Table Of ContentAlexander Horn
The Physics
of Laser
Radiation–Matter
Interaction
Fundamentals, and Selected
Applications in Metrology
The Physics of Laser Radiation–Matter Interaction
Alexander Horn
The Physics of Laser
Radiation–Matter Interaction
Fundamentals, and Selected Applications
in Metrology
AlexanderHorn
Mittweida,Sachsen,Germany
ISBN 978-3-031-15861-2 ISBN 978-3-031-15862-9 (eBook)
https://doi.org/10.1007/978-3-031-15862-9
©SpringerNatureSwitzerlandAG2022
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Tomywife,Sylke.
Sheinteractsseriouslywithme,
makinglifebetter.
Preface
Thistextbookisintendedforstudentsofphysics,physicalormechanicalengineering,
ornaturalsciences.Theideatostarttowriteabookontheinteractionoflaserradiation
withmatterbegantogrowwhenImovedtoMittweidain2013,toolingthereanew
professorshipinphysicsandlasermicrotechnology.Textbooksonthesetopicexist
forprofessionals,butmyresearchoncomprehensivebooksdidn’tgetanyvaluable
books on, in my opinion, very important derivations from equations and thoughts,
describing such processes. So, I started to collect passages, generated topics, and
finallyfinalizedthisbook.
These years of development were accompanied by numerous discussions with
myteammembers,whoinfactclearedmymindandallowedmetodetermineared
lineonwhichalectureonlaserradiation–matterinteractionshouldfollow.Myteam
colleagues were the “seeds and the plants” of most results described in this book.
Especially,MarkusOlbrich,M.Sc.,beingourfundamentalistinsenseofthephysical
understanding,pitchedthistextbookontherightlevel.Hewasmyfirstgroupmember,
andtogetherwesetupourlabatthelaserinstituteinMittweida.Heintroducedmy
grouptothenumericaltechniquesandtaughtallgroupmembers,andadditionally
alsoourstudentslearningphysicaltechnology,toapplythesewonderfultechniques
tomanyphysicalproblems.Thesecondkeyplayerinmygroup,Dr.rer.nat.Theo
Pflug,wastheexperimenter,whodevelopedmanynovelultra-fastmetrologiesand
whopublishedinaveryshorttimemanywonderfularticlesonourgroupactivities.
Bothsupportedmeduringmywritingofthistextbookwithfruitfuldiscussionsandin
settingupmanydiagramsandmodelingplots.Thelastmemberwhosupportedmeis
PhilippLungwitz,M.Sc.,whodevelopedoftenveryunorthodoxphysicaltechniques
andopenedsomenewresearchtopicsinmygroup.Heistheperfectionistinourlab,
whopushedsomeofourresearchtonewlevels.AllofthemIthankverymuchforthe
fruitfulyearsandthefriendship.ThelaserinstituteinMittweidaisajewel,asthere
best-skilledscientistsareworkingondifferentleadingtopicsinlasertechnology.I
thankallmycolleaguesforthestrongcollaboration.Onegreatpropertyisthatmany
of them work together when help is needed, even not being in the same research
group.Nothingwouldworkinourlabsattheinstitutewithoutthestrongsupportof
LarsHartwig,SaschaKlötzer,andAlexanderThurm.Theywerethefirstsettingup
vii
viii Preface
the illumination technology in my lab, making the room cleaner with flow boxes,
andallowingustostarttoworkveryquickly.
Thistextbookisstructuredintofourgreatparts,startingfromthecharacterization
oflaserradiation.Inmyopinion,themostimportanttopicsdeallittlewith“laser”
radiation,butjustonelectromagneticradiation.Asthistextbookdoesnotdealwith
ultra-high-energy physics, also the topic laser will just deal with pulse duration
downtothefemtosecondregime.Justsomeinsightonpulseshapingwillenlargethe
physicsoflaserradiationwithmatter.
The second part of this textbook describes the processes for the generation of
electromagneticradiation,asfirstlyoftenradiationisgeneratedduringlaserradia-
tion/matterinteraction,andsecondly,everyprocessofinteractionfeaturesakindof
scatteringofcharges.Oscillatingchargesemitradiation,aswillbeshownbysolving
the Maxwell equations. In my opinion, even these derivations are somehow very
theoretical,alsoanengineershouldbeabletofollowtheidea.Thisisimportantto
understandphysics!
The third and largest part describes the interaction of radiation with matter. As
a textbook, I decided to go step-wise from the simplest system, a free electron, to
themostcomplexone,condensedmatter,introducingsemi-classicalmodelsforthe
interaction.Inthistextbook,nostrongquantummechanicalderivationsaregiven,as
thisismoreadequateforthephysicist,notforauser.Eventhoughthesemi-classical
modelissomehowcrude,theydescribetheprocessesverywell.Manyexamplesare
given. Getting an understanding of the interaction of simple systems, linear optics
dealingwiththeinteractionofradiationwiththecondensedmatterwithoutabsorption
isdescribed.Asultra-fastlasermetrologyisinmyopinionthemetrologybeingable
toinvestigateveryfundamentalprocesses,non-linearopticsisthenintroduced,being
thekeyprocessforultra-fastphysics.Uptonow,noabsorptionisgiven,whichiswhy
inthefollowingsectionstheabsorptionisintroduced. Todescribethisproperlyin
condensedmatter,especiallyinthistextbooksolidstatematterisdiscussed,andthe
namemodelforcrystallinematterisintroduced.Beforethat,clearly,thefreeelectron
gasisusedasthesimplestmodeltodescribeabsorptionandasaconsequence,their
opticalproperties.Asnowtheinter-andintrabandtransitionsareunderstood,many
examplesontheexcitationofcondensedmatteraregiven,formetals,semiconductors,
andaswelldielectrics.Especiallyfordielectrics,asabsorptioncanonlytakeplace
whennon-linearprocessesaregiven,atopiconnon-linearabsorptionwilldescribe
thedifferentchannelsenablingradiationtoionizematter.
Thefourthandlastpartdealswithapplicationsinmetrologyusinglaserradiation.I
decidedtodescribesomespecialmetrologies,whereultra-fastlaserradiationfeatures
the best properties to get some very deep insight. Also, I focused on pump-probe
technologies only. I start with reflectometry, being the simplest metrology. There
I describe the fundamentals of the pump-probe idea. A very impressive setup is
thendescribedallowingtodetectspace-andtime-resolvedreflectancechange.The
nextchapterdealswithellipsometry,afantasticmetrology,allowingtodeterminethe
complexrefractiveindex.Aftersomefundamentals,Idescribespace-resolvedandin
thefollowingspace-andtime-resolvedellipsometry.Amorequalitativemetrology,
butquickinsettingup,isNomarskimicroscopy.Itallowstodeterminespace-and
Preface ix
time-resolvedrefractiveindexchanges.Finally,Iwilldescribeinthispartthewhite-
light interferometry. It is the royal league of interferometry, as using white-light a
biuniquedetectionofphasechangesispossible,andcombinedwithultra-fastlaser
radiation,itbecomesaverypowerfulmetrologyfortheinvestigationoflaser-induced
processes.
ManythankstoProf.Sauerbreyforallowingmetousehisveryfocusedlecture
notes on non-linear optics. I hope I got his message and could transpose it well.
Also,IadoptedsomenotesfromthelecturesonelectrodynamicsbyS.Brandtand
D. Dahmen I listened to as a student in physics at the University of Siegen in the
year1992.Finally,Iwanttothankmanystudents,likeMelwinGöse,B.Sc.,Philipp
RebentrostM.Sc.,EricSyrbeM.Sc.,KatrinZerbeM.Sc.,givingmealotofhelpful
commentsandrevisionstothetextbook.
Oberschöna,Germany AlexanderHorn
August2022
Contents
PartI ElectromagneticRadiation
1 PropertiesofElectromagneticRadiation ........................ 3
1.1 FundamentalInteractions .................................. 4
1.1.1 NuclearForces ................................... 5
1.1.2 ElectromagneticForce ............................. 6
1.1.3 GravitationalForce ............................... 6
1.2 WaveandParticleDescriptionofElectromagneticRadiation .... 7
1.3 PhotonDescription ....................................... 8
1.4 MaxwellEquations ....................................... 9
1.4.1 MaxwellEquationsinVacuum ...................... 9
1.4.2 ContinuityEquation ............................... 11
1.4.3 IntegralDescriptionofMaxwellEquations ........... 12
1.5 ElectromagneticWaves ................................... 12
1.5.1 DerivationofWaveEquations ...................... 12
1.5.2 FundamentalsonWaves ........................... 14
1.5.3 OrthogonalityoftheVectorFields ................... 15
1.5.4 ScalarandVectorPotential ......................... 17
1.6 EnergyDensityofElectromagneticWave .................... 20
1.6.1 ElectrostaticApproach ............................ 20
1.6.2 GeneralizationtoElectromagneticFields ............. 24
1.6.3 PlanarElectromagneticWaves ...................... 28
1.6.4 PhaseandGroupVelocity .......................... 33
1.7 LaserRadiation .......................................... 35
1.7.1 SpatialandTemporalProperties .................... 35
1.7.2 Coherence ....................................... 37
1.7.3 SpectralModulation ............................... 39
References .................................................... 50
xi
xii Contents
2 GenerationofElectromagneticRadiation ........................ 51
2.1 DiscreteandContinuousTransitions ........................ 51
2.2 SpontaneousEmission .................................... 52
2.3 AccelerationofaFreeCharge .............................. 54
2.3.1 GeneralAspectsontheRetardation .................. 56
2.3.2 GeneralSolutionofaRetardedWaveEquation ........ 58
2.3.3 MaxwellEquationsforaMovingCharge ............. 59
2.4 EmissionofAcceleratedCharges ........................... 65
2.4.1 CollinearVelocityandAccelerationVectors .......... 65
2.4.2 AccelerationPerpendiculartotheVelocity ............ 68
2.4.3 PeriodicOscillationofaChargedParticle ............ 70
2.5 Black-BodyRadiation .................................... 75
2.5.1 One-DimensionalHollowBlackBody ............... 76
2.5.2 Three-DimensionalHollowBlackBody .............. 79
2.5.3 High-andLowPhotonEnergyLimits ............... 82
2.5.4 TheStefan–BoltzmannLaw ........................ 83
2.5.5 Wien’sDisplacementLaw ......................... 83
2.5.6 EmittedRadiationPower .......................... 84
2.5.7 RealThermalEmitter ............................. 87
2.6 Laser-GeneratedX-Rays .................................. 87
2.7 ConcludingRemarks ..................................... 90
References .................................................... 91
PartII InteractionofParticleswithElectromagneticRadiation
3 ElasticScatteringatChargedParticles .......................... 95
3.1 FreeElectron ............................................ 95
3.1.1 RadiationForce .................................. 96
3.1.2 ExternalField .................................... 98
3.1.3 DipoleMomentandDifferentialPowerperSolid
Angle ........................................... 99
3.2 BoundedElectron ........................................ 101
3.2.1 EquationofMotionofaWeakly-BoundedElectron .... 102
3.2.2 RadiationForce .................................. 105
3.2.3 ExternalField .................................... 106
3.2.4 DipoleMomentandDifferentialPowerperSolid
Angle ........................................... 107
3.3 Cross-Section ............................................ 109
3.4 PolarizationofScatteredRadiation ......................... 113
3.5 Photo-ExcitationofAtoms ................................ 114
3.5.1 LinearScattering ................................. 114
3.5.2 Non-linearScattering .............................. 115
