激光原理及其应用课件-laser-and-its-applications教学讲义

激光原理及其应用（课件）Laseranditsapplications激光原理及其应用（课件）Laseranditsapp1LaseranditsapplicationsChapter(1):TheoryofLasing(2)

Chapter(2):Characteristicsoflaserbeam()

Chapter(3):Typesoflasersources()Chapter(4):Laserapplications()

ContentspageLaseranditsapplications2Chapter(1)TheoryofLasing1.Introduction(Briefhistoryoflaser)

Thelaserisperhapsthemostimportantopticaldevicetobedevelopedinthepast50years.Sinceitsarrivalinthe1960s,ratherquietandunheraldedoutsidethescientificcommunity,ithasprovidedthestimulustomakeopticsoneofthemostrapidlygrowingfieldsinscienceandtechnology

today.Chapter(1)TheoryofLasing1.3激光原理及其应用(课件-laser-and-its-applications教学讲义4激光原理及其应用(课件-laser-and-its-applications教学讲义5激光原理及其应用(课件-laser-and-its-applications教学讲义6

BeforeAfter

(i)Stimulatedabsorption

ii)Spontaneousemission

)(iii)StimulatedemissionBefore7)ii)Spontaneousemission

Consideranatom(ormolecule)ofthematerialisexistedinitiallyinanexcitedstateE2Noexternalradiationisrequiredtoinitiatetheemission.SinceE2>E1,theatomwilltendtospontaneouslydecaytothegroundstateE1,aphotonofenergyh

=E2-E1isreleasedinarandomdirectionasshownin(Fig.1-ii).Thisprocessiscalled“spontaneousemission”Notethat;whenthereleaseenergydifference(E2-E1)isdeliveredintheformofane.mwave,theprocesscalled"radiativeemission"whichisoneofthetwopossibleways“non-radiative”decayisoccurredwhentheenergydifference(E2-E1)isdeliveredinsomeformotherthane.mradiation(e.g.itmaytransfertokineticenergyofthesurrounding))ii)Spontaneousemission8(iii)Stimulatedemission

Quitebycontrast“stimulatedemission”(Fig.1-iii)requiresthepresenceofexternalradiationwhenanincidentphotonofenergyh

=E2-E1passesbyanatominanexcitedstateE2,itstimulatestheatomtodropordecaytothelowerstateE1.Inthisprocess,theatomreleasesaphotonofthesameenergy,direction,phaseandpolarizationasthatofthephotonpassingby,theneteffectistwoidenticalphotons(2h)intheplaceofone,oranincreaseintheintensityoftheincidentbeam.Itispreciselythisprocessesofstimulatedemissionthatmakespossibletheamplificationoflightinlasers.(iii)Stimulatedemission9GrowthofLaserBeam

Atomsexistmostofthetimeinoneofanumberofcertaincharacteristicenergylevels.Theenergylevelorenergystateofanatomisaresultoftheenergyleveloftheindividualelectronsofthatparticularatom.Inanygroupofatoms,thermalmotionoragitationcausesaconstantmotionoftheatomsbetweenlowandhighenergylevels.IntheabsenceofanyappliedelectromagneticradiationthedistributionoftheatomsintheirvariousallowedstatesisgovernedbyBoltzman’slawwhichstatesthat:Thetheoryoflasing

GrowthofLaserBeamA10

ifanassemblageofatomsisinstateofthermalequilibriumatanabsolutetemp.T,thenumberofatomsN2inoneenergylevelE2isrelatedtothenumberN1inanotherenergylevelE1bytheequation.WhereE2>E1clearlyN2<N1

KBoltzmann’sconstant=1.38x10-16erg/degree=1.38x10-23j/KTtheabsolutetemp.indegreesKelvinifanassemblageofatom11

Atabsolutezeroallatomswillbeinthegroundstate.Thereissuchalackofthermalmotionamongtheelectronsthattherearenoatomsinhigherenergylevels.Asthetemperatureincreasesatomschangerandomlyfromlowtotheheightenergystatesandbackagain.Theatomsareraisedtohighenergystatesbychanceelectroncollisionandtheyreturntothelowenergystatebytheirnaturaltendencytoseekthelowestenergylevel.Whentheyreturntothelowerenergystateelectromagneticradiationisemitted.Thisisspontaneousemissionofradiationandbecauseofitsrandomnature,itisincoherentAtabsolutezeroalla12

Asindicatedbytheequation,thenumberofatomsdecreasesastheenergylevelincreases.Asthetempincreases,moreatomswillattainhigherenergylevels.However,thelowerenergylevelswillbestillmorepopulated.Einsteinin1917firstintroducedtheconceptofstimulatedorinducedemissionofradiationbyatomicsystems.Heshowedthatinordertodescribecompletelytheinteractionofmatterandradiative,itisnecessarytoincludethatprocessinwhichanexcitedatommaybeinducedbythepresenceofradiationemitaphotonanddecaytolowerenergystate.Asindicatedbythee13

AnatominlevelE2candecaytolevelE1byemissionofphoton.LetuscallA21thetransitionprobabilityperunittimeforspontaneousemissionfromlevelE2tolevelE1.ThenthenumberofspontaneousdecayspersecondisN2A21,i.e.thenumberofspontaneousdecayspersecond=N2A21.Inadditiontothesespontaneoustransitions,therewillinducedorstimulatedtransitions.Thetotalratetotheseinducedtransitionsbetweenlevel2andlevel1isproportionaltothedensity(U)ofradiationoffrequency,where

=(E2-E1)/h,hPlanck'sconst.AnatominlevelE2c14

LetB21andB12denotetheproportionalityconstantsforstimulatedemissionandabsorption.Thennumberofstimulateddownwardtransitioninstimulatedemissionpersecond=N2

B21

U

similarly,thenumberofstimulatedupwardtransitionspersecond=N1

B12U

TheproportionalityconstantsAandBareknownastheEinsteinAandBcoefficients.Underequilibriumconditionswehave

LetB21andB12denote15bysolvingforU(densityoftheradiation)weobtainU[N1

B12-N2

B21]=A21

N2N2A21+N2B21U=N1B12USP

ST

Ab

bysolvingforU(densityof16AccordingtoPlanck’sformulaofradiation

)2))1)AccordingtoPlanck’sformula17fromequations1and2wehave

B12=B21

(3)equation3and4areEinstein’srelations.Thusforatomsinequilibriumwiththermalradiation.)4(

fromequation2and4

fromequations1and2wehave18(5)Accordingly,therateofinducedemissionisextremelysmallinthevisibleregionofthespectrumwithordinaryopticalsources(T103K.((5)Accordingly,therateofin19

Henceinsuchsources,mostoftheradiationisemittedthroughspontaneoustransitions.Sincethesetransitionsoccurinarandommanner,ordinarysourcesofvisibleradiationareincoherent.Ontheotherhand,inalasertheinducedtransitionsbecomecompletelydominant.Oneresultisthattheemittedradiationishighlycoherent.Anotheristhatthespectralintensityattheoperatingfrequencyofthelaserismuchgreaterthanthespectralintensitiesofordinarylightsources.

Henceinsuchsources20

AmplificationinaMedium

Consideranopticalmediumthroughwhichradiationispassing.SupposethatthemediumcontainsatomsinvariousenergylevelsE1,E2,E3,….letusfittourattentiontotwolevelsE1&E2whereE2>E1wehavealreadyseenthattherateofstimulatedemissionandabsorptioninvolvingthesetwolevelsareproportionaltoN2B21&N1B12respectively.SinceB21=B12,therateofstimulateddownwardtransitionswillexceedthatoftheupwardtransitionswhenN2>N1,.i.ethepopulationoftheupperstateisgreaterthanthatofthelowerstatesuchaconditioniscondrarytothethermalequilibriumdistributiongivenbyBoltzmann’slow.Itistermedapopulationinversion.Ifapopulationinversionexist,thenalightbeamwillincreaseinintensityi.e.itwillbeamplifiedasitpassesthroughthemedium.Thisisbecausethegainduetotheinducedemissionexceedsthelossduetoabsorption.AmplificationinaMedium21givestherateofgrowthofthebeamintensityinthedirectionofpropagation,anisthegainconstantatfrequency

givestherateofgrowthofth22QuantitativeAmplificationoflight

Inordertodeterminequantitativelytheamountofamplificationinamediumweconsideraparallelbeamoflightthatpropagatethroughamediumenjoyingpopulationinversion.Foracollimatedbeam,thespectralenergydensityUisrelatedtotheintensityinthefrequencyinterval

to

+bytheformula.QuantitativeAmplificationof23

DuetotheDopplereffectandotherline-broadeningeffectsnotalltheatomsinagivenenergylevelareeffectiveforemissionorabsorptioninaspecifiedfrequencyinterval.Onlyacertainnumber

N1oftheN1atomsatlevel1areavailableforabsorption.SimilarlyoftheN2atomsinlevel2,thenumber

N2areavailableforemission.Consequently,therateofupwardtransitionsisgivenby:DuetotheDopplereffecta24andtherateofstimulatedorinduceddownwardtransitionsisgivenby:

Noweachupwardtransitionsubtractsaquantumenergyhfromthebeam.Similarly,eachdownwardtransitionaddsthesameamountthereforethenettimerateofchangeofthespectralenergydensityintheinterval

isgivenby

where(h

B

NU)=therateoftransitionofquantumenergy

andtherateofstimulatedor25

Intimedtthewavetravelsadistancedx=c

dti.ethen

Intimedtthewavetravelsa26

inwhichisthegainconstantatfrequency

itisgivenby:anapproximateexpressionis

beingthelinewidthinwhichisthegaincon27Dopplerwidth

Thisisoneofthefewcausesseriouslyaffectingequallybothemissionandabsorptionlines.Letalltheatomsemitlightofthesamewavelength.TheeffectivewavelengthobservedfromthosemovingtowardsanobserverisdiminishedandforthoseatomsmovingawayitisincreasedinaccordancewithDoppler’sprinciple.Whenwehaveamovingsourcesendingoutwavescontinuouslyitmoves.Thevelocityofthewavesisoftennotchangedbutthewavelengthandfrequencyasnotedbystationaryobservedalter.DopplerwidthThisiso28

Thusconsiderasourceofwavesmovingtowardsanobserverwithvelocityv.Thensincethesourceismovingthewaveswhicharebetweenthesourceandtheobserverwillbecrowdedintoasmallerdistancethanifthesourcehadbeenatrest.Ifthefrequencyiso,thenintimetthesourceemitotwaves.IfthefrequencyhadbeenatrestthesewaveswouldhaveoccupiedalengthAB.Butduetoitsmotionthesourcehascausedadistancevt,hencetheseotwavesarecompressedintoalengthwhereThusconsiderasource29thus

Observer

wherenl=c

thusObserverwherenl=c30激光原理及其应用(课件-laser-and-its-applications教学讲义31EvaluationofDopplerhalfwidth:

AccordingtoMaxwelliamdistributionofvelocities,fromthekinetictheoryofgasses,theprobabilitythatthevelocitywillbebetweenvandv+visgivenby:

Sothatthefractionofatomswhosetheirvelocitiesliebetweenvandv+visgivenbythefollowingequationwhereB=m=molecularweight,K=gasconstant,T=absolutetempEvaluationofDopplerhalfwid32

Substitutingforvinthelastequationfromequation(1)andsincetheintensityemittedwilldependonthenumberofatomshavingthevelocityintheregionvand

then,i.e.

I(n)=const

.

n=

nat

I(n)=I=const

I)n)=I

max=constSubstitutingforvinthe33

Therefor

I)n)=I

max

beingthehalfwidthofthespectrallineitisthewidthat

,then

ThereforI)n)=Imaxbein34CalculationofDopplerwidth:1-CalculatetheDoppler’swidthforHg198.whereK=1.38x10-16ergperdegreeattemp=300kand=5460Ao

solution

=molecularweightm=const.(atomicmassm\)const.=1.668x10-24gmwavenumber

=

=.015cm-1

CalculationofDopplerwidth:1352-Calculatethehalf-maximumlinewidth(Dopplerwidth)forHe-Nelasertransitionassumingadischargetemperatureofabout400Kandaneonatomicmassof20andwavelengthof632.8nm.

(Ans.,n=1500MHz)2-Calculatethehalf-maximum36AnexpressionfortheGaintakingintoconsiderationDopplerbroadening:

Inthecaseofbroadeningduetothermalmotion,thekinetictheorygiventhefractionofatomswhosecomponentofvelocityliesbetweenvxandvxaswheremistheatomicmass,KistheBoltzman’sconstantandTistheabsolutetemperature

AspreviouslyexplainedduetotheDopplereffect,theseatomswillemitorabsorbradiationpropagatinginthexdirectionoffrequency

AnexpressionfortheGaintak37(1)whereisthefrequencyofthelinecenter.Itfollowsthatthefractionofatomsinagivenlevelthatcanabsorboremitinthefrequencyrangetoisgivenbywhere

fromeqn.(1))where

(1)whereisthefrequency38

Therateofupwardtransitionis

Therateofstimulatedorinduceddownwardtransitions

Thenettimeratechangeofthespectralenergydensityintheinterval

isgivenbyTherateofupwardtransiti39

whereB21=B12=Bwhereat

whereat40where

ispositiveifN2<N1whichistheconditionforamplification.otherwiseifN2<N1whichinthenormalequilibriumcondition)thenisnegative,wehaveabsorption.whereispositiveifN241PopulationInversion

InordertoinvertpopulationofatomiclevelstheatomsmustbeexcitedbydepositingenergyinthemediumusingsuchmethodastodecreasethenumberofatomsatthelowerlevelNLandtoincreasethenumberofatomsattheupperlevelNu

.Thisprocessiscalledpumpingsincetheatomsareredistributedasifpumpedfromthelowerleveltotheupperlevel.Themethodsofpumpingarei)opticalpumping,wheretheatomsareexcitedbyilluminationoflightii)excitationbyelectricdischargeinthecaseofgasesiii)Injectionofcarriersbyaforwardcurrentthroughap-njunctioninthecaseofsemi-conductorsiv)excitationbyirradiationwithelectronbeamsv)excitationbychemicalreaction.Historically,in1954,Townessucceededinrealizingpopulationinversionwithamolecularbeamofammoniatomakeamaserat1.25cmwavelength.PopulationInversion42

Astheammoniamoleculararedistributedamongenergylevelsinthermalequilibrium,themoleculesattheupperlevelwerecollectedandthoseinthelowerlevelwereeliminatedbytheactionofaninhomogeneouselectricfield,sothatpopulationinversioncanbeachieved.However,suchamethodwherepopulationinversionisestablishedbydecreasingthenumberofatomsinthelowerlevelcannotbeappliedsuccessfullytoopticaltransition.ThisisbecausethenumberofatomsNuandNLasrelatedbyBoltzmann’sformulanamelyKBBoltzmannconst

Astheammoniamolecu43

yieldsNuNLinthemicrowavecase,sinceh<<KBTatthemicrowavefrequency,whilethepopulationoftheupperlevelNuintheopticalcaseisverysmall,sinceh>>KBTattheopticalfrequency.Therefore,itisnotsufficientbymerelyeliminatingatomsatthelowerlevel,butitisnecessarytoincreasethenumberofatomsattheupperlevelbyaprocessofpumping.

Foratwo-levelsystem,whenitsatomsareexitedbyirradiationorbyelectroncollision,thenumberofatomsattheupperlevelwillincrease,butatthesametimetheprobabilityofde-excitationthatbringstheseexcitedatomsbacktothelowerlevelwillincreasewithincidentlightorelectrons.yieldsNuNLinthe44

Consequentlynomatterhowstrongtheatomsmaybeexcited,populationinversioncannotbeobtained.Therefore,threeorfouratomicsystemsmustbeusedtoachievepopulationinversion.Itisnotalwaysnecessarythattheenergylevelsconcernedshouldbediscreteandsharp.Bandlevelsmaybeused.Thus,dyelasersandsemiconductorlaserscanbeconsideredasfour-levellaserswhosedescriptionfollows.Consequentlynomatter45PopulationInversioninaThree-levelLaser:

Therearemanythree–levellaserssuchasrubylaserandtheopticallypumpedgaslaser.Lettheenergiesandpopulationsoftherelevantthreelevelsoflaseratomicsystembedenotedrespectivelybyw1,w2,w3andN1,N2,N3.Ifw3>w2>w1asshowninfigure,thenN1>N2>N3inthethree–levelsysteminthermalequilibrium.Heretheloweststate1isnotnecessarilythegroundstateoftheatom.Atomsinlevel1willbeexcitedatomsofappropriateenergy.Wedenotebytheprobabilityofexcitingtheatomsfromlevel1tolevel3byanysuchmethodofpumping.PopulationInversioninaThre46Fig.(6(

Whenthepumpingisremoved,theexcitedatomswillingeneralgraduallyreturntothestateofthermalequilibrium.Thisistermedrelaxation.Ifweconsidertheatomsindividuallytherelaxationprocesstakesplaceatthesametimeasotheratomsareexcited.

Fig.(6(Whenthepumping47

Besidestheradiativeprocess,wheretheexcitedatomsmakeatransitiontothelowerstatebyemittingaphoton,therearenon-radiativeprocessessuchascollisionofmoleculesingasesortheatomlatticeinteractioninsolids,wheretheexcitedatommakesatransitiontothelowerstatebyreleasingitsenergyintheformofmolecularkineticenergyorvibrationalenergyofthelattice.Sincerelaxationistheresultsofsuchstatisticalprocesses,therelaxationrateortherelaxationconstantisdefinedasastatisticalaverageoftherelaxationprobabilitiesoftheexcitedatomsperunittime.Thereciprocaloftherelaxationrateistheaveragelifetimeoftheexcitedatoms:Besidestheradiative48

Now,theprobability

Lu

ofanatombeingthermallyexcitedfromthelowerstatewLtotheupperstatewuisrelatedtotheprobabilityuLofthereveresprocessfromwutowLbythermalrelaxation.Thisrelationinthermalequilibrium.is

Nu

uL=NL

Lu

whereNu=

WhereTisthetemperatureofthemedium.

Therefor

(1(

Now,theprobability49Fig.(7)

Thislastrelationholdsgenerally,evenifNuandNLdonotrepresentpopulationsinthermalequilibrium.Iftheseprobabilitiesareconstantundertheconditionsconsideredtherateequationsexpressingtherateofchangeatthenumberofatomsineachlevelofthethree–levelsystemunderpumpingaregivenasfollows.Fig.(7)Thislastrelat50(2)(3)(4)WhereN1+N2+N3

=const.=Nthetotalnumberofatomsinthethree–levelsystem.(2)(3)(4)WhereN1+N2+N3=cons51

Inthesteadystate,thedistributionofthenumberofatomsunderconstantpumpingcanbeobtainedbyputtingtheleft–handsideofequations2,3&4equaltozero.AlthoughthesolutionsgivingN1,N2&N3canbereadilycalculated,yetweshallassumethattheseparationsbetweenthelevelaresufficientlygreaterthanthethermalenergyKBT,sothatwhenapplyingequation(1)wefindthat

,

wu-wL>>KBT

Sothat

,

Inthesteadystate,th52

Wecanthusneglect12,13,23andequations2,3&4yieldinthesteadystate(5)(6)(7)(8)Therefore(9)(10)Wecanthusneglect153Therefore(11)Fromequations5,6,7and11wecanwrite

Thusweobtainthesteady

–statesolution(12)Therefore(11)Fromequations554(13)Fromequation

12(14)(13)Fromequation12(14)55

fromequations(12,14)

(15)Iftheexcitationissostrongsuchthat

wehave

N2>N1(15\)fromequations(12,14)(1556

Thisistheconditionofpopulationinversion.Thustoobtainpopulationinversionwithmoderatepumping21shouldbesmalland32shouldbelargecomparedwith31

.Thismeansthatitisdesirablethattherelaxationfromtheupperlaserleveltothelowerlaserlevelshouldbeslow,whiletherelaxationfromtheuppermostlevel3towhichtheatomswasinitiallyexcitedtotheupperlaserlevel2shouldbefast.Fig.(8)Thisisthecondition57

ThepopulationinversionasdefinedbyN=N2-N1iscalculatedfrom12&14asafunctionoftheexcitationintensitytobeN

put

o=

Thepopulationinversi58=

(16)

Letusrepresentgraphicallythedependenceof

asafunctionofexcitationintensity

expressedintermsofo

.Considerthetwocaseswhen

)i)

32

=21.Where

21isthelasertransition)ii(

32

=9

21=(16)Letusrepresentgrap59(i)

Inthefirstcase

0

21015-104/1113/32(ii)

Inthesecondcase

010/9

4

9

1924

-1

0

0.520.71

0.81

0.82

(i)Inthefirstcase021015-60Fig.(9(Fig.(9(61Populationinversioninafour-levellaser

Sincethelowerlevelofthelasertransitionisthelowestlevelinathere-levellaser,themajorityofatoms(N1

N)areinthislevelatthermalequilibriumthusinordertoinvertthepopulation,thenumberofatomsinthelowestlevelmustbereducedtolessthanhalfbyintensepumping.Thisdemandismuchreducedinafour-levelsystem.Letusconsideranatom,whichhasfourenergylevelsasshowninfig(10).Itisrequiredtoinvertthepopulationbetweenlevels2and1.Sincethelowerlevel1liesatanenergyhigherthanKBTabovethegroundlevel,thenumberofthermallyexcitedatomsinthelowerlaserlevel1issosmallthatthepopulationcanbeeasilyinvertedbypumpingarelativelysmallnumberofatomsintotheupperlevel2.Theconditionsforpopulationinversioninthiscaseareasfollows.Populationinversioninafour62

Althoughseparationsbetweenlevels1,2&3areassumedtobemuchgreaterthanKBTasinthecaseofathreelevellaser,thenumberofthermallyexcitedatomsgo,NofromthemostpopulationgroundlevelOtolevel1arenotneglected.Therateequationsforatomicpopulationsinthefour-levels,thanbecome.Althoughseparationsb63SinceN=No+N1+N2+N3

LaserEmissionFig.(11)Energy-leveldiagramofafour-levellaser(17)SinceN=No+N1+N2+N3LaserEmis64where

2

=

20

+

21&

3

=

3o

+31+

32Thesteady–statesolutionisobtainedasbefore

o1No-

1oN1+

21N2+31N3=0-

2N2+

32N3

=0No-

3N3

=0Therefore,(18)where2=20+21&65fromequation19,20N2is>N1when(19)(20)fromequation19,20N2is>N66(21)

Thisistheconditionforpopulationinversionnow01inthenumeratorofthisequationistheprobabilityofthermalexcitationfromlevelOtolevel1,andisasmall

quantityasshownbytherelation

therefore,theexcitationintensity

necessaryforpopulationinversionislowered.

Since

&(21)Thisistheconditio67Thenequation(21)canbeapproximated

(22)Comparingequation(22)withequation(15\)forpopulationinversioninathreelevellaser,itisseenthattheyaresimilarexceptforthefactorSincethefour-levelsystemhasanextralevelO,itisobviousthatwehave

insteadof

insteadof

.Hereitisthefactor,

whichisimportant,becausepopulationinversioncanbeobtainedevenwithveryweekpumpingifthelowerlaserlevel1isabovethegroundlevelObyatleastafewtimesKBTinenergy.Thenequation(21)canbeappr68LaserOperation(1)EssentialElementsofLaser

Thelaserdeviceconsistsofbasicallyofthreeelements;Externalsource(pump),Amplifyingmediumandopticalcavity(resonator(LaserOperation(1)EssentialE69

Thepumpisanexternalenergysourcethatproducesapopulationinversioninthelasermedium.Pumpscanbeoptical,electrical,chemicalorthermalinnature.Forgaslasers(e.g.He-Nelaser),theusedpumpisanelectricaldischarge.Theimportantparametersgoverningthistypeofpumpingaretheelectronexcitationcross-sectionsandthelifetimesoftheenergylevels.Thepumpisanexternal70

Insomelasers,thefreeelectronsgeneratedinthedischargeprocesscollidewithandexcitethelaseratoms,ions,ormoleculesdirectly.Inothers,theexcitationoccursbymeansofinelasticatom-atom(ormolecule–molecule)collisions.Inthiscaseamixtureoftwogassesisusedsuchthatthetowdifferentspeciesofatoms,sayAandB,haveexcitedstatesA*andB*.Energymaybetransferredfromoneexcitedspeciestotheotherinaprocessasfollowsrelation

Insomelasers,thefr71

A*+BA+B*e.g.He-Nelaser,wherethelaser–activeneonatomsareexcitedbyresonanttransferofenergyfromheliumatomsinmetastablestate,wheretheHeatomsreceivetheirenergyfromfreeelectronsviacollisions.A*+BA+B*722-

Lasermedium

Theamplifyingmediumorlasermediumisanimportantpartofthelaserdevice.Manylaserarenamedafterthetypeoflasermediumused(e.g.He-Ne,CO2andNd:YAG).Thislasermediummaybegas,liquid,orsolid,determinesthewavelengthofthelaserradiation.Insomelaserstheamplifyingmediumconsistsoftwoparts,thelaserhostmediumandthelaseratoms.Forexample,inNd:YAGlaser,thehostmediumisacrystalofyttriumAluminumGarnet(orYAG),whereasthelaseratomsaretheNeodymiumions.Themostimportantrequirementoftheamplifyingmediumisitsabilitytosupportapopulationinversio