Experimentalandtheoretical
investigationofa
volume-Bragg-grating-lockedYb:KYW
laseratselectedwavelengths
Bj¨ornJacobsson
Laserphysics,KTH–RoyalInstituteofTechnology,10691Stockholm,Swedenbj@laserphysics.kth.se
Abstract:LaseractionisdemonstratedinYb:KYWatwavelengthsof990nm,997nmand1066nm,whenpumpedat980nmbyaTi:sapphirelaser,withalowestlaserquantumdefectof1.0%.Thelaseroutputpowersatthevariouswavelengthswere70mW,160mWand140mW,respectively.LockingofthelaserwavelengthandthespectrallyclosespacingofpumpandlaserwereachievedbytheuseofavolumeBragggratingasaninputcoupler.Atheoreticalmodelisalsopresentedthataccuratelydescribesthelaseratvariouswavelengths,bysolvingthelaserrateequationsatspatialpointsthroughoutthelasercrystal.
?2008OpticalSocietyofAmerica
OCIScodes:(140.3615)Lasers,ytterbium;(050.7330)Volumegratings.
Referencesandlinks
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#92968 - $15.00 USDReceived 21 Feb 2008; revised 18 Apr 2008; accepted 18 Apr 2008; published 22 Apr 2008
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1.Introduction
Solid-statelaserswithYb3+astheactiveionareimportantlasersourcesinthe1μmspectralregion.SinceYb3+showsabroadbandgain,alargelasertuningrangeisavailable.Further-more,suitablehighpowerlaserdiodesareavailableforpumpinginthe940-980nmregion.HighpowerlaseractioninYb3+alsobene?tsfromthecomparablylowheatgenerationinthelasermedium,thankstothelowquantumdefect,comparedtoe.g.Nd3+.Consequently,Yb3+lasers?ndapplicationswherehighpowerandhighbrightnessaredesirable,suchasprinting,markingandmaterialprocessing,aswellasinvariousspectroscopicapplicationsthankstotheavailabletunability.
Inordertoexploitytterbium’sbroadbandgainandobtainanarrowbandlaseroutputatade-siredwavelength,aspectrallyselectiveelementisneededforlockingofthelaser.Inpreviousworks,ithasbeenshownthatvolumeBragggratingsareanattractiveelementforspectralselec-tioninsolid-statelasers[1–6].VolumeBragggratingscombinethepossibilityof>99.5%peakre?ectivitywithnarrow,sub-nanometerbandwidth,andcaneasilybemanufacturedtomatchtheneededspectralspeci?cations.Thegratingsarewritteninaphoto-thermo-refractiveglassbyirradiationtoaUVinterferencepatternandsubsequentthermaldevelopment[7].Thankstothefabricationprocess,thegratingsarestableandshowgooddurability,asshownbythesuccessfuloperationintheabovecitedlaserexperiments.
Inthispaper,anewmethodtolocksolid-statelasersisemployedthatusesavolumeBragggratingsimultaneouslyasaninputcouplerandawavelengthselectorinanend-pumpedlaser.Themethodisparticularlyinterestingforlaserswithverylowquantumdefectandwas?rstpresentedin[8],whereupto3.6Woflaserpowerwasdemonstratedinadiode-pumpedYb:KY(WO4)2(Yb:KYW)laserlasingat998nmataquantumdefectof1.6%.Inthepresentwork,themethodisfurtherexplored,andlasingisobtainedinYb:KYWatasshortawave-lengthas990nmwithaquantumdefectofonly1.0%,whenpumpingat980nmdirectlyintotheemittinglevel.Infact,bytuningthepumpwavelength,lasingataquantumdefectof0.85%waspossible,comparabletothelowestreportedvalue,totheauthorsknowledge,at0.8%[9].Inaddition,lasingat997nmand1066nmisalsodemonstrated.Eventually,theselasersareofmostinterestwhendiode-pumped,butforbettercontrolofthepumpintensitydistributioninthisearlywork,IuseaTi:sapphirelaserat980nmforpumping.
Duetothelowquantumdefectinthestudiedlasers,thelowerlaserlevelissubstantiallythermallypopulated.Hence,intensepumpingisneededtoovercomethelargereabsorptionlossinthesystem.Thiscanbequanti?edbythegaincrosssectionsinFig.2,e.g.indicatingthattoobtainpositivegainat990nm,about35%ofthepopulationneedstobeintheupperlaserlevelforahomogeneouslypumpedcrystal.Sincethelaserispumpedat980nmdirectlyinto
#92968 - $15.00 USD
Received 21 Feb 2008; revised 18 Apr 2008; accepted 18 Apr 2008; published 22 Apr 2008
(C) 2008 OSA28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6444
theemittingupperlaserlevel,themaximuminversionthatcanbeachievedisslightlybelow50%,givenbytheinversionforwhichthegainatthepumpwavelengthbecomespositive(i.e.negativeabsorption),seeFig.2.Inordertoproperlydesignthelaser,itisneededtohaveatheoreticalmodelforthepumpingandlasingthatincorporatesthereabsorptionloss.Duetothestrongvariationinpumpandlaserintensitythroughoutthelasercrystal,themodelmustalsoaccountfor(atleast)atwo-dimensionalspatialvariation.Suchamodelhaspreviouslybeenpresentedin[10–12],andinthiswork,themodelisemployedtoevaluateitsaccuracyandusefulness.Sincethepresentlasersystemissomewhatdifferentthanthepreviouslymodelledone,somealterationstothemodelarealsonecessary,asexplainedinmoredetailbelow.
Thepaperisorganizedasfollows.Insection2,Ipresentthetheoreticalmodel,andinsection3,theexperimentalsetupofthelaserexperimentsisdescribed.Then,insection4,theexperi-mentalresultsarepresentedandcomparedwithnumericalresultsbasedonthetheory.Finally,adiscussionoftheresultsandconclusionsaregiveninsection5.2.Theoreticalmodel
Inthissection,atheoreticalmodelforthelaserispresented,tobecomparedwiththeexper-imentalresults.Intheinvestigatedlaser,reabsorptionduetothermalpopulationofthelowerlaserlevelisimportant.Thismeansthattheinversionindifferentpartsofthelasercrystalisverydifferent.Thusitisnecessarytomakeathree-dimensionalmodelofthepumpandlaserdistributioninthelasercrystal.Themodelisbasedontheonegivenin[11,12],thatisshowntogivegoodcorrespondencebetweentheoryandexperiments.Still,inthiswork,somemodi-?cationshavebeenmadetothemodeltosuitthisspeci?claser.Themostimportantdifferenceisthatthislaserispumpeddirectlyintotheupperlaserlevel,meaningthatstimulatedemissionatthepumpwavelengthcannotbeneglected.
Weassumealasersystemwithenergylevelsthatcanbedescribedbyalowerandanup-permanifold.ThepopulationconcentrationisNlinthelowerandNuintheuppermanifolds,withatotaldopingconcentration,N=Nl+Nu.Tomodelthetransitionprobabilityatdifferentwavelengthsλweusetheeffectivecrosssectionsforabsorption,σa(λ),andemission,σe(λ).Theseeffectivecrosssectionstakeintoaccountthethermalpopulationofthesublevelsofthemanifolds,withabsorptionandemissionrelatedbythereciprocitymethod[13].Forapumpwavelengthλpandalaserwavelengthλl,weusethefollowingnomenclatureforthecrosssec-tions:σap=σa(λp),σep=σe(λp),σal=σa(λl),σel=σe(λl).Furthermore,weassumeanupperlevellifetimeτ,apumpintensityIpandalaserintensityI(inunitsofW/m2).Therateequationforthesystemisgivenby
????????
λpλpdNu1λlλldNl
=?=+σelI+σepIpNu?σalI+σapIpNl.(1)dtdtτhchchchcAtsteadystate,thepopulationsarethen
Nl=N?Nu=N
λlp
σephcIp+σelhcI+1τλλpλl(σep+σap)hcIp+(σel+σal)hcI+1τ.(2)
Thegaingandabsorptionαaregivenby
g(λ)=?α(λ)=σe(λ)Nu?σa(λ)Nl,
yieldingapumpabsorptionof
(3)
αp=N
#92968 - $15.00 USD
λlτ(σelσap?σalσep)hcI+σapλlp
τ(σep+σap)hcIp+τ(σel+σal)hcI+1
λ(4)
Received 21 Feb 2008; revised 18 Apr 2008; accepted 18 Apr 2008; published 22 Apr 2008
(C) 2008 OSA28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6445
wl(z)wp+Ip-Ipwl00zl0dP+P-zFig.1.Setupinthelasercrystal,showingpump(dashedblue)andlaser(solidred)parame-ters.
andalasergainof
g=N
pτ(σelσap?σalσep)hcIp?σal
λλpλl
τ(σep+σap)hcIp+τ(σel+σal)hcI+1
.(5)
Theaboveexpressionsgiveacompletedescriptionatanyspatialpoint,sothenextstep
istode?neageometry,asdepictedinFig.1.Weassumeacylindricalsymmetryalongthepropagationaxis,whichisparameterizedbytheradiusrandtheaxialpositionz,withthecrystalextendingover0 ForthepumpweassumeaGaussianbeamwithaconstantradiuswpinsidethelasercrystal.Theincidentpumpintensityatz=0isthengivenbytheincidentpumppowerPinas Ip(0)=Pin 2 exp(?2r2/w2p).2πwp (6) Anaxiallyconstantpumpbeamradiusisagoodapproximationofthepresentexperiments withaTi:sapphirepumplaserwithaconfocalparameterthatislargerthanthecrystallength.However,forbeamswithashorterconfocallength,asisthetypicalcaseforadiode-pumpedlaser,thevariationwiththepositionzisimportantandshouldbeincludedinthemodel.Asdescribedbelow,thelaseremploysdoublepasspumping.Theintensityofthe?rstpassage +.Forthesecondpass,withintensityI?,theincidentpowerthroughthecrystalisdenotedIpp isafractionofthetransmitted?rstpasspump,givenbytheoutputcouplerpumpre?ectivityRp.Forsimplicityweassumethatthissecondpasshasthesamepositionandbeamradiusasthe?rstone,thoughthisisonlyapproximatelytrueintheexperiments.Thus,thetotalpump ++I?.intensityisIp=Ipp Forthelaserbeam,whichismoretightlyfocussedbythecavitydesign,theaxialvariationisincludedinthemodel.WeassumeaGaussianbeamofbeamwaistradiuswl0atposition 21/2 zl0,yieldingaradiuswl(z)=wl0(1+((z?zl0)λl/(πw2,forarefractiveindexn.Wel0n))) assumethelaserpowerinthecrystaltobecomposedofaforwardtravellingpartP+andabackwardtravellingpartP?.Forsimplicity,bothareassumedtohaveaxiallyconstantpower,whichisagoodapproximationforlowgainorequivalentlyhighoutputcouplerre?ectivity.ThelaseroutputpowerPoutisrelatedtothesebytheoutputcouplerre?ectivityRatthelaserwave-lengthasP+=P?/R=Pout/(1?R).Theeffectsofspatialhole-burningarenotincludedinthemodel,asitisassumedthatasuf?cientnumberoflongitudinalmodesoscillatetocompletely #92968 - $15.00 USDReceived 21 Feb 2008; revised 18 Apr 2008; accepted 18 Apr 2008; published 22 Apr 2008 (C) 2008 OSA28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6446 saturatethegain.Finally,thelaserintensityinsidethelasercrystalis I(z)= 21+RPoutexp(?2r2/w2l(z)).21?Rπwl(z)(7) Next,thespatialvariationofthepumpintensityistobecalculated.Hereweassumethatthe axialvariationoftheintensityateachradialpositionisindependentoftheneighbouringradialintensity.Thus,theintensitycanbefoundseparatelyforthedifferentradialpositions.Thisthencorrespondstonoradialtransportofpower.Withthisassumption,theintensitydistributioncanbefoundbysolvingthedifferentialequationdIp/dz=?α(Ip)Ipwiththeincidentpowerasboundarycondition.However,duetothedoublepasspumping,thesituationissomewhatcomplicated.Thedifferentialequationthatneedstobesolvedisthenasystem +dIp +?+ =?α(Ip+Ip)Ipdz?dIp +?? =+α(Ip+Ip)Ipdz (8)(9) withboundaryconditions + (0)=Ip(0)Ip ?+Ip(d)=RpIp(d). ?and(9)×I+,onecanseethatTodecouple(8)and(9),wenotethatbyadding(8)×Ipp +?+2 Ip(z)Ip(z)=constant=RpIp(d). (10)(11) (12) Nowthesystemcanbedecoupledandwegetthesingledifferentialequation ++2(d)RpIpdIp ++ =?α(Ip+)Ip,+dzIp (13) +(0)=I(0).SincetheequationincludesitsownsolutioninwiththeboundaryconditionIpp z=d,itissolvediteratively,usingineveryiterationstepafourthorderRunge-Kuttawith +(d)=0andhaltingatarelativeerrorofautomaticstep-sizeadjustment,thestartingvalueIp ?isgivenby(12).1%.Finally,Ip Thelaseroutputpoweriscalculatedindirectlyby?ndingthepointwherethelasertotalgainGequalsthetotalloss,givenbytheoutputcouplerre?ectivityRandtheroundtrippassivelossinthecavityL 1 .(14)G= R(1?L) Asshownin[10],thetotalroundtripgainisgivenby ????d??G=1+dz 0 ∞ 0 ??2 4 rdrg(r,z)2exp(?2r2/w2.l(z))wl(z)(15) Finally,atagivenpumppower,thepointwhere(14)issatis?edisfoundbyanumericalmini-mizationprocedurewiththelaseroutputpowerasvariationalparameter.Aspecialcaseisthe laserthreshold,whichisfoundwhere(14)issatis?edatzerolaserpower,whichisacompar-ativelyeasynumericalproblem.Fortheminimizationatanarbitrarylaserpower,theMatlabfunctionfzeroisused.Thefunction?ndsaminimumforalaserpowerinanintervalbetween #92968 - $15.00 USD Received 21 Feb 2008; revised 18 Apr 2008; accepted 18 Apr 2008; published 22 Apr 2008 (C) 2008 OSA28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6447
(二极管三极管)2008_实验和理论研究了一种体布拉格光栅锁相Yb,KYW激光器在选定波长下的性能
