Basics of Laser Physics: For Students of Science and Engineering

617 Pages·2017·8.422 MB·English

by  Karl F. Renk

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Karl F. Renk
Basics
of Laser Physics
For Students of Science and Engineering
With333 Figures
123
ProfessorDr.KarlF.Renk
Universita¨tRegensburg
Institutfu¨rAngewandtePhysik,Universit¨atsstr.31
93053Regensburg,Germany
E-mail:[email protected]
ISSN1868-4513 e-ISSN1868-4521
ISBN978-3-642-23564-1 e-ISBN978-3-642-23565-8
DOI10.1007/978-3-642-23565-8
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber: 2011945843
©Springer-VerlagBerlinHeidelberg2012
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To Marianne,Christiane,andPeter
’
Preface
Thistextbookaddressesstudentsofscienceandengineering.Itshouldbeappropri-
ateforaseniorlevelappliedphysicsorengineeringcourseonlasers.
Therearemanytextbooksonlasers.Whymayitbeusefultohaveanotherone?
I have tried to unify the description of different types of lasers: gas lasers; solid
state lasers, including semiconductor lasers; dye lasers; and free-electron lasers.
Semiconductorlasersaredescribedinmoredetailthaninothertextbooksonlasers.
This may be adequate according to the very different types of semiconductor
lasersandthemanydifferentapplications.
What is the working principle of a laser and how is it realizable in different
typesoflasers?Iintroducealaserasanoscillator(Dlaseroscillator)thatgenerates
coherentradiationviatheinteractionofradiationwithanactivemedium.Anactive
mediumconsistsofanensembleofatomicsystemswithapopulationinversion.
I make use, on an elementary quantum mechanical basis, of the Einstein
coefficients of absorption, spontaneous and stimulated emission of radiation to
characterizetheinteractionofradiationwithanatomicsystem.Einsteincoefficients
aredeterminablefromquantitiesthatareexperimentallyaccessible.Iformulatethe
workingprincipleofa laserbytheuseofrateequations,yieldingtheconditionof
laseroscillationandotherpropertiesofalaser.
Themaintopicsofthebookconcern:theworkingprincipleofalaser;theparts
of a laser — like the laser resonator and the active medium; beams of radiation
generated by a laser; femtosecond laser pulses; and different types of lasers.
Additionaltopicsdeepentheunderstandingofmorespecificquestionsconcerning,
inparticular:originofgaininatitanium–sapphirelaser;opticalfrequencyanalyzer;
theoryofgainofradiationindopedglassfibers.
Itseemsthatanimportanttypeoflaser—thefree-electronlaser—doesnotmeet
the criteria of a laser: classical physics is well suited to analyze operation a free-
electronlaser.Iwill,nevertheless,illustrateoperationofafree-electronlaserbyuse
of an energy-leveldescription. An active medium of a free-electronlaser consists
of oscillating free electrons. I attribute, to an oscillating free electron, an energy-
ladder system. In this description, population inversion occurs in an ensemble of
vii
viii Preface
energy-laddersystems;theconceptisknownforaparticularsemiconductorlaser—
the superlattice Bloch laser (also called Bloch oscillator) — that exists, however,
onlyas an idea based on theoreticalwork.The energy-leveldescriptionillustrates
similarities of free-electron lasers and conventional lasers as well as differences
betweenthem.
A chapter comparing laser oscillators and quasiclassical solid state oscillators
providesaconnectiontotextbookscoveringthefieldofmicrowaveoscillators;addi-
tionally,thevanderPoloscillatorisintroducedasamodelofaclassicaloscillator.In
contrasttoalaser,withapopulationinversioninanensembleofquantumsystems,a
quasiclassicaloscillatoroperateswithoutpopulationinversion:radiationinanactive
mediuminteracts with collectivesof electrons— the interaction is determinedby
classical physics but the ability to form appropriate collectives of electrons is of
quantummechanicalnature.
A reader may skip, in a first study, several chapters or sections that serve for
deepening: Chap. 9 (dynamics of the active medium); Sect. 11.7 (Gouy phase);
Sects.12.9, 12.10, 13.3–13.9 (laser applications); Chap. 17 (physical basis of
broadband solid state lasers); Chap. 18 (theory of fiber lasers and amplifiers);
Sects.19.5–19.12 (energy-level description of the free-electron laser); Chap. 21
(theory of semiconductor lasers); Sects.25.8–25.15 (theory of electromagnetic
waves in layered materials); Chap. 26 (discussing quantum well lasers in
detail); Chap. 30 (theory of electron waves in semiconductor heterostructures);
Chap. 31 (comparing lasers with quasiclassical oscillators); Chap. 32 (Bloch
laser); Chaps. 33–35 (laser-relatedtopics). Deepening of topics related to solid
state physics (including semiconductor physics) corresponds to my experience in
researchinsolidstatespectroscopy.Severalothertextbooksdeepenthediscussion
oflasersmoretowardatomicphysicsorquantummechanics.
Text illustrations, examples, and exercisesshould allow a studentto follow the
mainlinebutalsosinglearguments.
I wouldlike to thankthestudentswhoattendedmy“LaserPhysics” coursefor
askingquestionsaboutafirstmanuscript.IthankAlfonsPenzkoferforexamininga
largeportionofthemanuscriptandsuggestingmanyimprovements.Iamindebted
to Al Sievers for very helpful advice with respect to manuscript and exercises.
I appreciate many valuable comments from Laurence Eaves, Max Maier, Peter
Renk, Jens Siewert, Benjamin Stahl, Herbert Welling, and Ernst Werner. I thank
RupertHuber,JoachimKeller,TobiasKorn,JohnLupton,ChristophStrunk,Werner
Wegscheider for discussions, and Peter Olbrich for advice on electronic data
processing.UllaTurbahasdrawnalargepartofthefiguresandhaswrittenalarge
partofthemanuscript.Iamverygratefulforherengagementduringpreparationof
variousversionsofthemanuscriptandforallowingmetopermanentlychangetext,
formula,anddrawings.IamindebtedtoClausAscheronforhisencouragementto
writeabook.
Regensburg,Germany KarlF.Renk
September2011
Contents
PartI GeneralDescriptionofaLaserandanExample
1 Introduction................................................................. 3
1.1 LaserandLightBulb ............................................... 3
1.2 SpectralRangesofLasersandListofaFewLasers.............. 4
1.3 LaserSafety......................................................... 6
1.4 SizesofLasers,CostofLasers,andLaserMarket................ 6
1.5 QuestionsAbouttheLaser ......................................... 8
1.6 DifferentTypesofLasersintheSameSpectralRange ........... 9
1.7 ConceptoftheBook................................................ 9
1.8 References........................................................... 11
1.9 ARemarkabouttheHistoryoftheLaser.......................... 11
Problems ..................................................................... 14
2 LaserPrinciple.............................................................. 17
2.1 ALaser.............................................................. 18
2.2 CoherentElectromagneticWave................................... 18
2.3 AnActiveMedium.................................................. 22
2.4 LaserResonator..................................................... 26
2.5 LaserDLaserOscillator ........................................... 31
2.6 RadiationFeedbackandThresholdCondition..................... 32
2.7 FrequencyofLaserOscillation..................................... 34
2.8 DataofLasers....................................................... 35
2.9 OscillationOnsetTime ............................................. 38
Problems ..................................................................... 39
3 Fabry–PerotResonator .................................................... 43
3.1 LaserResonatorsandLaserMirrors............................... 43
3.2 VFactorandRelatedQuantities ................................... 45
3.3 NumberofPhotonsinaResonatorMode ......................... 46
3.4 IdealMirror ......................................................... 47
3.5 Fabry–PerotInterferometer......................................... 48
ix
x Contents
3.6 ResonanceCurveofaFabry–PerotResonator .................... 50
3.7 Fabry–PerotResonatorContainingaGainMedium .............. 52
Problems ..................................................................... 53
4 TheActiveMedium:EnergyLevelsandLineshapeFunctions........ 55
4.1 Two-LevelBasedandEnergy-LadderBasedLasers.............. 56
4.2 Four-Level,Three-Level,andTwo-LevelLasers.................. 57
4.3 Two-BandLaserandQuasibandLaser ............................ 59
4.4 Energy-LadderBasedLaser........................................ 61
4.5 Lineshape:HomogeneousandInhomogeneous
LineBroadening .................................................... 61
4.6 LorentzFunctions................................................... 63
4.7 GaussianLineshapeFunction...................................... 66
4.8 ExperimentalLinewidths........................................... 67
4.9 ClassicalOscillatorModelofanAtom............................ 68
4.10 NaturalLineBroadening ........................................... 70
4.11 EnergyandPhaseRelaxation ...................................... 70
4.12 Three-DimensionalandLow-Dimensional
ActiveMedia........................................................ 71
Problems ..................................................................... 72
5 Titanium–SapphireLaser ................................................. 75
5.1 PrincipleoftheTitanium–SapphireLaser......................... 75
5.2 DesignofaTitanium–SapphireLaser ............................. 77
5.3 AbsorptionandFluorescenceSpectraofTitanium–Sapphire..... 78
5.4 PopulationoftheUpperLaserLevel............................... 79
5.5 HeatandPhonons................................................... 80
Problems ..................................................................... 80
PartII TheoreticalBasisoftheLaser
6 BasisoftheTheoryoftheLaser:TheEinsteinCoefficients........... 83
6.1 LightandAtomsinaCavity ....................................... 83
6.2 SpontaneousEmission.............................................. 85
6.3 Absorption .......................................................... 86
6.4 StimulatedEmission................................................ 86
6.5 TheEinsteinRelations.............................................. 86
6.6 EinsteinCoefficientsontheEnergyScale......................... 89
6.7 StimulatedVersusSpontaneousEmission......................... 90
6.8 DeterminationofEinsteinCoefficientsfromWaveFunctions.... 92
Problems ..................................................................... 93
7 AmplificationofCoherentRadiation..................................... 95
7.1 InteractionofMonochromaticRadiationwithan
EnsembleofTwo-LevelSystems .................................. 96
7.2 GrowthandGainCoefficient....................................... 98
7.3 GainCrossSection.................................................. 101