design: Second Edition, Revised and Expanded, Milton Laikin49. Thin Films for Optical Systems, edited by Francoise R. Flory50. Tunable Laser Applications, edited by F. J. Duarte51. Acousto-Optic Signal Processing: Theory and Implementation, Second Edition,edited by Norman J. Berg and John M. Pellegrino52. Handbook of Nonlinear Optics, Richard L. Sutherland53. Handbook of Optical Fibers and Cables: Second Edition, Hiroshi Murata54. Optical Storage and Retrieval: Memory, Neural Networks, and Fractals, edited by Francis T. S. Yu and Suganda Jutamulia55. Devices for Optoelectronics, Wallace B. Leigh56. Practical Design and Production of Optical Thin Films, Ronald R. Willey57. Acousto-Optics: Second Edition, Adrian Korpel58. Diffraction Gratings and Applications, Erwin G. Loewen and Evgeny Popov59. Organic Photoreceptors for Xerography, Paul M. Borsenberger and David S. Weiss60. Characterization Techniques and Tabulations for Organic Nonlinear OpticalMaterials, edited by Mark G. Kuzyk and Carl W. Dirk61. Interferogram Analysis for Optical Testing, Daniel Malacara, Manuel Servin,and Zacarias Malacara62. Computational Modeling of Vision: The Role of Combination, William R. Uttal,Ramakrishna Kakarala, Spiram Dayanand, Thomas Shepherd, Jagadeesh Kalki,Charles F. Lunskis, Jr., and Ning Liu63. Microoptics Technology: Fabrication and Applications of Lens Arrays and Devices, Nicholas Borrelli64. Visual Information Representation, Communication, and Image Processing,edited by Chang Wen Chen and Ya-Qin Zhang65. Optical Methods of Measurement, Rajpal S. Sirohi and F. S. ChauEndo&Walter/GasLasers DK553X_C000 FinalProof page iv 17.11.2006 4:29pm66. Integrated Optical Circuits and Components: Design and Applications, edited by Edmond J. Murphy67. Adaptive Optics Engineering Handbook, edited by Robert K. Tyson68. Entropy and Information Optics, Francis T. S. Yu69. Computational Methods for Electromagnetic and Optical Systems, John M. Jarem and Partha P. Banerjee70. Laser Beam Shaping, Fred M. Dickey and Scott C. Holswade71. Rare-Earth-Doped Fiber Lasers and Amplifiers: Second Edition, Revised and Expanded, edited by Michel J. F. Digonnet72. Lens Design: Third Edition, Revised and Expanded, Milton Laikin73. Handbook of Optical Engineering, edited by Daniel Malacara and Brian J. Thompson74. Handbook of Imaging Materials: Second Edition, Revised and Expanded,edited by Arthur S. Diamond and David S. Weiss75. Handbook of Image Quality: Characterization and Prediction, Brian W. Keelan76. Fiber Optic Sensors, edited by Francis T. S. Yu and Shizhuo Yin77. Optical Switching/Networking and Computing for Multimedia Systems,edited by Mohsen Guizani and Abdella Battou78. Image Recognition and Classification: Algorithms, Systems, and Applications,edited by Bahram Javidi79. Practical Design and Production of Optical Thin Films: Second Edition, Revised and Expanded, Ronald R. Willey80. Ultrafast Lasers: Technology and Applications, edited by Martin E. Fermann,Almantas Galvanauskas, and Gregg Sucha81. Light Propagation in Periodic Media: Differential Theory and Design, Michel Nevire and Evgeny Popov82.Handbook of Nonlinear Optics, Second Edition, Revised and Expanded, Richard L. Sutherland83. Polarized Light: Second Edition, Revised and Expanded, Dennis Goldstein84. Optical Remote Sensing: Science and Technology, Walter Egan85. Handbook of Optical Design: Second Edition, Daniel Malacara and Zacarias Malacara86. Nonlinear Optics: Theory, Numerical Modeling, and Applications, Partha P. Banerjee87. Semiconductor and Metal Nanocrystals: Synthesis and Electronic and OpticalProperties, edited by Victor I. Klimov88. High-Performance Backbone Network Technology, edited by Naoaki Yamanaka89. Semiconductor Laser Fundamentals, Toshiaki Suhara90. Handbook of Optical and Laser Scanning, edited by Gerald F. Marshall91.Organic Light-Emitting Diodes: Principles, Characteristics, and Processes, Jan Kalinowski92.Micro-Optomechatronics, Hiroshi Hosaka, Yoshitada Katagiri, Terunao Hirota,and Kiyoshi Itao93.Microoptics Technology: Second Edition, Nicholas F. Borrelli94. Organic Electroluminescence, edited by Zakya Kafafi95. Engineering Thin Films and Nanostructures with Ion Beams, Emile Knystautas96.Interferogram Analysis for Optical Testing, Second Edition, Daniel Malacara,Manuel Sercin, and Zacarias Malacara97.Laser Remote Sensing, edited by Takashi Fujii and Tetsuo Fukuchi98.Passive Micro-Optical Alignment Methods, edited by Robert A. Boudreau and Sharon M. Boudreau99.Organic Photovoltaics: Mechanism, Materials, and Devices, edited by Sam-Shajing Sun and Niyazi Serdar Saracftci100. Handbook of Optical Interconnects, edited by Shigeru Kawai101. GMPLS Technologies: Broadband Backbone Networks and Systems,Naoaki Yamanaka, Kohei Shiomoto, and Eiji OkiEndo& Walter/GasLasers DK553X_C000 FinalProof page v 17.11.2006 4:29pm102. Laser Beam Shaping Applications, edited by Fred M. Dickey, Scott C. Holswadeand David L. Shealy103. Electromagnetic Theory and Applications for Photonic Crystals,Kiyotoshi Yasumoto104. Physics of Optoelectronics, Michael A. Parker105. Opto-Mechanical Systems Design: Third Edition, Paul R. Yoder, Jr.106. Color Desktop Printer Technology, edited by Mitchell Rosen and Noboru Ohta107. Laser Safety Management, Ken Barat108. Optics in Magnetic Multilayers and Nanostructures, Stefan Vi s novsky109. Optical Inspection of Microsystems, edited by Wolfgang Osten110. Applied Microphotonics, edited by Wes R. Jamroz, Roman Kruzelecky, and Emile I. Haddad111. Organic Light-Emitting Materials and Devices, edited by Zhigang Li and Hong Meng112. Silicon Nanoelectronics, edited by Shunri Oda and David Ferry113. Image Sensors and Signal Processor for Digital Still Cameras, Junichi Nakamura114. Encyclopedic Handbook of Integrated Circuits, edited by Kenichi Iga and Yasuo Kokubun115. Quantum Communications and Cryptography, edited by Alexander V. Sergienko116. Optical Code Division Multiple Access: Fundamentals and Applications, edited by Paul R. Prucnal117. Polymer Fiber Optics: Materials, Physics, and Applications, Mark G. Kuzyk118. Smart Biosensor Technology, edited by George K. Knopf and Amarjeet S. Bassi119. Solid-State Lasers and Applications, edited by Alphan Sennaroglu120. Optical Waveguides: From Theory to Applied Technologies, edited by Maria L. Calvo and Vasudevan Lakshiminarayanan121. Gas Lasers, edited by Masamori Endo and Robert F. Walter122. Lens Design, Fourth Edition, Milton Laikin123. Photonics: Principles and Practices, Abdul Al-Azzawi124. Microwave Photonics, edited by Chi H. LeeEndo&Walter/GasLasers DK553X_C000 FinalProof page vi 17.11.2006 4:29pmGasLasersedited byMasamori EndoRobert F. WalterCRC Press is an imprint of theTaylor & Francis Group, an informa businessBoca Raton London New YorkEndo&Walter/GasLasers DK553X_C000 FinalProof page vii 17.11.2006 4:29pmCRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1International Standard Book Number-10: 0-8493-3553-1 (Hardcover)International Standard Book Number-13: 978-0-8493-3553-2 (Hardcover)Thisbookcontainsinformationobtainedfromauthenticandhighlyregardedsources.Reprintedmaterialisquoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any informa-tion storage or retrieval system, without written permission from the publishers.Forpermissiontophotocopyorusematerialelectronicallyfromthiswork,pleaseaccesswww.copyright.com(http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For orga-nizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.TrademarkNotice:Productorcorporatenamesmaybetrademarksorregisteredtrademarks,andareusedonlyfor identification and explanation without intent to infringe.Library of Congress Cataloging-in-Publication DataGas lasers / edited by Masamori Endo and Robert F. Walter.p. cm. --(Optical science and engineering ; 121)Includes bibliographical references and index.ISBN 0-8493-3553-1 (978-0-8493-3553-2 : alk. paper)1.Gas lasers.I. Endo, Masamori, 1965- II. Walter, Robert F., 1950- III. Title. IV. Series.TA1695.G3385 2006621.3663--dc22 2006030226Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.comEndo&Walter /GasLasers DK553X_C000 FinalProof page viii 17.11.2006 4:29pmPrefaceMore than 40 years have passed since the first demonstration of the laser. Lasers are the onlycoherent electromagnetic waves at the optical frequency, and they never existed on earth until1960, when T.H. Maiman* demonstrated the first atomic lamp.** Now lasers have becomeindispensabletoolsinourmodernlife. Inparticular, theapplicationoflasertechnologytocommunicationandinformationprocessingis sosuccessful that morethanabillonlaserdiodes are manufactured annually. It should be mentioned that lasers involve in some way inmostoftheinnovativeadvancesineveryotherareaofscienceaswell.Thisbookdealswithaspecialkindoflaser. Thebookfocusesonthelaserwhoseactivemediumisgaseous. Today, thenumberof gaslasersmanufacturedissignificantlygreaterthan the number of semiconductor lasers; however, the contribution of gas lasers to our life isjustasimportantasthatofsemiconductorlasers.The variety of laser mediamakes it possible for gas lasers toextendtheir oscillatingwavelengthrangefromfarinfraredtovacuumultraviolet.Todaysrevolutioninmicroelec-tronics is largely due to the sophisticated UV excimer laser lithography technology. The CO2laser has dominated the machine tool market for almost 30 years. The substitution of the lasersourcetothesolid-stateoneshasjuststartedrecentlyowingtotherecentadvancesinhigh-powerdiodelasers.However,theCO2laserisstillmorecost-effectiveness,hasbetterbeamquality,andbetteroutputpowerscalability.Currently, theinterests of research in laserdevicesseemto be shiftingtosolid-state lasers.However, solid-state lasers are not almighty, and one should know about other laser sourcesbefore starting something. In this context, the editors thought that it is worth publishing a bookdevoted to gas lasers that contains not only their basics, but also their up-to-date research.The target of this book is not undergraduate students who have just started studying laserphysics. Instead,this bookisdevotedtograduate students, scientists,and engineers whoareor will be involved in gas lasers. The latest and most comprehensive information on the mostpopulargaslaserswillbefoundinthisbook.Thepropertiesofthisbookmaybesummarizedasfollows:1. Informationonthestate-of-arttechnologyofeachlaserisfeatured.2. The first chapter begins with the properties of gas lasers in general, and then goes on todiscuss the general aspects of gas lasers, namely, gas dynamics, electric circuits forexcitation,andopticalresonators.3. Thebasicphysicsofeachlaserareespeciallyemphasizedinthisbook, whichiscom-parablewithbooksdevotedtothosespecificlasers.4. Applicationofgaslasers,especiallytheirpotentialapplicationstomodernengineering,aredescribed.In summary, this book is devoted to readers who are working with or interested in gas lasers,frombasicresearchtonovel applications. Theauthorsareexpertsofspecificlaserphysicsfrom all over the word. Each chapter includes the basic physics, characteristics, applications,andcurrentresearchtasksofspecificlasers.Thetypesoflaserschosentobeincludedinthe*Maiman, T.H.,Nature,493,1960.**Headline ofAsahiShinbun,daily newspaper, Japan,July7,1960.Endo&Walter/GasLasers DK553X_C000 FinalProof page ix 17.11.2006 4:29pmbookweremadeonthebasisof their importanceintodaysscienceandengineering. Weselected the authors carefully; however, the selection may be biased by our personal relation-shipsandtheauthorsavailability.Chapter1providesadefinitionofgaseousmediaandisfollowedbyadescriptionoftherovibrational spectral characteristics of gaseous media without the requirement of knowledgeof advancedquantummechanics. Then, a descriptionof spectral broadening, especiallyDopplerbroadeningcausedbytranslationalmovementandpressurebroadeningcausedbythecollisionofatoms, isdiscussed. FromChapter2toChapter4, fluiddynamics, electricexcitationcircuits, andoptical resonators of gas lasers ingeneral are discussed. As theexcitation of gaseous media is much more diverse than solid-state lasers, it must be classified.Though fluid dynamics are important for gas lasers, optical resonators need to be consideredspeciallyinadiscussiononenergyextractionfromgaseousmedia.FromChapter 5toChapter 10, selectedspecific laser devices are featured. These areclassifiedbythelasermediumandsubclassifiedintermsoftheexcitationschemeandkindsof atomsormolecules, whennecessary. Chapter11discussesothergaslasersthat arenotdiscussed in the previous chapters. We hope this book serves as a comprehensive encyclopediaforgaslaserscientistsandengineers.MasamoriEndoEndo& Walter/GasLasers DK553X_C000 FinalProof page x 17.11.2006 4:29pmEditorsMasamori EndowasborninTokyo, Japan, in1965. HereceivedtheBAandPhDdegreesfromKeioUniversityin1988and1993, respectively. Afterthat, heworkedforMitsubishiHeavyIndustries, Ltd. for 3 years. He studiedmicrowave heatingandcomplexdielectricpropertiesofmaterials. Since1996, hehasbeenatTokai University, wherehehasworkedwith chemical oxygen iodine lasers (COIL), laser material processing, and theoretical model-ingofopticalresonators.Since2004,hehasalsobeenanassociateprofessorattheDepart-ment of Physics,Schoolof Science ofTokaiUniversity. He is a memberof the InternationalSocietyforOptical Engineering(SPIE), theAmericanInstituteof AeronauticsandAstro-nautics,theAppliedPhysicsSocietyofJapan,andtheLaserSocietyofJapan.RobertF.WalterisGroupLeaderforDirectedEnergySystemsattheSchaferCorporation,Albuquerque, New Mexico. He was born in Conyngham, Pennsylvania, in 1950. He receivedthe SB, SM, and PhD degrees in aeronautics and astronautics from Massachusetts Institute ofTechnology(MIT)in1972,1973,and1978,respectively.BeforejoiningtheSchaferCorpor-ationin1982, Dr. Walterworkedasahigh-energylasergas-dynamicsspecialistattheAirForceWeaponsLaboratory.Hehasover30 yearsofexperiencewithhigh-powergaslasers.Hehasmadesignificantcontributionsinthemodelingandsimulationofawidevarietyofhigh-powergaslasers,includingtheCOIL,theelectricoxygeniodinelaser(EOIL),theCO2gas-dynamicandelectricdischargelaser,excimerlasers(XeF,XeCl,andKrF),andRamanlasers. He is a member of the Plasmadynamics andLaser Technical Committee of theAmericanInstituteofAeronauticsandAstronautics, whichhechairedfrom1922to1994.Dr.WalterisalsoamemberoftheInternationalAdvisoryCommitteeoftheGasFlowandChemical Laser Symposiumand editor of the volume High Power Laser: Science andEngineering,publishedin1996forNATO.Endo&Walter/GasLasers DK553X_C000 FinalProof page xi 17.11.2006 4:29pmEndo&Walter/GasLasers DK553X_C000 FinalProof page xii 17.11.2006 4:29pmContributorsKrzysztofM.AbramskiWrocawUniversityofTechnologyWrocaw,PolandWilhelmH.BehrensFluid&ThermophysicsDepartmentNorthropGrummanSpaceTechnology(NGST)RedondoBeachCaliforniaAnatolyS.BoreyshoBalticStateTechnicalUniversityLaserSystemsInc.St.PetersburghRussiaStevenJ.DavisAppliedSciencesDepartmentPhysicalSciencesInc.AndoverMassachusettsMichaelC.HeavenDepartmentofChemistryEmoryUniversityAtlantaGeorgiaAlanE.HillPlasmatronicsInc.Albuquerque,NewMexicoandTexasA&MUniversityCollegeStation,TexasAndreyA.IoninP.N.LebedevPhysicalInstituteofRussianAcademyofSciencesMoscowRussiaVladimirV.KhukharevD.V. Efremov Scientific Research InstituteofElectrophysicalApparatusSt.PetersburghRussiaPeterD.LohnRetiredfromFluid&ThermophysicsDepartmentNorthrop Grumman Space Technology(NGST)RedondoBeachCaliforniaVictorM.MalkovBalticStateTechnicalUniversityLaserSystemsInc.St.PetersburghRussiaWilliamE.McDermottUniversityofDenverResearchInstituteDenverColoradoAnatolyP.NapartovichTroitsk Institute for Innovationand Fusion ResearchTroitskRussiaEdwardF.PlinskiWrocawUniversityofTechnologyWrocaw,PolandNikolaV.SabotinovInstituteofSolidStatePhysicsBulgarianAcademyofSciencesSofiaBulgariaEndo&Walter /GasLasers DK553X_C000 FinalProof page xiii 17.11.2006 4:29pmAndreyV.SavinBalticStateTechnicalUniversityLaserSystemsInc.St.PetersburghRussiaRobertF.WalterSchaferCorporationAlbuquerqueNewMexicoSergeyI.YakovlenkoGeneralPhysicsInstituteMoscowRussiaEndo&Walter /GasLasers DK553X_C000 FinalProof page xiv 17.11.2006 4:29pmTable of ContentsChapter1 PrinciplesofGasLasers ......................................................................................1KrzysztofM.AbramskiandEdwardF.PlinskiChapter2 FluidDynamics.................................................................................................39AnatolyS.Boreysho,AndreyV.SavinandVictorM.MalkovChapter3 OpticalResonators.......................................................................................... 161AnatolyP.NapartovichChapter4 ElectricCircuits ............................................................................................... 183VladimirV.KhukharevChapter5 ElectricDischargeCOLasers.......................................................................... 201AndreyA.IoninChapter6A DC-ExcitedContinuous-WaveConventionalandRF-ExcitedWaveguideCO2Lasers ...................................................... 239EdwardF.PlinskiandKrzysztofM.AbramskiChapter6B High-PowerElectricCO2Lasers .................................................................. 287AlanE.HillChapter7 HydrogenandDeuteriumFluorideChemicalLasers ..................................... 341WilhelmH.BehrensandPeterD.LohnChapter8 ExcimerandExciplexLasers........................................................................... 369SergeyI.YakovlenkoChapter9 AtomicIodineLasers ...................................................................................... 413StevenJ.Davis,WilliamE.McDermott,andMichaelC.HeavenChapter10 MetalVaporLasers....................................................................................... 449NikolaV.SabotinovChapter11 OtherGasLasers........................................................................................... 497KrzysztofM.AbramskiandEdwardF.PlinskiIndex................................................................................................................................... 541Endo&Walter/GasLasers DK553X_C000 FinalProof page xv 17.11.2006 4:29pmEndo&Walter /GasLasers DK553X_C000 FinalProof page xvi 17.11.2006 4:29pm1Principles of Gas LasersKrzysztof M. Abramski and Edward F. PlinskiCONTENTS1.1 Introduction................................................................................................................. 21.2 GasMedia.................................................................................................................... 41.2.1 IonizedGas....................................................................................................... 51.2.2 Interactions ....................................................................................................... 51.2.3 FreeElectrons................................................................................................... 51.2.4 ElectronEventsinDischarge............................................................................ 71.3 SpectroscopyofGases ................................................................................................. 91.3.1 QuantizedStatesofAtoms ............................................................................... 91.3.2 QuantizedStatesofMolecules......................................................................... 111.3.2.1 VibrationalStatesofDiatomicMolecules .........................................111.3.2.2 RotationalStatesofaDiatomicMolecule ........................................ 131.4 SpectralLines..............................................................................................................151.4.1 NaturalBroadening .........................................................................................161.4.2 Collisional(Pressure)Broadening.................................................................... 161.4.3 DopplerBroadening ........................................................................................ 171.5 GainConditions.......................................................................................................... 191.6 LaserActionASimpleModel..................................................................................221.6.1 EmptyCavityModel .......................................................................................231.6.2 LaserAction ....................................................................................................241.6.3 SchawlowTownesFormula ............................................................................ 251.6.4 MultimodeOperationofLasers ...................................................................... 251.6.5 PulseOperation ...............................................................................................251.7 LaserResonators ........................................................................................................261.8 PumpingTechniques...................................................................................................271.8.1 DCDischarge .................................................................................................. 281.8.2 PulseDischargeExcitation .............................................................................. 301.8.3 RFDischargeExcitation ................................................................................. 341.8.4 MicrowaveExcitation...................................................................................... 341.8.5 Gas-DynamicExcitation..................................................................................351.8.6 OpticalPumping ..............................................................................................351.9 CoolingSystems.......................................................................................................... 351.9.1 DiffusionCooling ............................................................................................361.9.2 FlowingSystems ..............................................................................................37References ........................................................................................................................... 37The year 1960 witnessed the beginning of a new revolution in optics. The effect of stimulatedemission, predictedin1917byAlbert Einstein, was finallyimplementedinpractice. TheEndo&Walter/GasLasers DK553X_C001 FinalProof page 1 17.11.2006 6:36pm1discovery of the new optical device, called laser, was preceded by several theoretical works ofCh. Towns, N.G. Basov, and A.N. Prokhorov, who won a Nobel Prize in 1964. The man, whofirst admired a coherent radiation fromhis ruby laser was T.H. Maiman; however, he was not aNobel Prize Laureate. In fact, the revolution in optics was rather calm, and it would be muchbetter to call it a velvet revolution. Nobody expected any practical use for the new, sophis-ticatedtoy of scientists. At that time, the laser was calledthe device waiting for a job. The year1960 brought a newdevicea heliumneon (HeNe) laser elaborated by A. Javan. The HeNelaser operating on a 1.15 mm wave initiated a new branch in opticsgas lasers. Soon, the nextmilestonewasreachedin1964byC.K.N. Patel, whoinventedalaseroperatingoncarbondioxide (CO2) molecules. After a few modifications such as the addition of nitrogen (N2) andHe,thelasergaveanoutputof100watts.Itwasabigbreakthroughinlaserphysics,anditkindled the imagination of scientists and engineers. Applications of lasers in different branchesof scienceandtechnologybecameareality. Eventoday, gas lasers fulfill leadingroles inresearch, technology, techniques, and many unexpected branches of human activity.1.1 INTRODUCTIONWhatdoesthetermLasermean?TheacronymLASER(light amplificationbystimulatedemissionof radiation) suggeststhat the device is an amplifier. However, it is not true; it is an oscillator. Moreover, replacingamplificationbyoscillationcouldbringfunnyassociations.Letusleaveitasitis.Whatadjectivesusuallyprecedethewordlaser?Thetermsgas, solidstate, andliquid givethemostgeneral descriptionoflasers. Thissystematics is very natural, taken from the names of media, which occur in nature surrounding us.In practice, more precise adjectives describing the types of a laser can be met. Adjectives HeNe,carbon monoxide (CO), CO2, and N2are examples of names, which directly describe the lasermedium. In that case, they are gas lasers. They can be divided into atomic or molecular lasers. NdYAG, fiber anddiode lasers belongtoagroupof solid-state lasers. Words like rare-gas, copper, goldvapor, ion, and free electron indicate specific laser media. The adjective chemical refers to lasersgoverned by chemical reactions, and they are also gas lasers. The adjective excimer describes thespecificmediumexistingonlyinanexcitedstatelikeXeF*. X-rayor e-beamindicates themechanismoftheexcitation. SometimesanacronymisusedasanadjectivelikeSSDPL(solid-statediodepumpedlaser); ofcourse, thedevicebelongstosolid-statelasers. AsimilarexampleisaCOIL(chemical oxygeniodine laser) or TEA laser (transverse excited atmospheric laser)certainly gas lasers. Dye lasersbelong tothe liquidlaser group. More systematic descriptionof gas lasers is giveninChapter 11.Whywasgaslaserdevelopmentsodynamic?Since the 1960s, gas laser technology has demonstrated a very rapid rate of development. Gaslasershitanextremelyfavorablehistoricalperiod.Flourishinginvestigationsongases,highvacuum technology, discharges, and plasma were the factors that accelerated the developmentof gas lasers at that time. Additionally, well-developedspectroscopy brought significantinformationaboutenergystructuresofdifferentgasmediathebasetodiscovernewlasertransitions.We should also remember thenew technologies oflow-loss laserdielectric opticsandinfrared(IR)components,likeZnSeorZnS(irtrans).Whyaregaslaserssointeresting?Thewell-developedtechniqueofgasdischargesallowsexcitinggasmediainreasonable,easyilyformable,lasercavities.Endo&Walter/GasLasers DK553X_C001 FinalProof page 2 17.11.2006 6:36pm2 Gas LasersAccordingtoitsnature,gasadoptsshapeslimitedbyalasercavity. Gas lasers can be easilyscaledinlength, area,and volumewithouta significant increaseinthecostofthedevice. Longlifetimehasbeenachievedforgaslaserdevicesbecauseof well-developedhigh-vacuum technologies. For instance, many who work in the laboratory or industry can useaHeNelaserevenafewdecadesoldwithoutanynoticeabledegradation.Inmanylasers,recyclingofthegassufficientlyincreasestheirlifetime. Only gas media have the possibility of flowing fast through the laser device. In that way,refreshingandheatremovalcanbeeasilyachieved.Ahuge advantage of gases is their abilitytomixindifferent ratios andat differentpressurestoformhighlyhomogeneousmedia.Arelativelylowdensityofgasmediumdemonstratesnarrowandwell-definedspectralemissionlines, whichmakesthemstablesourcesofoptical radiation(inoutputpowerandfrequency).Theotheradvantageisthepossibilityof usingisotopestoshift thespectrumof laserradiation. Gaslaseroutput coversall optical spectrafromfarinfrared(FIR) radiationtox-ray.SomerepresentativeexamplesareshowninFigure1.1.Ar-ion (488 nm)Xe (488 nm)Cu vapor (510.6 nm)Ar-ion (514 nm)Cu vapor (578.2 nm)HeNe (594 nm)HeNe (612 nm)Au vapor (628 nm)HeNe (632.8 nm)Kr-ion (676 nm)UVUltravioletVisibleNINear infraredMIMedium infraredFIFar infraredKr-ion (416 nm)HeCd (441.6 (325) nm)100 nmH2 (110162 nm)F2 (152 nm)ArF (193 nm)KrCI (222 nm)KrF (248 nm)XeCI (308 nm)N2 (337 (428) nm)XeF (351 nm)Ar-ion (364 (351) nm)HeNe (1152 nm)COIL (1315 nm)400 nm750 nm3 m30 m100 m1 mmFIMINIUVHF over tone (=1.7 m)~ArXe (1.73 m)HF (2.063 m)DF (3.54 m)HeNe (3.391 m)Hbr (3.46 m)DF (3.64 m)CO overtone (2.54.2 m)CO (5.78.2 m)CO2 (911.8 m)N2O (1011 m)Ammonia (=13 m)Methanol (371217 m)Methyl fluoride (4961222 m)FIGURE 1.1Thespectralmapofpopulargaslaserradiation.Endo&Walter/GasLasers DK553X_C001 FinalProof page 3 17.11.2006 6:36pmPrinciples of Gas Lasers 3WhattoRead?This chapter gives some elementary knowledge about gas laser operation. It includes adescriptionofpropertiesofneutral andweaklyionizedgases. Next, itintroducesgasspec-troscopyandoptical gainconditions. Thesimplemodel ofalaseractionispresented, anddifferent kinds of laser excitation are reviewed. A systematic description of different gas lasersis given. However, the basic knowledge given in this chapter is limited. The reader who wantstoextendhisbasicknowledgeabout lasersassuchcanfindit inwell-knownandreliablehandbookswrittenbyfamousauthors. WeencouragetoreachforbooksbySiegman[1],Verdeyen[2], Svelto[3], Milloni [4], andtwobooksbyYariv[5,6]. Wewouldalsoliketorecommend an important book edited by Eden [7] which contains a set of the most significantpublicationsthatarethemilestonesingaslaserscienceandtechnology.Inthesuccessivechaptersof thisbook, thereaderwill finddetailedinformationabout:fluiddynamics (Chapter 2), optical resonators (Chapter 3), electric circuits (Chapter 4),molecularCOandCO2lasers(Chapter5andChapter6), chemical HFlasers(Chapter7),excimer lasers (Chapter 8), iodine lasers (Chapter 9), metal vapor lasers (Chapter 10), and theothergaslasers(Chapter11).1.2 GAS MEDIAGas media were the first to be recognized as laser media. There is, of course, one exceptionruby, which was the first operating laser, but it is the exception proving the rule that randomcharacter of science development has its own charm. Irrespective of the competitions betweendifferentkindsofmedia, thegaslaserswerethefirstandfastest developingdevicesatthebeginning of their history, which was in the late fifties of the twentieth century. Gas medium,treatedasachaoticassemblyofspecies(atoms,molecules)thathavenovolumeandforcesbetweenthem,canbedescribedbyanidealgasequation:pV RT, (1:1)where p is the absolute pressure,V the specific volume,T the absolutetemperature, andR isthegasconstant.Equation1.1canberewritteninadifferentform:pV NkT, (1:2)wherekistheBoltzmannconstantandNisAvogadrosnumber(6.02481023).The specific property of the gas medium is the so-called Avogadro law, which states: equalvolumes of ideal gases at the same temperature andpressure containthe same number of species(atoms or molecules). The equations considered here are valid for diluted gases. In practice, thegas at atmosphericpressurecanbestill consideredas diluted. Most gas lasers operateatpressuresequalorbelowoneatmosphere.Hence,theidealgasequationcanbeappliedformost gas laser media. The neutral gas considered here does not fulfill conditions for laser action.The medium has to be excited between the chosen internal energy levels of atoms or moleculesfortheappearanceofpopulationinversion. Itcanbeachievedbydifferentmechanismsofexcitation. The main technique to obtain the population inversion in a gas mediumis excitationbydischarge.Experimentaland theoreticalresearchesondischargestogetherwiththedevel-opment of gas spectroscopy have been well elaborated since the middle of the twentieth century.Allthisknowledgehadformedaverysolidbasetothefastandnaturaldevelopmentofgaslasers from the beginning of laser history, which started just after the Second World War.Endo&Walter/GasLasers DK553X_C001 FinalProof page 4 17.11.2006 6:36pm4 Gas LasersGas as alaser mediumis easilyformable inlengthandshapethe reservoir andtheexcitationgeometrydeterminethelaserdimensions. Thehugeadvantageofgasmediumisthe homogeneity andscalability. The researches dealing withgas lasers showthat lasermediumparameterscanbecontrolledatareasonablylargescalebychangingthepressure,excitationparameters(dischargecurrent),andgascomponents.Generally, neutral gas does not fulfill conditions for quantumgainandlaser action.Although, there are cases, like FIRlasers (submillimeter lasers), whenthe neutral gas isexcitedviaexternal pumpinglaser beam(noelectrical species like free electrons or ionsinthe gas). Nevertheless, most gas lasers use gas discharge mediaobtainedbydifferenttechniques.1.2.1 IONIZED GASGas laser discharge can be considered as the so-called weakly ionized plasma, which containssomechargedspecies (freeelectrons,ions)necessarytoobtainexcitation ofthegasmedium.Ionizedgas is describedbyits basic parameterfreeelectrondensityne. For typical gasdischarges, theelectrondensityfallsintherangene1016=1020=m3[8], comparedwiththedensityofgasinnormalconditions(atmosphericpressureat08C)N2.71025=m3.A weakly ionized gas discharge can be still considered as a neutral gas. Such a gas dischargeformstheso-calledquasineutralplasma,wherestrongelectricfieldsdonotappear.Fromaphysicalpointofview,itmeansthatthenextnetchargedensityoffreeelectronsni,positiveni,andnegativeniionsproducedintheplasmaisclosetozero:neni% ni: (1:3)For ionized media,apart from free electrons thereare several species ofions,which can givequiteacomplicatedpictureofdischarge,particularlyinthecaseofmoleculargases.1.2.2 INTERACTIONSAtoms or molecules have two kinds of energy: internal and kinetic. The exchange of energy inthe process of chaotic motions occurs via collision mechanisms. Two kinds of speciescollisionscanbedistinguished:1. Inelasticcollisionswheninternalenergyofspeciesundercollisionischanged.2. Elastic collisionwhen only the kinetic energy (not internal) of species under collisionexchanges(billardballcollisionanalogy).There are different processes inaplasmatoobtainpopulationinversion, necessarytoachievethelasingcondition.Table1.1summarizessomeofthemostimportantinteractionsthatoccuringasdischarges[8].Electrical properties of plasma are mainly determined by inelastic collisions responsible forcreatingfree electrons andionizedspecies. Nevertheless, elastic collisions alsocontributesubstantiallytoelectricalpropertiesofdischarge(seeTable1.2).1.2.3 FREE ELECTRONSElectrons play the most important role in inelastic collisions. They are responsible forionization and excitation of atoms and molecules. There are two basic parameters character-izingelectrons: theelectrondensityneandelectrontemperatureTe. Theelectrondensityisdirectlyrelatedtotheelectrical currentdischarge(DCorRFexcitation). FreeelectronsinEndo&Walter/GasLasers DK553X_C001 FinalProof page 5 17.11.2006 6:36pmPrinciples of Gas Lasers 5discharge, aslightparticles,aremostmovable. Hence,kinetictemperatureTecanbemuchhigherthanthekinetictemperatureTofmuchheavierspecies(molecules,atoms,andions),accordingtothesolution:mv22 3kTe2, (1:4)wheremistheelectronmass, v2themeansquareelectronvelocity, andkisBoltzmannsconstant.Theelectrontemperatureindischargecanreacharangeoftensofthousandkelvin,whenthe temperature of the rest of species (ions, neutrals, and excited atoms or molecules) is muchlower;thatis,atthelevelof300Kandhigher.Thetemperaturedistributioninsideplasmadischargeisdescribedbytheheattransferdifferentialequationasfollows:r(l(T)r(T)) w(x,y,z), (1:5)TABLE 1.1List of Important Inelastic Interactions in Gas Discharges1 e X ! X* e Collisionalexcitationofanatom ormolecule byanelectrone X*!X** e2 e X*!X e Deexcitationofan atomandproducingafastelectron viasuperelasticcollisionofanexcited atomandanelectron3 e X ! X e e Electron collisionalionizatione X*!X e e4 X e e ! X e Collisionalrecombination5 e YZ !e X ZDissociationsandionizations ofmoleculese YZ !e Y Ze YZ !Y Z6 e X ! X hn Forming anegative ionby radiativeattachment7 X hn !e X Photodetachment8 e YZ!Y Z*DissociativerecombinationIonicProcesses9 X Y! X Y Charge transfer10 X Y! XY Ionion recombinationCollisions withNeutrals11 X* Y !X Y*Excitationexchange andcollisionaldeexcitationX* Y !X Y kin.en.12 X* Z !X Z e Penning ionizationSource:From Charrington, B.E.,GaseousElectronicandGasLasers,PergamonPress,Oxford,NewYork,1979.TABLE 1.2List of Important Elastic Interactions in Gas Dischargese X !(e kin.en.) (X kin.en.)e1 e2!(e1 kin.en.) (e2 kin.en.)X Y !(X kin.en.) (Y kin. en.)Source:From Charrington, B.E.,GaseousElectronicandGasLasers,PergamonPress,Oxford,NewYork,1979.Endo&Walter/GasLasers DK553X_C001 FinalProof page 6 17.11.2006 6:36pm6 Gas Laserswherel(T) isthethermal conductivityof thegas(gasmixture) andw(x,y,z) isthepowerdistributionperunitvolume.The movement of a free electron in a gas discharge is determined by the local electric E andmagneticBfieldsanditscollisionswithionsandneutrals.ItcanbedescribedbyLangevinequation:ddtmv eE v B_ mvnc, (1:6)whereeistheelectroncharge, vtheelectronvelocity, andncisthecollisionfrequencyformomentumtransfer.The electric field Eplays a dominating role in creating plasma. Ignoring the magnetic fieldBinEquation(1.6),wehavemdvdt eE mvnc: (1:7)ItisconvenienttoconsiderDCdischarge,wheredriftvelocityv %const.Hence,v eEmnc: (1:8)Introducingameanfreetimebetweencollisions,t 1=vc,themainparameterofdischarge,mobility me,canbedefinedasme vE emncetm : (1:9)ThevectorofacurrentdensityindischargeisgivenbyJ neev: (1:10)Taking into account Equation 1.9 and Equation 1.10, the conductivity s can be introduced ass JE nee2mnc: (1:11)Powerdensitylostindischarge,oftencalledspecificpower,isgivenbyre E J mee2mncE2(1:12)anditistheelectricalpowerconsumedbyheating.1.2.4 ELECTRON EVENTSIN DISCHARGETheenergyofelectroninanelectricfieldofadischargechangesintimeandspace, anditdetermines its behavior in plasma. The main source of the electron energy in an electric field,theelectrongainsenergyfromthefield.However,inthemeantime, itlosesusuallyasmallpart of its kinetic energy in the process of an elastic collision. Much higher losses of the kineticEndo&Walter/GasLasers DK553X_C001 FinalProof page 7 17.11.2006 6:36pmPrinciples of Gas Lasers 7energyofelectronscanoccurbecauseofinelasticcollisionwithatomsormolecules.Inthatprocessinternal quantumenergyof atommoleculeincreases. Theslowerelectronisagainaccelerated in the electric field. Following the qualitative model presented by Verdeyen [2], themean kinetic energy we of electron gas with ne density changes with time: increasing (becauseofthefield)anddecreasing(becauseofbothkindsofcollisions):dwedt electricalpower gasheating excitation Pelncdne322k 322A_ _

jneninelDwj,(1:13)wherewe ne322k_ _,2k is the characteristic energy of the electrons (kTe), 2A the characteristic energy of the atom(kTA),d 2m=Mthefractionoftheexcessenergylostperelasticcollision,nineltheinelasticcollisionrate,and Dwjistheenergylostinaninelasticcollision.TheexcitationterminEquation1.13representstheelementaryexcitationmechanism[8]thatisdescribedinTable1.1e(Wkin:) A A*(DW) e(Wkin:DW) (1:14)For the established conditions of discharge, dwe=dt 0 in Equation 1.13. Additionally,neglectingeffectsofinelasticexcitationinEquation1.13,theequationcanberewrittenas32(2k 2A) 2d12meEmnc_ _2: (1:15)Keepinginmindthatthecollisionfrequencyncofelectronsisnc NsV, (1:16)where sisthecollisioncrosssection andNistheneutralgasdensity;formanyreasons,itisconvenienttodescribetheright-handsideofEquation1.15asafunctionofpracticalratio,theelectricalfield=gasdensity(E=N)parameter:32(2k 2A) 2d12memsV_ _2EN : (1:17)It is clear that electron energy 2kkTeof the electron gas is an increasing function of E=Nratio.The E=N parameter plays a basic role in many calculations and descriptions of gas discharges:ThecharacteristicenergyofafreeelectroninplasmacanbemeasuredasafunctionofE=N.IonizationbalanceconditionscontrolE=Nofadischarge.E=Ncontrolstheperformanceofthelaser.DriftelectronvelocitystronglydependsonE=Nratio.Endo&Walter/GasLasers DK553X_C001 FinalProof page 8 17.11.2006 6:36pm8 Gas LasersIf the reader wants to gain more knowledge to that presented here, we recommend the classicbook by Brown [9] and additionally, the book by Hirsh and Oskam [10].1.3 SPECTROSCOPY OF GASESThe quantum nature of matter is particularly easy to observe in gases. Glowing discharge is aspectacular phenomenon, where this quantumnature appears. Generally, the gas matterconsistsof atoms, molecules, andtheirions. Qualitativelygasescanbedistinguishedintoatomicgasesormolecularones. Themaindifferencebetweenatomsandmoleculesliesintheir spectroscopic nature or their internal energy storage. The energetic state of the particles(atomsandmolecules)isdescribedbySchro dingerwaveequation:HC("rr,t) i"htC("rr,t), (1:18)whereC("rr,t) isthewavefunctionof theparticle(accordingtoMaxBorn, C("rr,t) C*("rr,t)providestheprobabilityofobservingtheparticleattheposition "rr,attimet),H "h22mr2V(r) (1:19)is the Hamiltonian operator and V("rr) is the potential energy operator of the particle of mass m.Thesolutionofawavefunctionisexpectedtobeoscillatingwithangularfrequencyv,C("rr,t) C(r)eivt, (1:20)andthetime-independentSchro dingerequationtakesthesingularform:HC(r,t) "hvC(r) EC(r), (1:21)whereEistheso-calledeigenvalue(quantizedenergy)ofwavefunction C("rr,t).1.3.1 QUANTIZED STATESOF ATOMSLet us consider the Schrodinger equation that describes the Bohr atom (single electron in thefieldofchargee).ThepotentialenergyV("rr)istheelectrostaticpotentialinaCoulombfield:V(r) e24p0r: (1:22)Thesolutiongivesthequantizedenergy(eigenvalues)ofahydrogen-likeatom:En 1(4p0)2e4me2"h21n2_ _ 13:6 (eV)n2, (1:23)wherenisaninteger.ThesolutionforthewavefunctionforsphericalcoordinatesisC(r,Q,f) Cn,l,m(r,Q,f) C(n,l,m) (1:24)Endo&Walter/GasLasers DK553X_C001 FinalProof page 9 17.11.2006 6:36pmPrinciples of Gas Lasers 9anddepends onthreen, l, mnumbers, where: nis theprinciplequantumnumber (n 1,2, . . . , 1), l theazimuthal quantumnumber(l 0, 1, 2, . . . , n1), andmisthemagneticquantumnumber(m0, +1, . . . , +l).Addingtwopossiblespinstatesofelectrons,thenumberofstatespossessingEnenergyis2

nll0(2l 1) 2n2:We call it 2n2-fold degenerated. The energy levels n with azimuthal levels l for the hydrogenatomareillustratedinFigure1.2a.Figure1.2bshowstheenergylevelsofannitrogenatom(heavier than a hydrogen one), for which the hydrogen-like rules are not fulfilled. Such a clearquantum model of energy levels can be described only for hydrogen (and possible for helium).The atoms with Z protons and Z electrons are much more complicated in finding the analyticsolutionfortheirquantumenergylevels.Therearepossibleradiativetransitions(emissionsandabsorptions) betweensomelevels. Wecall themopticallyallowedtransitionsbetweenlevels. Theelectronoftheatomjumpsfromupperlevel E2tothelowerlevel E1andemitsphotonswithenergydescribedbyBohrformula:hn E2E1: (1:25)TheselectionruleDl 1 (1:26)FIGURE 1.2Anenergy-leveldiagramforhydrogenandnitrogen.Endo&Walter/GasLasers DK553X_C001 FinalProof page 10 17.11.2006 6:36pm10 Gas Laserssays that only these transitions that differ in azimuthal quantum number l by unit are allowed.As can be seen from Figure 1.2, the typical transitions have energies in the range 1=10 eV andtheirspectraspreadfromnearIRviavisibletoUVrange.1.3.2 QUANTIZED STATESOF MOLECULESAmolecule, whichisacomplexquantumstructureoftwoormoreatoms, ischaracterizedbyadditional forms of internal energies: vibrational androtational. Adiatomicmolecule(H2,N2,O2,andCO),apartfromitselectronicstates,hasadditionalstatesassociatedwithitsvibrationsandrotations(Figure1.3),whicharealsoquantized[11].1.3.2.1 Vibrational States of Diatomic MoleculesLetusstartwiththephenomenonofvibrations.Atwo-atommoleculecanbetreatedastheso-calledharmonic oscillator. When theSchrodinger equation is applied to sucha two-atomvibratingsystemwiththeparabolicpotentialfunctionV(r)oftheoscillator:V(r) 12km2r, (1:27)where k is the restoring force constant and mrm1m2=(m1m2) is the reduced mass of nuclei,thesolutionforeigenvaluesofvibrationalenergyalsogivesquantizedvalues:En hnoscn 12_ _, (1:28)where nistheso-calledvibrationalquantumnumberandnosc 12pkmr(1:29)isthefrequencyofharmonicoscillation.The harmonic oscillations are illustratedinFigure 1.4a, where the parabolic shape ofpotential function V(r) forms the envelope of equally separated oscillating levels. The quantumselection rule for the vibration transitions is Dv +1.However, the parabolic shape of the oscillation potential operates well only for lowquantumv numbers. When the internal vibrational energy increases, the amplitude ofvibrationsincreasesandtheshapeofthepotential changesintoanharmonic(theso-calledBorn-Oppenheimerapproximation).ThisisdemonstratedinFigure1.4b.FIGURE1.3Simpledemonstrationof vibrational (a) androtational (b) movements of atwo-atommolecule.Endo&Walter/GasLasers DK553X_C001 FinalProof page 11 17.11.2006 6:36pmPrinciples of Gas Lasers 11The allowed vibrational energies for the two-atom anharmonic oscillator are modified andaregiven:En hnoscv 12_ _hnoscXev 12_ _2, (1:30)whereXeistheanharmonityparameter.Theenergydistancebetweenneighboringlevels, DE,isnolongerconstantDE Ev1Ev hvosc[1 2Xe(v 1)] (1:31)anditdecreaseswhennincreases(Figure1.3b).WheninternalvibrationalenergyreachestheD0level,themoleculedissociates.AtypicaldissociationD0levelhasa valueofa fewelectronvoltsforadiatomicmolecule.Ithastobe12Dissociation level3456En = 0n = 012345678910121113141618E1715r r r equilibriumr equilibriumr equilibriumr (a)(b)rFIGURE 1.4Theillustrationofharmonic(a)andanharmonic(b)vibrationallevels.Endo&Walter/GasLasers DK553X_C001 FinalProof page 12 17.11.2006 6:36pm12 Gas Laserspointedthat becauseof anharmonicity, quantumselectionruleforvibrational levelsisnolongersostronganditacceptstransitions:Dv 1, 2, . . . (1:32)Energeticdifferencesbetweenneighboringvibrational levelsaretypicallyequaltotenpartsof electron volts and their typical spectra appear in the near- and mid-IR. However, it shouldbe noted that for more complicated multiatommolecules, possessing permanent dipolemoment(seechapterOtherGasLasers)theselectionruleforvibrational levelscanalsobe Dv 0.1.3.2.2 Rotational States of a Diatomic MoleculeA molecule can be considered as a rigid rotator as shown in Figure 1.2b, with fixed separationR0 between atoms. The molecule rotates around its axis and the Schrodinger equation for thatcasehastheform"h22mrr2C ErotC: (1:33)TherotationenergyofamoleculeisquantizedandisgivenbyEJ "h22mrR2 J(J 1) BeJ(J 1), (1:34)whereJistherotational quantumnumberandcanobtainanyintegervalueandBeistherotational constant characterizingamolecule. Therotationenergyincreases quadraticallywithJ.ThequantumselectionruleforradiativetransitioninamoleculeisgivenbyDJ 1: (1:35)TheenergeticdistancebetweentwoneighboringrotationallevelsJandJ 1isgivenbyDE Be(J 1), (1:36)and the structure of rotational levels belonging to succeeding vibrational levels is illustrated inFigure1.5.However, therotational constant Bedepends ontheparticular vibrational level nof amoleculeandcanbereplacedbytheso-calledeffectiverotationalconstantBv:Bn Beaev 12_ _, (1:37)where aeisasmall(comparedwithBe)positiveconstant.Thetotal internal energyofthemoleculeisasumofvibrational Ev(Equation1.30)androtationalEJenergies(Equation1.37):E(v,J) EnEJ hnoscv 12_ _hnoscXev 12_ _2BvJ(J 1): (1:38)Endo&Walter/GasLasers DK553X_C001 FinalProof page 13 17.11.2006 6:36pmPrinciples of Gas Lasers 13Theschematicenergy-leveldiagramforavibratingrotatingmodelisshowninFigure1.5.Thequantumselectionruleformoleculeswithzeroelectronmomentumabouttheinter-nuclearaxisisdescribedbyEquation1.35asDJ +1. However, formoleculespossessingnonzeroelectronangularmomentum,thequantumselectionruleisgivenbyDJ 0, 1: (1:39)Combiningthe selectionrules for vibrational androtational levels (Dv +1, +2, . . . andDJ +1),theallowedradiativetransitionscanbesetintotwobranches:1. R-branchformedbytransitionsJ ! (J 1)2. P-branchformedbytransitionsJ ! (J 1)This ideaof formingthe R- andP-branches is illustratedinFigure 1.6. For the rulesDn +1and DJ 0,transitionsJ ! JformQ-lineandtheyoverlapintoonestrongline.Eachfreeelectronhasthreedegreesoffreedom.Accordingtostatisticalmechanics,eachdegree of freedom is represented by kT energy, where k is a Boltzmann constant and T is theabsolute temperature. Hence, translation energy of the atom is 3=2kT. A polyatomic N-atommoleculehas3Ndegreesof freedom. Threeof themareoccupiedbythetotal translationmotion of the molecule and two (for a linear molecule) or three (for a nonlinear molecule) arerepresentedbyfreerotationsof amolecule. Hence, wehave(3N6) possiblevibrationalmodesinnonlinearmoleculesand(3N5)modesinlinearmolecules.Similar toanatom, amoleculealsohas its electroniclevels. Therefore, threekinds oftransitionscanbedistinguishedinamolecule:1053210105105105RotationallevelsVibration levelFIGURE1.5Vibrational androtational levels, weighedbyMaxwell distributionof populationforthermodynamicequilibrium.Endo&Walter/GasLasers DK553X_C001 FinalProof page 14 17.11.2006 6:36pm14 Gas Lasers1. Rotational transitions (when thevibrational quantumnumberand the electronicstatedonotchange).TheirtypicalspectrarangeintheFIRandsubmillimeterregions.2. Vibrationalrotational transitions (whenthe electronic state does not change). ThetypicalspectrarangefromnearIRtoFIR.3. Electronic transitions (when all quantum numbers change). The typical spectral range:visibleandnearIR.To spread further knowledge to the reader, we would like to direct the reader to good booksaboutquantummechanics[1114].1.4 SPECTRAL LINESThequantumnatureofatomsormoleculescausesoneofthemechanismsofchangingtheirinternal energytoberadiative transitionemissionor absorption. Theallowedradiativetransition is possible between two levels E2 and E1 (Figure 1.7), when quantum selective rulesaccept it. According to the quantum theory, radiative transition between two levels can occurbytheemissionofaphotonwithenergyhn:E2E1 hn (1:40)10987654321J = 0J = 0R4R3R2R1R0P5P-branch R-branch Q10987654321P4P3P2P1P9 P8 P7 P6 P5 P4 P3 P2 P1 R0 R1R2R3 R5R4 R6R8R7R9FIGURE 1.6Modelofrotationaltransitions:formingP-branch,Q-line,andR-branch.Endo&Walter/GasLasers DK553X_C001 FinalProof page 15 17.11.2006 6:36pmPrinciples of Gas Lasers 15orbyabsorptionof thephotonwiththesameenergy, demonstratedbyaspectral lineofradiation(emissionorabsorption)atthefrequency y.Althoughthelevelsarequantized,thetermline doesnot meanthemathematical line(whichforareaderfamiliarwithmath-ematicsmeansd-Diracfunction).Becauseofdifferentphysicalmechanismsthelevelsarebroadened.1.4.1 NATURAL BROADENINGThe finite lifetime of the level causedbyspontaneous emissioneffect gives the so-callednatural broadening. Whenwehaveanatomwithtwodistinguishedlevels as is showninFigure 1.7 and the atom is in state 2, it can radiate the photon spontaneously to state 1. Thisspontaneoustransition21occursstatisticallyint21time, whichiscalledlifetimeof 21transition.Foranassemblyofatomsexcitedtolevel2,thelifetimet21canbeinterpretedasthe decayrate that decreases the populationof level 2andsimultaneouslyincreases thepopulationoflevel 1. Thespontaneousemissioneffectleadstothenatural spectral broad-eningofasingleradiativetransitionorsingleseparatedtwo-levelatom.The spectrum of the natural broadened line is given by the so-called Lorentzian shape andisdescribedbytheformula:GL(v) 1t21_ _2(v v0)21t21_ _2 , (1:41)where v0isthecentralangularfrequencyoftheline.Fromthisequationonecanseethat thefull widthat half maximumDvncanbeeasilycalculatedasDvn 2t21or Dnn 1pt21: (1:42)Typical lifetimes of radiative transitions are at 108=sec. Hence, the natural lifewidthoftypical radiativetransitions aretens of MHz. However, therearelinesingasesthat havemuchlonger lifetimes. Theycanbe as longas 1sec, 1h, 1day, andsome lines canbeparticularlynarrow.1.4.2 COLLISIONAL (PRESSURE) BROADENINGDifferentkindsofcollisionsofatomsormoleculesinthegasenvironmentarethesourceofextraperturbationsleadingtothebroadeningoftransitionlines. ThecollisionsreducetheE2g(n)nn = FWHM (Full width at half maximum) n0E1FIGURE 1.7Line-broadeningdemonstration.Endo&Walter/GasLasers DK553X_C001 FinalProof page 16 17.11.2006 6:36pm16 Gas Laserslifetime of the excited state. They can also perturb the energy separation between two levels oftheemittingorabsorbingatomormolecule. Themeasureof collisional broadeningisthecollisionallifetimetcgivenbytheformula1tc Nsvav Nfc, (1:43)whereNisthegasdensity,fcsvavistheeffectivefrequencyofcollisions,sisthecollisioncross section of the atom or molecule, and vav is the average velocity of the atom or molecule.ThenatureofcollisionalbroadeningissimilartonaturalbroadeningandithasthesamestatisticalcharacterandthesameLorentzianshape:GL(v) 1t_ _2(v v0)21t_ _2 , (1:44)where1t 1t211tc,and t!t21whenthepressureofgasachieveszero.Inpractice, collisional (pressure)broadeningdependsonatomsormoleculestakingpartinthe collisions. Hence different lines are describedby pressure broadening coefficientsexpressingfrequencybroadeningbyunit pressure(MHz=Torr). Forexample, typical lasertransitions are: HeNe (line 632.8 nm)70MHz=Torr, CO2 (CO2, H2, He mixture, 10.6 mm)~5MHz=Torr,andtheydependonthepartial ratiosofusedspecies.Itisinterestingtonoticethatatthepressure1barofthemixtureCO2laserthepressure-broadened spectral line has 40 GHz linewidth. The lines of the vibrationalrotational branchof aCO2moleculeareseparatedat about 50GHz, andat atmosphericpressurethelinesoverlapintoonespectral branch. Dependingonthepartners under collisions, thebroad-eningscanbedistinguishedinto:1. Holtzmarkbroadening(collisionsbetweenthesamespecies)2. vanderWaalsbroadening(collisionsbetweenunlikespecies)1.4.3 DOPPLER BROADENINGWhentheradiatingatomormoleculeisinrandommovementamongmanyspeciesanditsvelocitycomponentisvzalongtheaxis(chosenbyanobserver,Figure1.8),astheresultofDoppler effect, the frequencyof aphotonemittedtowardthe observer will be Dopplershifted:v v01 vzc_ _, (1:45)wherevzcanbepositiveornegativedependingonthedirectionoftheatommovementandcisthelight velocity.Endo&Walter/GasLasers DK553X_C001 FinalProof page 17 17.11.2006 6:36pmPrinciples of Gas Lasers 17The gas in the thermodynamic equilibrium is governed by Maxwellian velocity distributionf(vz)withtheGaussianshape:f (vz) 1ppvpexp vzvp_ _2 G0 expvzvp_ _2, (1:46)where vp(2kT=m)1=2is the most probable velocity and m is the atomic mass of the emitter.TheMaxwelliandistributionf(vz)inthevelocitydomaincan be replacedby thefrequencydomainbysimpletransformationofEquation1.45:vz n n0n0c (1:47)andthenweobtainthelineshapeGD(v)determinedbyaDopplereffect:GD(n) G0 exp m2kTc2n0(n0n)2_ _, (1:48)whichstillpreservestheGaussianshape.Theelementarycalculationallowsestablishingthefullwidthathalfmaximum DnDofaDoppler-broadenedline:DnD n08 ln 2kTmc2 :_(1:49)It is clear fromEquation1.49that Doppler broadeningdepends linearlyonatransitionfrequency. It means that this type of broadening dominates strongly in UV and visible regions,lessinnearIRand mid-IR,and it isalmostnegligibleintheFIRand submillimeterregions.The secondfactor increasingDoppler linewidthis the temperature (square root). AfewexamplesofDopplerlinewidthsDnDandpressure-broadenedlinesDncollforrepresentativegas lasers are presented in Table 1.3.FIGURE 1.8Radiationfromrandommovementofspecies.Velocitycomponentvzisindicated.Endo&Walter/GasLasers DK553X_C001 FinalProof page 18 17.11.2006 6:36pm18 Gas LasersDepending on circumstances (pressure, temperature, gas ratio, and wavelengths), differentkinds of broadening can determinethespectral linewidths. The collisionand Dopplereffectsdetermine the shape of the spectral line, which is generally given by the convolution integral:G(n) _11GD(n0)GL(n n0) dn0, (1:50)where GL(n,n0) is the Lorentzian shape of emission at frequency n for the emitting atom with acentral frequencyn0(seeFigure1.9), andGD(n0) representstheGaussianshapecausedbyDoppler effect. This is thesituationwhentheDoppler broadeningovershadows collisionprofiles,anditformstheGaussianenvelopeofDoppler-shiftedLorentzianlines.1.5 GAIN CONDITIONSFollowingthefamousanalysisbyEinstein, dealingwithblackbodyradiationpresentedinmanybooksonlaser[14],threeelementaryquantummechanismsofradiationinasimpletwo-level model of anatomcanbedistinguished: absorption, spontaneous emission, andstimulatedemission(Figure1.10).Introduced by Einstein, a coefficient of stimulated emission is very sufficient to explain themechanismoftheso-calledblackbodyradiation,butcontributionofstimulatedphotonstoall radiativeeffectslikeabsorptionandspontaneousemissioninanexcitedmediumisverypoor. It explains whyalaser was not inventedimmediatelyafter Einsteins analysis waspublished. The picture of radiative processes is completely different when the excited mediumisplacedintoanopticalresonator. Veryquickly(afterafewhundredtransitionsalongtheG ( ) G ( ) G ( ) 90GL (0 9)GL (0 + 9)00 FIGURE 1.9CreationofaDoppler-broadenedline.TABLE 1.3Doppler Linewidths DnD and Pressure-Broadened Lines DnColl for Some Gas LasersLaser l DnDDncollArgon 514.5 nm(visible) ~3.5GHz ~20MHzHeNe 632.8 mm(visible) ~1.5GHz ~20MHzHeNe 3.39 mm(infrared) ~300 MHz ~50MHzCO2(10Torr) 10.6 mm(infrared) ~60MHz ~60MHzCO2(1bar) 10.6 mm(infrared) ~60MHz ~40GHzEndo&Walter/GasLasers DK553X_C001 FinalProof page 19 17.11.2006 6:36pmPrinciples of Gas Lasers 19resonator), as it was proved in a famous work by Fox and Li [15], stimulated photons becomepredominantinthelasercavity.Tofindthe amplificationconditions, let us consider areservoir withtwo-level atoms of densityn1n2n, wheren1, n2areatomdensitiesinstates1and2, respectively. Thetransparentreservoir is illuminatedby the monochromatic wave of intensity I(n) as presented in Figure 1.11.WhenthefrequencynofexternalwavecoincideswiththebroadenedspectrallineG(n)of2!1transition, it causestheabsorptionof photonsandemissionaswell. Thenumberofemittingnemandabsorbingnabatomsisgivenbythefollowingequations:dnemdt n2[BI(n) A], (1:51)dnabdt n1BI(n): (1:52)ThedifferenceofEquation1.51andEquation1.52inemittingandabsorbingatomsisthemeasureofgainpropertiesofthegas:dnemdtdnabdt_ _ n2[BI(n) A] n1BI(n): (1:53)Becauseof theisotropicnatureof spontaneous emission, it canbetotallyignoredinourconsiderations. Multiplyingbothsidesof Equation1.53bydzandmultiplyingbyphotonenergyhyweightedbytheshapelineG(n),wegettheincreaseindI(n)overdzdistance:d(nemnab)dthv dz dI I(n)(n2n1)hvGdz: (1:54)2 2 2Stimulated emission Spontaneous emission Absorption1 1 1dP21 = Uv B12 dt dP12 = Uv B12 dtspdP21 = Uv B21 dtst aFIGURE1.10Threeelementaryquantummechanismsofradiation: dP12a, dP21sp, dP21stprobabilityofabsorption, spontaneous emission, and stimulated emission, respectively, B12, B21Einstein coefficientsof absorptionandstimulatedemission(B12B21B), A21Einsteincoefficient of spontaneousemission,andUnenergydensityofelectromagneticradiation.Active mediumZdzn = n1 + n2l(n)MonochromaticwaveFIGURE 1.11Theplanewavepenetratingtheassemblyoftwo-levelatoms.Endo&Walter/GasLasers DK553X_C001 FinalProof page 20 17.11.2006 6:36pm20 Gas LasersTransformingEquation1.54leadstothedefinitionofdifferentialequationforintensity:dII g dz, (1:55)whereg(n) (n2n1)BhvG(n) (1:56)is the so-called differential gain of the medium and (n2n1) is the difference in population ofbothlevels.ThesolutionofdifferentialEquation1.55isI(n) I0(n)eg (n)dz: (1:57)Itisclearthatthenecessaryconditiontoobtaintheamplificationisn2n1> 0, (1:58)which is called population inversion. The gain g(n) is not constant along the z axis. Because ofsaturationeffect, thegaindecreaseswhentheintensityoftheincidentwaveincreases. Thisphenomenon is illustrated in Figure 1.12, which presents nonlinear behavior of gain with theintensityfortwocharacteristicgainlines:collisionalandDopplerbroadened.Thisbehaviordistinguishedtwocharactersoflines:homogenouslybroadenedline(allatomsinteractwiththemonochromaticwave)andinhomogenouslybroadenedline(onlyapartoftheDoppler-shiftedatomsinteractswiththemonochromaticwave).The gainis the functionof intensityandit depends onthe character of the line. Forhomogenouslybroadenedlinesg(I) g01 IIs, (1:59)andforinhomogenouslybroadenedlinesg(I) g01 IIs_ (1:60)Thegasmediumischaracterizedbytwobasicparameters:g0unsaturateddifferentialgain(or small signal gain); Issaturation intensity. Saturation intensity is defined as the intensityat which the gain drops twice (homogenous case) or the gain drops2ptimes (inhomogenouscase).Table1.4givessomeexamplesforsaturationintensityIsandunsaturatedgainvalues.(a) (b)MonochromaticwaveI(9)g() g()09 09FIGURE 1.12Saturation effect in (a) homogenously broadened line and (b) inhomogenouslybroadened line.Endo&Walter/GasLasers DK553X_C001 FinalProof page 21 17.11.2006 6:36pmPrinciples of Gas Lasers 211.6 LASER ACTIONA SIMPLE MODELAlaser,aswas saidintheintroduction,is anopticaloscillator.Usingan electronicanalogy,theelectronicoscillator consists of anamplifier withaspeciallyformedfeedbacklooptoenablesuchasystemtoobtainstableandperiodicself-oscillations(Figure1.13a).To obtain self-oscillations, a part of the output signal has to be coupled back into the inputof the amplifier. Two conditions have to be fulfilled; the amplitude of the feedback signal hasto have enough value and the phase of this signal should have approximately the same phaseas theinput signal. Thesetwoconditions arecalledamplitude=phaseconditions for self-oscillations.ThefeedbackanalogyisevenclearerintheopticalcasepresentedinFigure1.13b,wherethe optical amplifier was set inthe optical ring resonator forming the optical feedbackrunningwave (signal). Whenamplitude=phase conditions are fulfilled, the runningwavestartstravelinginsidetheringresonator.Inpracticewehavetworunningwaves,clockwiseandanticlockwise,whichcanappearintheresonator.Theoutputbeamleavestheresonatorasauseful laserbeamwhentheoutputmirrorispartly transparent. The qualitative difference between electronic and optical oscillators reliesonD=lratioofaveragephysicaldimensionDofanoscillatortotheoscillatingelectromag-netic wavelength l. The D=l ratio is much less than unity for typical electronic oscillators andit is much higher than unity for optical devices. Somewhere between these devices are locatedmicrowaveoscillators,forwhichD=liscomparablewithunity.Considering the ring system illustrated in Figure 1.13b, one can imagine the evolution of thering resonator into the so-called linear resonator by parallel translation of two mirrors towardtwo left, forming a corner cube configuration into planeplane or FabryPerot (FP) reson-ator.ThelinearresonatoristhemostfrequentlyusedconfigurationandthelaserwithFPresonator is the most representative. The running wave in a ring resonator becomes a standingwave (two waves traveling in opposite directions) in a linear FP resonator (Figure 1.14).TABLE 1.4Examples of Saturation Intensities and Small Signal GainsLaser l Isg0HeNe 632.8 nm ~5W=cm20.02=mHeNe 3.39 mm(1Torr) ~3mW=cm20.6=mCO210.6 mm(20Torr) ~20W=cm2~0.3=mCO210.6 mm(100Torr) ~10kW=cm2~0.6=m >> DElectronic amplifier 350u, there is the far-field wake area. Froma physical standpoint, as proved in [13], these three wake development areas are specified by amixingdegreeoftwoboundarylayerscomingfromtherearedge.Variationof maximumfaultsof densityandvelocitybehindthenozzlebladesisshowninFigure2.20andFigure2.21(externalflowconditionsareappliedhereUEandrEratherthanconditions at infinityU1andr1). Onecanseethat maximumfaults arealteredinproportion (x=~uu)1=2that is, in our case we also obtain certain wake theory ratios. The point isthat here~uu is taken as a nondimensionalizing parameterit is the average momentumthicknessvaluefortheentiremeasurementareaandforalltheblades.Asmentionedbeforefortheunlimitedflowu constantinourconditions,thereexistsanaxialpressuregradientand u alters slightly. That is the reason why during processing~uu is applied (for information onthevalue~uuseebelow).ThelineinFigure2.21correspondstothemeasurementsobtainedinan incompressible isobaric wake [8,11,14]. Results obtained in [9,10] at M2 and 3 relatively,thatis,inacompressiblecaseactuallycomeinlinewiththesedata.WhereasinourtestsatME5,velocityfaultatthewakeaxisdecreasesmoreslowly.Cross-sectiondistributionof flowparameters inthewakeinfar-fieldwakevariables isshown in Figure 2.22. There are results for a thick blade wherec t 0.75 mm and a thin onewheret 0.15mm.Pointsareplottedfromallthecrosssections.Thevaluebisthewakeshalf-width(itisrelatedto~uu)andisdefinedwiththecoordinatewherevelocityequalshalfof02468101214200 600 1000 1400 1800 2200x~2rErE r0FIGURE 2.20Densitydefectatwakesaxis.58 Gas LasersEndo&Walter /GasLasers DK553X_C002 FinalProof page 58 17.11.2006 11:40amthesumof Uvaluesat theaxisandat theboundary, that is, at U(UE U0)=2. Upony 0.5b velocity fault (U1U)=(U1U0) 0.5. The results prove that in spite of the presenceof disturbing factors all the points (taking into account experimental dispersion extent) fall ona universal curve. It all goes to show that the flow pattern in a wake and in our case is actuallyleftself-similarandthattandadidnotaffecttheflowpattern(dataforalltheotherbankscoincide with the ones shown in Figure 2.22). Thus, the idea of flow self-similarity in a wakeexpressedin[15]andsupportedinnumeroustestsbothinincompressibleandcompressibleflows, forexamplein[811,14], isalsotruebothfortheproblemconsideredatM5andwhenawakeisundertheimpactofdisturbancesofspecial character(expansionwaveandshockwave).Just as in other researches velocity distribution is approximated (as well as in the case of theincompressibleisobaricwake)UE UUEU0 exp0:69yb=2_ _2_ _:0100200300400500600200 400 600 800 1000 1200 1400 1600 1800 2000 22002UEUE U0x~qFIGURE 2.21Velocitydefectatwakesaxis.1.500.2(uE u)/(uE u0)( rE r)/( r E r0)0.40.60.81.01.0 0.5 0 0.5 1.0 1.51.50(b) (a)0.20.40.60.81.01.0 0.5 0 0.5 1.0 1.5t = 0.75 mmt = 0.15 mmt = 0.75 mmt = 0.15 mmy/dy/dFIGURE 2.22(a)Transversevelocityprofileand(b)densityprofileintermsoffarwake.Fluid Dynamics 59Endo&Walter /GasLasers DK553X_C002 FinalProof page 59 17.11.2006 11:40amAs emphasized above, the parameters in the wake were calculated on the basis of a conditionofconsistencyofT00, thatis, asamatteroffact, theidentityoftemperatureanddynamicprofileswasestablished, eventhoughtheincompressiblefluidexperimentsprovedthatthetemperatureprofileisalittlewider.TE TTE T0 exp0:45yb=2_ _2_ _Asthevelocitydistributioninourtestscoincidedwiththeacknowledgedresults,itwasalsoassumed that the temperature profiles would be the same as in [9,10] at M2, 3. The densityprofilehasasimilarview.Itcanalsobedefinedonthebasisofthetemperatureprofilewiththeconstitutiveequationandtheconditionofpressureconsistencyacrossthewake.Momentum thickness and wake thickness. Thus, the momentum thickness u is a typical linearscale in the wake theory. This value as demonstrated in [8,9] equals the body resistance factorwakegeneratorbyvirtualbodythickness, thatis,thevalueisconstant.Inourcase, astheflow is not unlimited and there are variations of PE along the wake, it is not observable. For aplate inanunlimitedincompressible flow, the theoryandthe experiment provide amereconnection of u and the momentumthickness inthe boundary layer at a plates end: u 2uw.Figure 2.23represents the dataobservedinour conditions. The same way as earlier,pointsforallthebladesareplotted;theywereobtainedatP00 %20atm.Itisobviousthatthepointsarelocatedalittlehigherthanthelineu=2uw1.Onflowingroundtheedgesofsomethicknesstheboundarylayercomingfromabladefirstundergoesanintensiveexpan-sionwaveimpact andapparentlyatrailingshockwavedoes not compensatethis impactcompletely. Thus, points for a very thick blade (t 2.3 mm) on all the parameters processing(e.g., wake thickness) are always located higher than others. However, noticeable difference ofu from an average value is only observed at the beginning of the wake (x < 20 mm). That is thereason why in the case of practical applications, average value of u ~uu can be assumed constant00.51.01.550 1000.15 00002.54.00.352.30.750.751.0150t, mm a, degx, mmq2q WFIGURE 2.23Momentumthicknessinwake.60 Gas LasersEndo&Walter /GasLasers DK553X_C002 FinalProof page 60 17.11.2006 11:40amalongtheentireareaandonecanconsiderthat~uuisnotaffectedbythetandaparameters(in the value range under consideration: t1 mm, a48), and its value is~uu 2.2 uw.Figure2.24showsthedependenceof thewakethicknessbondistanceanduisalocalmomentum thickness value. It is obvious that the obtained results are colligated as usually bytheconnection(b=u)~(x=u)1=2.Thediagramlinestandsforconnectionb(x)foranincom-pressiblecase[8,14],thatis,pointsforthiswakegeneratorlayhigher.Generallytocombinethe location of experimental points with the central point of coordinates, a virtual wake originx0 is introduced. The parameter x0 is defined for each wake generator in an experiment, thatis, it is empiric and depends on the generators configuration and the Re number. (Technically,it means transferring wake thickness increase mechanisms to the laws of wall boundary layergrowth).Inthiscase,itwasobtainedx0=u 380.Figure 2.25 shows the results of correlation b(x) for the GDL blades but rebuilt with respecttox0, andinsteadofuthereisanaveragevalue~uu, whichbasicallyextendedthespreadofpointsbutitmakespractical applicationofthedataobtainedeasier. Noticeabledifferenceof the points from linear dependence for the incompressible case is only observed at the initialcrosssection~ xx=~uu500.ThisdependencecanactuallybeconsideredasanexpressionoftheTownsendlawofwakeindependenceonReynoldsnumber.On pulsation properties in a wake. Detailed studies of turbulence characteristics in asupersonicwakebehindathinplatewerecarriedout[16,17].Thetransitionofflowstreamfromlaminarconditionstoturbulentones[17], thatis, all thethreewakeareashavebeenreflected: near-field,intermediate, andfar-fieldones. Figure2.26andFigure2.27representthedata,whichareofthegreatestimportancetous.Figure 2.26 shows variations in the pulse intensity r and U along the wake, and Figure 2.27shows variations inintegral scale of densityturbulent pulses LL. As one cansee, pulse200 400 600 800 1000 1200 1400 1600 1800 2000 2200 02bxxFIGURE 2.24Wakethicknessalongtheflow(ulocalmomentumthicknessvalue).Fluid Dynamics 61Endo&Walter /GasLasers DK553X_C002 FinalProof page 61 17.11.2006 11:40amintensityrintheturbulentwakeareaalmoststopsalteringandthescaleLL~L(Listhetransversalscaleinawake,e.g.,itshalf-width).Depictedresultscanbeconsideredanempiricmethodofdefiningmeanflowparametersbehind the blade nozzle bank in the first approximation. The flow is reckoned to consist of acore, inwhichtheparameters areconstant inatransversal directionandvaryalongthestreamand a wake area. Parameters at the exit of a certain nozzle are defined by itsexpansiondegreewithcorrectiononboundary-layerdisplacement thicknessd*. Thereare020040060080010000.15 0a, deg0.35 00.75 02.3 00.75 2.51.0 4.0t, mm500 1000 1500 2000 2500 30002bq~+ 380xq~FIGURE 2.25Wakethickness(~uuaveragedvalue u;x0virtualwakebeginning).450.01.1120Transitional Turbulent500 1000xUU U(O)rr r(O)rrUUFIGURE 2.26Intensityofpulsationsinwake.62 Gas LasersEndo&Walter /GasLasers DK553X_C002 FinalProof page 62 17.11.2006 11:40amanumberofcalculationmethodsandempiriccorrelationsincludingtheonesmentionedinthisresearchtoestimated*andmomentumthicknessat nozzleexit uW. Coreparameterscorrespondtotheconditionsatthewakesexternalboundaryandtheyareestimatedonthebasis of Figure 2.17throughFigure 2.19. The point is that it is necessary totake intoaccount that the model channel walls boundary layer had considerable impact on theextent of parametervariations. Inreal conditionswhenachannelsheight issubstantiallyhigher, the effect will lessen. At that the extent of parameter variation will app-roximately be less by half. Thus, the velocity variationat a 160 mmlengthis 2.5%, ifthereisnoboundarylayerimpact thevariationwill be1.2%. Parametervariationpatterncanbeapproximatedbylines(e.g., rE=rE01 ax). Wakeaxisparameterswill bedefinedon the basis of their defect distribution in Figure 2.20 and Figure 2.21, at~uu 2.2uW.Parameterdistributioninawakes cross sectionis foundwithapproximationexpressionsforU,r, andT.Themainconclusionisasfollowing:withintherangeoftheexecutedmeasurements(x 160 mm) the distribution of mean velocities and density in a wake behind a certain blade of abladeMNBisuniversalinspiteofdisturbancescomingfromtheadjoiningblades, andthewakewidthisdescribedbytheasymptoticlaw:b~x1=2.2.2.2.4 Impact of Real Blade Nozzle Bank Assembly Defects on Flow Gas DynamicsIn the previous paragraph, we considered flows behind the banks of an ideal assembly: therewas no displacement of the blades forming one nozzle in relation to each other; all the nozzleswere of the same critical cross section permanent along the entire blade length, and so on. Inreality, somewayor another, thesituationis reversed: therearebothdisplacements anddispersioninthroat dimensions. Apart fromthis, uncooledblades of bigsize(morethan150mm)bendrightafterthefirststartswhenaffectedbythermal stresses. Thefactcausesanincreaseinthroatdispersionandthroatinequalityinthebladeheight.Thinbladeedgesbreakoff.Therefore,theimpactsuchdefectshaveonmeanflowparametersisexaminedinthissectionbriefly.Deviationof acertainbanknozzles throat dimensionfromthedesignvalue. Figure2.28juxtaposesanoverallpatternofaflowbehindanideallyassembledbank(Figure 2.28a)andthe cases when a bank has a defective nozzle the throat of which differs from the designed oneh*0.Firstofall,itisobviousthatassoonassuchadefectemergesthewakesstartdistorting.Theybendtowardthe side of the smaller densityflow: whenh*1h*0. The case of converging wakes is representedby pictures obtainedwithavertical andhorizontal knife (Figure 2.28bandFigure 2.28c), the case of divergingwakeswith a horizontal one (Figure 2.28d). Wakes converge (or diverge) until the densitiesinadjoiningflowsdividedbywakesgetleveledoff,andthentheybecomeparallelagain.Violation of the strict pattern of a flows layered structure with parallel wakes, isonlypossibleduringideal assembly(Figure2.28aandFigure2.9), emergingof areaswithnonparallelboundariesanddensityvaryingvisiblyalongtheflowcauses,first,differenceinmean optical paths by resonators aperture, that is, decrease in optical quality of the medium(andconsequentlydecreaseinlaserradiationquality), andsecond, italsocausesresonatordeficiency because of its beam course deformation. In this case, the beams will diverge, that is,experience a refraction effect, as they do not pass completely perpendicular to the boundariesof various densities mediathesamewayas onideal assembly(theresonator is generallylocated right behind the blade bank exit). Direct measurements of Woutput GDL radiationpowerprove it. The more considerable is h* dimensions dispersion in a bank, the greater isthe Wvalue reductionwith other conditions similarthan in the case of ideal MNBassembly,thatis,theresonatorsefficiencyreallydecreases.Apart fromwake deformation, there mayalsoemerge alterationof aflowmode inanarrowingflowcore. Figure2.28bshowsthat startingwithx 30mmwhenwakescomeclose enough to each other they start interrelating and turbulize the entire flow area betweenthewakes.Sincetheflowareaintheresonatorcavityoccupiedbytheturbulentflowgrows,suchaneffectcausesadecreaseintheopticalqualityofthemedium.Furtheron,inrealitythecriticalcrosssectiondoesnotchangeuniformlyalongtheentireblade length as it happens in this model experiment. Bank blades can bend and consequentlyareas with different meandensity by channel height emerge in the flow, that is,optical pathsbyresonatorsaperturebecomedifferent,andthisfactorasmentionedabovemeansdeteri-orationintheoutputradiationquality.Blade slots. Because of thermal stress, a blade bends and its thin edges break off. In order toreducetheeffectitwasofferedtomakeslotsinabladetorelievetheedgesfromthestress.Such a bank (t 0.5 mm, a0) with slots exit in the middle of blades was tested. Notch width(a)(b)h0h1h0h0h2h0h0h1h0(c)(d)FIGURE2.28Photos of flow behind the nozzle bank with deformed nozzles: (a) all throat equal (h0*0,49 min); (b),(c),(d) h0*0.49 mm, h1* 0.22 mm, h2* 0.8 mm.64 Gas LasersEndo&Walter /GasLasers DK553X_C002 FinalProof page 64 17.11.2006 11:40amwasD0.35mm,length15mm.Figure2.29showsthenozzleexitparameterdistribution(x0) for an ideal assembly bank. The measurements were made in the slot plane. Measure-mentofcoordinateyismadefromthemiddleofanend-buttofanadjoiningblade. Lightpoints mean that a slot is open, dark points mean that a slot is puttied and the slots profile isrestoredcompletely.Parameterdisturbanceintheareay 911mmistheresultoftheslotexitinablade.Maximumdensityvariationis Dr=~ rr %5%.The pattern of slot flowing around is the same as in a blade edge: in the slot root, at the stepcornertheflowturnsroundthereemergesanexpansionwave(incrosssectionx0thisareapassesthroughy 910mm), andtheshockwavewheretheflowturnsbackpassesthroughy 10mm. Disturbancesfromtheslotbeginningspreadunderapproximatelythesame angles as the disturbances from the blade edge and fade out at about x 30 mm distance(incaseoftheidealbankassembly).Disturbances consist of compressionand expansion areas,butdensitydeviations from theaverage value are close, that is the reason why the optical path along the slot will be the sameas above and below the slot, that is, wavefront aberration by aperture are minimal. However,thepatternchangeswhenabankisdistorted.Combinedeffectofbladeslotsandthroatdimension fringeinabank.Thereare results for abankwithadistortednozzleof critical crosssectionh* 0.22mm, andtheothersareof0 2141210864M2y, mm4 0 0.4Region ofdisturbancesP1 2 3 4 5M0.6P0 102P 103r P0r 102FIGURE 2.29Influence of slots in blades on flow parameters at nozzle bank outlet; x 0, D 0, slot;.closed, openedslot.Fluid Dynamics 65Endo&Walter /GasLasers DK553X_C002 FinalProof page 65 17.11.2006 11:40amadesigncriticalcrosssectionh*00.49mm.First,P00wasmeasuredinsidethenozzlewithaspecial-purposevertical proberight abovetheslot (z 0mm) andalittleawayfromtheslot (z 3mm). Figure2.30showstheresultsandthetest diagram. TheP00valuesabovethe slot and beside it do not differ much (P00is much less than the value measured in this spotby the horizontal Pitot tube), that is, actually the gas is not blown through the slot in a nozzlewithminorH=h*.Figure2.31arepresentstheflowparametersat abankexitfrombothpartsof ablade(aslottedone),whichdividesdistortednozzlesofh* 0.22mmandanundistortedone.Itisobviousthat thewakeintheslot planedoesnot coincidewiththewakeof theentireblade (unlike the ideal bank assembly case). The wake behind the slot step is distorted in thesamewayastheentirebladeswakebutitbeginsearlier(atx 15mm)andtothebladeexit (x 0 mm) is had already diverged from the axis by 2 mm. As it is observed on the basisof measurements, inthecross-section7, 20, and50mm(thecross-section7isshowninFigure 2.31b), the further slot wake development leads to the fact that a layer withpropertiesdiffergreatlyfromtheadjoiningareasisformedinthisplane. It isalayerofsignificantly expanded wake. Nonuniformity covers all the flow core area from one wake totheother.Itwaseven possibletovisualizeanarrowlayerwithdifferentdensityina flowbehindtheslot.Figure2.32showsthecorrespondingpictures(thebladeishorizontal).Thetoppicturerepresents an ideal assembly case where all the critical cross sections are equal, and the bottomone represents a bank with a distorted nozzle. The pictures are taken across the blades ratherthanalongthemasinFigure2.28(throughthetopandbottomwindows),thatis,alongthe00.511.522.5y, mmx 15 mmyxh1h2P0z = 0z =3 mmh1 = 0.22 mmh2 = 0.49 mm0.15 0.25 0.1 0.2 0.3 P0 102P0 102x = 10 mmFIGURE2.30Resultsofmeasurementsbyvertical Pitottubeunderslot(z0)andnotunderslot(z 3mm).66 Gas LasersEndo&Walter /GasLasers DK553X_C002 FinalProof page 66 17.11.2006 11:40amaxisof anassumedresonator(throughthesidewindows). Theshockwavescomingfromthe nozzle neck and from the glass joints (at the top and bottom windows) with the operationarea have been marked.It is obvious that the shockinclination angle from the neck dependsonthenozzlesexpansiondegree.Thatisthereasonwhyforanidealassemblybankalltheshocks coming from the throat area converge into one in the picture, whereas in the distortedbank case as much as two shocks have been recorded. The fact that the flow area occupied bythe shock waves whose plane is parallelto the resonators axis increases in the second case isalsoadisadvantagefromthepointofviewofopticalqualityoftheflow.Thus nonuniformity forms along the resonators axis in the slot plane in a distorted nozzlebank that will cause wavefront aberration at the resonators output, that is, it causes radiationqualitydeterioration(apartfromtheresultsrepresentedheresomedataforotherh*valuesthat differ fromh*0toa smaller extent alsohave beenobtained. Fromthe qualitativestandpoint all theeffectsobservedintheflowarepreserved). Asit isimpossibletoavoiddifferences in h* in a real bank and right after the first starts the h* values variation generallyincreases, thestructural solutionof thebladeedgerelief asaslot cannot beconsideredsatisfactoryone.Bladedisplacementrelativetoeachother.Figure2.33demonstratestheresultofanozzleshalves displaced relative to each other. The data are obtained for different displacements D, andthere were selected different h* so that distributions P00 and P could not converge on the graph.Displacementleadstoasituationwhenatanozzlesoutputfromonesideashockwaveisrecordedandontheoppositesideanexpansionsideisrecorded.Disturbancesarecertainlyformedintheneck. UpondisplacementofD %h*(suchdisplacementsarereal takingintoaccount the fact that inthe present dayGDLs h* 0.10.2mm) disturbances become noticeable.Themeasurements provethat inageneral casedisturbances causedbyvarious factors(slots, displacements etc.) a summed up intensifying each other. In addition, fromthe0(a) (b)18161210h* = 0.22 mm8642y, mmy, mmx = 1 mmx = 7 mm z = 3 mm z = 0 z = 3 mm z = 02.0 4.0118161412108642 3 4 5P0 102P 103h* = 0.49 mmh* = 0.49 mmP P0P0102h* = 0.22 mmFIGURE2.31Joint influenceof slot anddifferenceof h*: (a)crosssectionx1mm; (b)crosssectionx 7mm.Fluid Dynamics 67Endo&Walter /GasLasers DK553X_C002 FinalProof page 67 17.11.2006 11:40amstandpointoftheirinfluenceonopticalflowuniformitytheyaresimilar.Allthefaultscauseemergingofdensitynonuniformitiesandflowsymmetryviolation,whereasinageneralcaseboth these factors affect the optical quality of the medium. Thus, the tests prove that the flatstructure of nozzle banks (especiallywhenblades are of abigheight) turns tobe quitesensitive tothe effects of real assembly factors andreal operationconditions. AscreenMNBstructureappearstobemorestablefromthementionedstandpoint.2.2.3 THREE-DIMENSIONAL STRUCTUREOF FLOWAFTER SNB2.2.3.1 Models and Their GeometryAscreennozzlebankinitsmostsimpleversionisaplatewithsmall-dimensionaxisym-metric nozzles drilled in it. The plate is fixed between flanges separating the forechamber fromthe operationchannel. It is sucha version that was applied in gas dynamictests. Figure 2.34shows a banks layout drawing for an operation channel of the 2180 mm cross section. Alsochannels of the 41 80mmand51 60mmcross sections were used. The 41 80mm5(b)(a)411262331124 5Slot 0.35 mm32Slot 0.35 mmGlassFIGURE 2.32Flow field behind the blades with slot. 1Shock waves from the throat; 2shock wavesfromthe jointofglasswithwall; 3supersonicpart of blade;4throatof nozzle;5subsonicpart ofblade;6wakeasaresultofslotexistence.(a)Allthroatsareequal;(b)throatsaredifferent.68 Gas LasersEndo&Walter /GasLasers DK553X_C002 FinalProof page 68 17.11.2006 11:40amchannel banks are similar plates withabigamount of nozzle rows (for the 5160mmchannelthe bank view is shown in Figure 2.59, they were mostly used in aero-optical tests).Thesubsonicsection ofSNBwas ofthesame type:eachmicronozzlehad aconicinputofthe 608 semiangle. Critical cross section of all the micronozzles is a cylinder area of ~0.5 mm,and the supersonic section is either conic or profiled. The banks main geometrical parametersarespecifiedinthetablebelow.Here d*, de are the diameters of an output and a critical cross section of a micronozzle; l thelengthoftheprofilessupersonicsection; A*, Aetheareasofathroatandanoutputcrosssectionofanindividualmicronozzle;SA*, SAethetotalareasofthethroatsandtheoutput0246 = 0.3 mmx = 11 mm(h* = 0.25 mm)(h* = 0.22 mm)(h* = 0.24 mm)(h* = 0.2 mm) = 0.1 mm = 0 = +0.1 mm810y, mm1 2 3P 103P0 102PP0FIGURE 2.33Bladesdisplacementsrelativetoeachother(distributionofparametersatx 11mm).218066l20.560o/*dc5jFIGURE 2.34SNBgeometry.Fluid Dynamics 69Endo&Walter /GasLasers DK553X_C002 FinalProof page 69 17.11.2006 11:40amcross sections in a bank; Af the channel cross-section area; Me0and Mf0the geometrical Machnumbers defined on the basis of correlationAe=A* and Af=SA* relatively; w is the semiangleofamicronozzlesconicexpansion.Versions of banks III, IV had profiled micronozzles (calculation methods for theprofilednozzlesarespecified, forexample, inreference[18]). However, thenozzleshadanexit profileratherthana full-sizeone:in bank III atthespotwheretheflowtrailing angleisa18, and in bank IV, a48. Owing to this difference in bank widths, the l value of the baseareaschanged. Figure2.35showsdetailsof thebanks output crosssections. InbanksIIandIII,crosssectionsofadjoiningmicronozzlesintercrossedandinthetable,thevalueAecorresponds to this hexagon. SAe=Af specifies the base areas value and it is not equal to 1 evenfor bank II, as there are base areas at the bank edges (SAe=Afis closer to 1 forbigger