Table Of ContentOXFORDMASTERSERIESINATOMIC,OPTICAL,ANDLASERPHYSICS
OXFORDMASTERSERIESINPHYSICS
The Oxford Master Series is designed for final year undergraduate and beginning graduate students in physics and
related disciplines. It has been driven by a perceived gap in the literature today. While basic undergraduate physics
textsoftenshowlittleornoconnectionwiththehugeexplosionofresearchoverthelasttwodecades,moreadvanced
and specialized texts tend to be rather daunting for students. In this series, all topics and their consequences are
treated at a simple level, while pointers to recent developments are provided at various stages. The emphasis in
onclearphysicalprincipleslikesymmetry,quantummechanics,andelectromagnetismwhichunderliethewholeof
physics. At the same time, the subjects are related to real measurements and to the experimental techniques and
devices currently used by physicists in academe and industry. Books in this series are written as course books, and
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CONDENSEDMATTERPHYSICS
1. M.T.Dove:Structureanddynamics:anatomicviewofmaterials
2. J.Singleton:Bandtheoryandelectronicpropertiesofsolids
3. A.M.Fox:Opticalpropertiesofsolids,secondedition
4. S.J.Blundell:Magnetismincondensedmatter
5. J.F.Annett:Superconductivity,superfluids,andcondensates
6. R.A.L.Jones:Softcondensedmatter
17. S.Tautz:Surfacesofcondensedmatter
18. H.Bruus:Theoreticalmicrofluidics
19. C.L.Dennis,J.F.Gregg:Theartofspintronics:anintroduction
ATOMIC,OPTICAL,ANDLASERPHYSICS
7. C.J.Foot:Atomicphysics
8. G.A.Brooker:Modernclassicaloptics
9. S.M.Hooker,C.E.Webb:Laserphysics
15. A.M.Fox:Quantumoptics:anintroduction
16. S.M.Barnett:Quantuminformation
PARTICLEPHYSICS,ASTROPHYSICS,ANDCOSMOLOGY
10. D.H.Perkins:Particleastrophysics,secondedition
11. Ta-PeiCheng:Relativity,gravitationandcosmology,secondedition
STATISTICAL,COMPUTATIONAL,ANDTHEORETICALPHYSICS
12. M.Maggiore:Amodernintroductiontoquantumfieldtheory
13. W.Krauth:Statisticalmechanics:algorithmsandcomputations
14. J.P.Sethna:Statisticalmechanics:entropy,orderparameters,andcomplexity
20. S.N.Dorogovtsev:Lecturesoncomplexnetworks
Laser Physics
SIMON HOOKER
and
COLIN WEBB
DepartmentofPhysics,UniversityofOxford
1
3
GreatClarendonStreet,OxfordOX26DP
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Hooker,Simon,1965–
Laserphysics/SimonHookerandColinWebb.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-19-850692-8—ISBN978-0-19-850691-1 1. Lasers.
2. Optics. 3. Light. I. Webb,ColinE.,1937- II. Title.
QC688.H66 2010
(cid:2)
621.366—dc22 2010019282
TypesetbySPIPublisherServices,Pondicherry,India
PrintedinGreatBritain
onacid-freepaperby
CPIAntonyRowe,Chippenham,Wiltshire
ISBN 978–0–19–850691–1(hbk)
978–0–19–850692–8(pbk)
1 3 5 7 9 10 8 6 4 2
Preface
Thisbookaimstogiveacomprehensivedescriptionofthephysicsunderlying
the operation of lasers. It is intended for undergraduates in the third or final
year of a four-year physics course, and for graduate students—either those
engagedinresearchintonewlasersystems,orthosewhowishtoknowmore
aboutthe‘blackbox’inthemiddleoftheiropticaltable.
Muchofthematerialincludedstemsfromafinal-yearoptioncourseonlaser
physicsdevelopedandtaughtbyCEWformanyyears.Thisformedthebasisof
ashortintroductorycourseforthird-yearphysicists,andanoptionalfinal-year
course, both presently taught by SMH. We assume that the reader is familiar
with the core material of the first two years of an undergraduate degree in
physics, andinparticularelectromagnetism, quantum mechanics, andatomic
physics.
The book roughly divides into: (i) chapters describing the physics of laser
operation,usuallywithoutreferencetoanyparticularsystem;and(ii)chapters
givingadetaileddescriptionofsomerepresentativetypesoflaser.Laseroscil-
lation has been demonstrated on thousands of transitions in atoms, ions, and
moleculesandinthegas,liquid,solid,andplasmastates.Abookofthistype
canonlyincludeatinyfractionofthese;thelasersystemsincludedherehave
beenselectedbecausetheyillustrateoneormoreofthekeyconceptsdescribed
in the introductory chapters, or because they are of particular technical or
scientificimportance.Ifthelasersystemyouareworkingwithisnotincluded,
wehopethatneverthelessthematerialcoveredherewillhelpyouunderstand
itsoperation.
Mosttopicsaredealtwithinasinglechapter,ratherthanbeingcoveredin
severalplacesatanincreasinglyadvancedlevel.Althoughthisapproachhelps
reducerepetition,andallowsacomprehensiveunderstandingofeachsubject,
we recognize that a newcomer to the field cannot be expected to master all
the material in one go. We have indicated the more advanced sections by a
dagger†;thesemaybesafelyskippedonafirstreading.Wewouldencourage
thereadertorevisittheseastheirexpertisedevelops.
Wehaveincludedproblemsattheendofeachchapter.Thesearedesignedto
helptestunderstanding,ortoleadthereaderthroughproofsthatwouldother-
wise be distracting. The problems range from simple numerical calculations,
designedtogiveanappreciationoftheordersofmagnitudeinvolved,tomore
advancedquestions(alsodenotedbyadagger†).
Wehopethatthebookwillbeusedinmanyways:asanintroductiontothe
subject; as a text for intermediate-level courses; and as a reference for those
usinglasersintheirwork.Asuggestedintroductorycourseisgiveninthetable
vi Preface
Table1 Suggestedsectionsforanintroductorycourseonlaserphysics.
Chapter Topics Sectionsa Suggestedproblems
1 Electromagneticradiation all 1.1,1.2,1.3,1.4
2 Einsteintreatment,conditionsfor all 2.1,2.2,2.3,2.4
opticalgain
3 Linebroadening all 3.1,3.2,3.3,3.4,3.5
4 Theopticalgaincross-section,gain all 4.1,4.2,4.3,4.4,4.5
narrowing
5 Gainsaturation all 5.1,5.3,5.4,5.5,5.11
6 Opticalcavities,Gaussianbeams, all 6.1,6.2,6.3,6.4,6.5,
laseroscillation,outputpower 6.12,6.13
7 Solid-statelasers,therubyand 7.1,7.2.1–7.2.5, 7.1,7.2,7.3,7.7
Nd:YAGlasers 7.3.2
aAdvanced†sectionsshouldbeomitted.
above;wetrustthatmoreadvancedreaderswillbeabletoidentifythesections
relevanttotheirneeds.
Many students and colleagues have contributed to the development of the
text. We would like to record our thanks to the generations of undergraduate
andgraduatestudentswhoroad-testedmanyoftheproblemsandwho,bycon-
stantquestioning,helpedreduceourconfusiontoitscurrentlevel.Wewould
liketoexpressparticularthankstoGeoffreyBrookerfordetailedandconstruc-
tivecriticismofseveralchapters,forhelpwiththetechnicalitiesofproducing
atextbook,andforFig.6.12.Wearegratefultoseveralcolleaguesforcareful
reading of draft sections of the book: Patrick Baird and Ian Walmsley of the
Department of Physics at Oxford; Roy Taylor and Gareth Parry of Imperial
College, London; and Mark Fox of Sheffield University. We thank Rodney
Loudon of the University of Essex, for many informative discussions. CEW
wouldalsoliketorecordhisthankstoMartyFejerofStanfordUniversityfor
very informative discussions on the teaching of semiconductor laser physics;
andtoJohanNilssonoftheOptoelectonicsResearchCentreoftheUniversity
ofSouthamptonandCyrilRenaudofUniversityCollege,Londonforproviding
thereferencesforthedataofTable10.5.
Finally,wearesincerelygratefultoourfriendsandfamily,whoprovideda
healthymixtureoftolerance,encouragementanddistraction.
Website:
www.physics.ox.ac.uk/users/hooker.Thissitecontainssupplementaryinform-
ationandcorrections.
Contents
1 Introduction 1
1.1 Thelaser 1
1.2 Electromagneticradiationinaclosedcavity 3
1.2.1 Thedensityofmodes 7
1.3 Planck’slaw 7
1.3.1 Theenergydensityofblackbodyradiation 8
Furtherreading 9
Exercises 9
2 Theinteractionofradiationandmatter 12
2.1 TheEinsteintreatment 12
2.1.1 RelationsbetweentheEinsteincoefficients 14
2.2 Conditionsforopticalgain 16
2.2.1 Conditionsforsteady-stateinversion 16
2.2.2 Necessary,butnotsufficientcondition 18
2.3 Thesemi-classicaltreatment† 19
2.3.1 Outline 19
2.3.2 Selectionrulesforelectricdipoletransitions 20
2.4 Atomicpopulationkinetics† 21
2.4.1 Rateequations 22
2.4.2 Semi-classicalequations 22
2.4.3 Validityoftherate-equationapproach 23
Furtherreading 24
Exercises 25
3 Broadeningmechanismsandlineshapes 27
3.1 Homogeneousbroadeningmechanisms 27
3.1.1 Naturalbroadening 27
3.1.2 Pressurebroadening 32
3.1.3 Phononbroadening 35
3.2 Inhomogeneousbroadeningmechanisms 35
3.2.1 Dopplerbroadening 36
3.2.2 Broadeninginamorphoussolids 38
3.3 Theinteractionofradiationandmatterinthepresenceof
spectralbroadening 38
3.3.1 Homogeneouslybroadenedtransitions 38
3.3.2 Inhomogeneouslybroadenedatoms† 39
3.4 Theformationofspectrallines:TheVoigtprofile† 40
viii contents
3.5 Otherbroadeningeffects 42
3.5.1 Self-absorption 42
Furtherreading 43
Exercises 43
4 Lightamplificationbythestimulatedemission
ofradiation 46
4.1 Theopticalgaincross-section 46
4.1.1 Conditionforopticalgain 48
4.1.2 Frequencydependenceofthegaincross-section 48
4.1.3 Thegaincoefficient 49
4.1.4 Gainnarrowing 49
4.2 Narrowbandradiation 50
4.2.1 Amplificationofnarrowbandradiation 50
4.2.2 Formofrateequations 51
4.3 Gaincross-sectionforinhomogeneousbroadening† 52
4.4 Ordersofmagnitude 53
4.5 Absorption 54
4.5.1 Theabsorptioncross-section 54
4.5.2 Self-absorption 55
4.5.3 Radiationtrapping 56
Furtherreading 56
Exercises 57
5 Gainsaturation 60
5.1 Saturationinasteady-stateamplifier 60
5.1.1 Homogeneousbroadening 60
5.1.2 Inhomogeneousbroadening† 67
5.2 Saturationinahomogeneouslybroadenedpulsed
amplifier† 73
5.3 Designoflaseramplifiers 77
Exercises 78
6 Thelaseroscillator 83
6.1 Introduction 83
6.2 Amplifiedspontaneousemission(ASE)lasers 83
6.3 Opticalcavities 85
6.3.1 Generalconsiderations 85
6.3.2 Low-loss(or‘stable’)opticalcavities 89
6.3.3 High-loss(or‘unstable’)opticalcavities† 97
6.4 Beamquality† 103
6.4.1 The M2beam-propagationfactor 103
6.5 Theapproachtolaseroscillation 106
6.5.1 The‘cold’cavity 106
6.5.2 Thelaserthresholdcondition 110
6.6 Laseroscillationabovethreshold 111
6.6.1 Conditionforsteady-statelaseroscillation 112
6.6.2 Homogeneouslybroadenedsystems 113
contents ix
6.6.3 Inhomogeneouslybroadenedsystems† 115
6.7 Outputpower 117
6.7.1 Low-gainlasers 117
6.7.2 High-gainlasers:theRigrodanalysis† 120
6.7.3 Outputpowerinothercases 123
Furtherreading 123
Exercises 123
7 Solid-statelasers 132
7.1 Generalconsiderations 132
7.1.1 Energylevelsofionsdopedinsolidhosts† 132
7.1.2 Radiativetransitions† 137
7.1.3 Non-radiativetransitions† 138
7.1.4 Linebroadening† 142
7.1.5 Three-andfour-levelsystems 142
7.1.6 Hostmaterials 146
7.1.7 Techniquesforopticalpumping 149
7.2 Nd3+:YAGandothertrivalentrare-earthsystems 157
7.2.1 Energy-levelstructure 157
7.2.2 Transitionlinewidth 157
7.2.3 Nd:YAGlaser 158
7.2.4 Othercrystallinehosts 163
7.2.5 Nd:glasslaser 164
7.2.6 Erbiumlasers 165
7.2.7 Praseodymiumions 169
7.3 Rubyandothertrivalentiron-groupsystems 169
7.3.1 Energy-levelstructure† 169
7.3.2 Therubylaser 174
7.3.3 Alexandritelaser 177
7.3.4 Cr:LiSAFandCr:LiCAF 180
7.3.5 Ti:sapphire 180
Furtherreading 184
Exercises 184
8 Dynamiccavityeffects 188
8.1 Laserspikingandrelaxationoscillations 188
8.1.1 Rate-equationanalysis 190
8.1.2 Analysisofrelaxationoscillations 190
8.1.3 Numericalanalysisoflaserspiking 192
8.2 Q-switching 193
8.2.1 TechniquesforQ-switching 194
8.2.2 Rate-equationanalysisofQ-switching 198
8.2.3 Comparisonwithnumericalsimulations 203
8.3 Modelocking 203
8.3.1 Generalideas 204
8.3.2 Simpletreatmentofmodelocking 206
8.3.3 Activemodelockingtechniques 208
8.3.4 Passivemodelockingtechniques 214
