2.1-watts intracavity-frequency-doubled all-solid-state light source at 671 nm for laser cooling of lithium

1.1 MB·

by  Ulrich Eismann

2.1-watts intracavity-frequency-doubled
all-solid-state light source at 671nm for
laser cooling of lithium
UlrichEismann1,AndreaBergschneider1,2,ChristopheSalomon1and
3 Fre´de´ricChevy1
1 1LaboratoireKastlerBrossel,ENS,UPMC,CNRSUMR8552
0
24rueLhomond,75231Paris,France
2 2PhysikalischesInstitut,Ruprecht-Karls-Universita¨tHeidelberg
n ImNeuenheimerFeld226,69120Heidelberg,Germany
a [email protected]
J

3
Abstract: Wepresentanall-solid-statelasersourceemittingupto2.1W

]
of single-frequencylight at 671nm developed for laser cooling of lithium
s
c atoms. It is based on a diode-pumped, neodymium-doped orthovanadate
i
t (Nd:YVO4) ring laser operating at 1342nm. Optimization of the thermal
p
management in the gain medium results in a maximum multi-frequency
o
outputpowerof2.5Watthefundamentalwavelength.Wedevelopasimple
.
s
theory for the efficient implementation of intracavity second harmonic
c
i generation,and its application to our system allows us to obtain nonlinear
s
y conversion efficiencies of up to 88%. Single-mode operation and tuning
h is established by adding an etalon to the resonator. The second-harmonic
p wavelength can be tuned over 0.5nm, and mode-hop-free scanning over
[
more than 6GHz is demonstrated, corresponding to around ten times the

1 laser cavity free spectral range. The output frequency can be locked with
v respect to the lithium D-line transitions for atomic physics applications.
9 Furthermore,weobserveparametricKerr-lensmode-lockingwhendetuning
4
thephase-matchingtemperaturesufficientlyfarfromtheoptimumvalue.
4
0 © 2013 OpticalSocietyofAmerica
.
1
OCIScodes:(020.1335)Atom optics, (020.3320) Lasercooling, (140.3480) Lasers,diode-
0
pumped,(140.4050)Mode-lockedlasers,(190.2620)Harmonicgenerationandmixing.
3
1
:
v Referencesandlinks
i
X 1. S.Giorgini,L.P.Pitaevskii, andS.Stringari, “Theoryofultracold atomicfermigases,”Rev.Mod.Phys.80,
1215–1274(2008). 2
r
2. C.Chin,R.Grimm,P.Julienne,andE.Tiesinga,“Feshbachresonancesinultracoldgases,”Rev.Mod.Phys.82,
a
1225–1286(2010). 3
3. F.Hou,L.Yu,X.Jia,Y.Zheng,C.Xie,andK.Peng,“Experimentalgenerationofopticalnon-classicalstatesof
lightwith1.34µmwavelength,”TheEuropeanPhysicalJournalD62,433–437(2011).3
4. F.Camargo,T.Zanon-Willette,T.Badr,N.Wetter,andJ.Zondy,“Tunablesingle-frequencyNd:YVO4BiB3O6
ringlaserat671nm,”IEEEJournalofQuantumElectronics46,804–809(2010). 3,9
5. U.Eismann,F.Gerbier,C.Canalias,A.Zukauskas,G.Tre´nec,J.Vigue´,F.Chevy,andC.Salomon,“Anall-solid-
statelasersourceat671nmforcold-atomexperimentswithlithium,”AppliedPhysicsB106,25–36(2012). 3,
5,6,7,8,9,10,11
6. D. Fernandes, F.Sievers, N. Kretzschmar, S. Wu, C. Salomon, and F.Chevy, “Sub-doppler laser cooling of
fermionic40Katomsinthree-dimensionalgrayopticalmolasses,”arXivpreprintarXiv:1210.1310(2012).3
7. A.Miffre,M.Jacquey,M.Bu¨chner,G.Tre´nec,andJ.Vigue´,“Atominterferometrymeasurementoftheelectric
polarizability oflithium,”TheEuropeanPhysicalJournalD-Atomic,Molecular,OpticalandPlasmaPhysics
38,353–365(2006).3
8. H. Mu¨ller, S.-w. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-
momentum-transferbeamsplitters,”Phys.Rev.Lett.100,180405(2008). 3
9. I.E.Olivares, A.E.Duarte, E.A.Saravia, andF.J.Duarte, “Lithium isotope separation withtunable diode
lasers,”Appl.Opt.41,2973–2977(2002). 3
10. S.A.Payne,L.K.Smith,R.J.Beach,B.H.T.Chai,J.H.Tassano,L.D.DeLoach,W.L.Kway,R.W.Solarz,
andW.F.Krupke,“PropertiesofCr:LiSrAIF6crystalsforlaseroperation”,Appl.Opt.33,5526(1994).3
11. L.McDonagh, R.Wallenstein, R.Knappe,andA.Nebel,“High-efficiency 60WTEM00 Nd:YVO4 oscillator
pumpedat888nm,”Opt.Lett.31,3297–3299(2006).3
12. G.Tre´nec,W.Volondat,O.Cugat,andJ.Vigue´,“Permanentmagnetsforfaradayrotatorsinspiredbythedesign
ofthemagicsphere,”Appl.Opt.50,4788–4797(2011).4
13. P.Laporta andM.Brussard,“Designcriteria formodesizeoptimization indiode-pumped solid-state lasers,”
IEEEJournalofQuantumElectronics27,2319–2326(1991).4
14. Y.F.Chen,T.M.Huang,C.F.Kao,C.L.Wang,andS.C.Wang,“Optimizationinscalingfiber-coupledlaser-
diodeend-pumpedlaserstohigherpower:influenceofthermaleffect,”IEEEJournalofQuantumElectronics33,
1424–1429(1997). 4
15. W.Rigrod,“Gainsaturationandoutputpowerofopticalmasers,”JournalofAppliedPhysics34,2602–2609
(1963).5
16. E.Khazanov,N.Andreev,A.Mal’shakov,O.Palashov,A.Poteomkin,A.Sergeev,A.Shaykin,V.Zelenogorsky,
I.Ivanov,R.Aminetal.,“Compensation ofthermallyinducedmodaldistortions inFaradayisolators,” IEEE
JournalofQuantumElectronics40,1500–1510(2004). 5
17. F.Lenhardt, M.Nittmann, T.Bauer, J.Bartschke, andJ.L’huillier, “High-power 888-nm-pumped Nd:YVO4
1342-nmoscillatoroperatingintheTEM00mode,”AppliedPhysicsB96,803–807(2009). 6,11
18. R.Smith,“Theoryofintracavityopticalsecond-harmonicgeneration,”IEEEJournalofQuantumElectronics6,
215–223(1970).6
19. G.D.BoydandD.A.Kleinman,“Parametricinteractionoffocusedgaussianlightbeams,”JournalofApplied
Physics39,3597–3639(1968). 7
20. K.Fradkin,A.Arie,A.Skliar,andG.Rosenman,“Tunablemidinfraredsourcebydifferencefrequencygenera-
tioninbulkperiodicallypoledKTiOPO4,”AppliedPhysicsLetters74,914–916(1999).7,8,10
21. S.EmanueliandA.Arie,“Temperature-dependent dispersionequationsforKTiOPO4 andKTiOAsO4,”Appl.
Opt.42,6661–6665(2003).7,8,10
22. M.Peltz,U.Ba¨der,A.Borsutzky,R.Wallenstein, J.Hellstro¨m,H.Karlsson,V.Pasiskevicius, andF.Laurell,
“Opticalparametricoscillatorsforhighpulseenergyandhighaveragepoweroperationbasedonlargeaperture
periodicallypoledKTPandRTA,”AppliedPhysicsB73,663–670(2001).7
23. U.Eismann,“Anovelall-solid-statelasersourceforlithiumatomsandthree-bodyrecombinationintheunitary
bosegas,”Ph.D.thesis,Universite´PierreetMarieCurie–ParisVI(2012).8,9
24. K.I.Martin,W.A.Clarkson,andD.C.Hanna,“Self-suppressionofaxialmodehoppingbyintracavitysecond-
harmonicgeneration,”Opt.Lett.22,375–377(1997). 8,10
25. S. Helmfrid and K. Tatsuno, “Stable single-mode operation of intracavity-doubled diode-pumped Nd:YVO4
lasers:theoreticalstudy,”J.Opt.Soc.Am.B11,436–445(1994).8,10
26. W.Leeb,“Lossesintroducedbytiltingintracavityetalons,”AppliedPhysicsA:MaterialsScience&Processing
6,267–272(1975). 9
27. L.Rothmanetal.,“TheHITRAN2008molecularspectroscopicdatabase,”JournalofQuantitativeSpectroscopy
andRadiativeTransfer110,533–572(2009). 9
28. R.DeSalvo,D.J.Hagan,M.Sheik-Bahae,G.Stegeman,E.W.V.Stryland,andH.Vanherzeele,“Self-focusing
andself-defocusingbycascadedsecond-ordereffectsinKTP,”Opt.Lett.17,28–30(1992).9
29. S.Holmgren,V.Pasiskevicius,andF.Laurell,“Generationof2.8-pspulsesbymode-lockingaNd:GdVO4laser
withdefocusingcascadedkerrlensinginperiodicallypoledKTP,”Opt.Express13,5270–5278(2005).9
30. C. Scha¨fer, C. Fries, C. Theobald, and J. A. L’huillier, “Parametric kerr lens mode-locked, 888nm pumped
Nd:YVO4laser,”Opt.Lett.36,2674–2676(2011). 9
31. F.Lenhardt,A.Nebel,R.Knappe,M.Nittmann,J.Bartschke,andJ.A.L’huillier,“Efficientsingle-passsecond
harmonicgenerationofacontinuouswaveNd:YVO4-laserat1342nmusingMgO:ppLN,”in“Conferenceon
LasersandElectro-Optics,”(OpticalSocietyofAmerica,2010),p.CThEE5.11
1. Introduction
Lithiumatomsareoneofthemostversatilespeciesusedforresearchonquantumgases.Nature
offers significantly abundantbosonic and fermionic isotopes to the experimentalist, allowing
thestudyofbothtypesofquantumstatistics[1]intheatomicphysicslab.Thesimpleyetpow-
erfultechniqueofmagneticFeshbachtuningoftheatomicinteractions[2]isthequintessential
ingredientfora largenumberof experiments,and itexplainsthe outstandingrole the lithium
atomhasplayedinthedevelopmentofthefield.
For realizing a degenerate quantum gas, one needs to implement different laser cooling
schemes whichtypically requirenear-resonantsingle-frequencylightinputin the watt range.
Thebenefitsofall-solid-statedesignslikelargeoutputpower,highreliability,lowmaintenance
effort and high intrinsic stability are helpful for realizing light sources that will be welcome
toolsforeveryultracoldatomexperiment.
We will present in this article an all-solid-state laser emitting multi-watt single-frequency
radiationnear671nm.Thediode-pumpeddesignisbasedonneodymium-dopedorthovanadate
(Nd:YVO ) as the gain medium, lasing at the fundamental wavelength of 1342nm. Second
4
harmonicgeneration(SHG)isthenestablishedusingperiodically-poledpotassiumtitanylphos-
phate(ppKTP)asthenonlinearmedium.Thedevelopmentofanumberofrelatedlasersources
has been published recently[3, 4, 5], and the system developed in our group[5] has proven
highlyreliableinevery-dayoperationovertheperiodofoneyear.However,thesesourcesare
currently limited to output powers in the few-hundred-milliwattsregime. We have identified
twomajorlimitationsforpushingtheNd:YVO -SHGconceptintothemulti-wattrange,which
4
are the loss introduced by thermallensing in the gain medium, and the nonlinear conversion
efficiency.Therefore,thekeyingredientsofournovelhigh-powerdesignareanimprovedheat
managementintheNd:YVO ,andtheimplementationofintracavitySHG,bothofwhichwill
4
be discussed extensively. Furthermore, we carefully specify the important parameters of the
laser output and find that it largely satisfies the exigencies of laser cooling. Our source has
successfully been used in the implementationof a gray-molassescoolingscheme for lithium
atoms,seeRef.[6].
Apart from laser cooling of atoms, more applications in the fields of atomic physics and
nonlinearopticsarecurrentlylimitedbytheavailablesingle-frequency671-nmpower.Inatom
interferometers,a largerand thusmore homogeneousgaussianbeam can increase the signal-
to-noiseratio.Thelargespatialsplittingoftheatomicwavepacketsemployingthelightweight
lithium species is favorable[7], and can even be increased using multi-photon Bragg scatte-
ring[8]whenhigh-intensitylaserbeamsareemployed.Furthermore,thelithiumD-lineisotope
splittingis largeenoughto allowselectiveaddressingoftheisotopesin hotvapors,makinga
narrow-bandwidthsourceattractiveforlithiumisotopeseparation[9].Inaddition,thecreation
and long-distance transmission of entangled photons in the low-dispersion, low-absorption
wavelengthregionofstandardsilicafibersnear1.3µmhasrecentlybeenproposed.Thescheme
usestheoutputofasub-thresholdopticalparametricoscillatorinthedegenerateregimepumped
byasingle-frequency671-nmlaser[3].Finally,ourlasercouldserveasa low-intensity-noise
pumpforCr:LiSAFlasers[10].
The article is organizedas follows: In Section2 we presentthe optimization of the funda-
mental laser design. In Section3, we implement intracavity second harmonic generation. In
Section4,wereportonthecourseandcontinuousfinetuningbehaviorandnonlinear-Kerr-lens
modelocking,andweconcludeinSection5.
2. Thefundamentallaser
Afirststeptowardsastablehigh-powerfrequencydoubledlasersourceistheavailabilityofan
efficientlasersystematthefundamentalwavelength.Tominimizedetrimentalthermaleffects
in the gain medium, the followingpathway has been chosen:A pump wavelength of 888nm
in contrastto the former808nm[5] leadsto a lower quantumdefectper absorption-emission
cycle[11], and thus to lower heating for a given pump rate. In addition, a larger value for
the laser crystal length has been chosen in order to spread the heat input over a bigger vol-
ume. Therefore,heattransportfromthe centralregionto the crystalmountis facilitated.The
Nd:YVO peaktemperatureislower,andthermalissuesarelessofaconcern.
4
f f FP
2 1 λ/2 E
TGG
M
2
Nd:YVO
4
M
4
M ppKTP
1
M
3
Fig. 1. (Color online) The laser setup. The pump source, a fiber-coupled diode laser
bar(FP), is imaged into the gain medium by a pair of lenses f and f . The Nd:YVO
1 2 4
gainmediumisplacedinafour-mirrorbow-tieringresonatorconsistingofmirrorsM ,
1 4
whicharehighlyreflectingat1342nm.Unidirectionaloperationisforcedemployingat−er-
biumgalliumgarnet(TGG)-basedFaradayrotatorincombinationwithahalf-waveplate
(l /2).Theuseofanetalon(E)allowsforstablesingle-longitudinal-modeoperation.The
nonlinearcrystal(ppKTP)isinsertedatthetightfocusbetweenthecurvedmirrorsM and
3
M .Thesecondharmonicoutputbeam(red)istransmittedthroughM .Forthemeasure-
4 3
mentspresentedinSection2,theppKTPwasremovedandthedistanceM -M adjusted
3 4
accordingly,andthehigh-reflectivitymirrorM wasreplacedbyapartlytransmittingout-
2
putcouplingmirror.Thefundamentallaserbeam(green)isthencoupledoutthroughM .
2
A schematic overviewof the laser setup is givenin Fig.1. The outputof an 888-nmfiber-
coupled diode laser bar (NA = 0.22, 400µm fiber core diameter) is imaged by two lenses
(f =75mm, f =200mm)intothe1.0%at.-dopedNd:YVO crystal.Thecrystal(a-cut,4
1 2 4
4 25mm3,anti-reflectioncoatedonbothsidesfor1342nmand888nm)iswrappedinindiu×m
×
foilandmountedinawater-cooledcopperblock.ThemirrorsM constituteabow-tiecavity.
1 4
M , M and M are highly reflective at 1342nm, and M is tra−nsmitting at 888nm. M and
1 3 4 1 3
M are concave mirrors with a radius of curvature of 100mm. M is the output coupler for
4 2
which mirrors with different values of transmission are available. The cavity dimensions are
M M 300mm,M M M M 210mmandM M 97mm.Forforcingunidirectional
1 2 2 3 1 4 3 4
≈ ≈ ≈ ≈
operationwe use a Faradayrotator consistingof a terbium-gallium-garnetrod-shapedcrystal
(TGG) of 6mm length embedded in a strong permanent magnet [12] in combination with a
true-zero-orderhalf-waveplate.An uncoatedinfraredfusedsilica etalonof500µmthickness
servesasawavelengthselectiveelement.
For maximum power output, it is crucial to optimize the overlap of the pump beam and
thecavitymode[13,14].Forsimplicity,weperformthisoperationontheemptylasercavity,
consistingofM andtheNd:YVO only.Weapplythemaximumvalueoftheabsorbedpump
1 4 4
power P =−32.5W, and a T =5%-transmissionoutputcoupler(M ). By changingthe
abs,max 2
magnificationofthepumpimagingsetupconsistingof f and f ,thetop-hatshapedpumpspot
1 2
diameter was altered between 1080µmand 1400µm, see Fig.2. The size of the cavity mode
inthelasercrystalcanbechangedusingthecurvedmirrordistanceM M ,andwasoptimized
3 4
for each data point. The maximum output power is obtained at a pump diameter of around
1300µm,whereitiskeptfortheremainderofthisarticle.
Fig. 2. (Color online) (a) Optimization of the output power by changing the pump spot
diameter,performedonthelasercavitypresentedinFig.1withalltheintracavityelements
removed,exceptfortheNd:YVO4.ForaT =5%outputcoupler(M2),themodeoverlap
was optimized for each pump spot diameter by slight adjustments of the curved-mirror
distanceM -M .Linesareguidestotheeyeonly.(b)Rigrodanalysis.Theinfraredoutput
3 4
powerPw ismeasuredasafunctionoftheoutputcouplertransmissionT andfittedwith
theRigrodmodel(1)forbidirectional(reddiamonds,dashedline)andunidirectional(blue
circles,solidline)operationatPabs,max=32.5Wandoptimizedmodeoverlap.Inbothcases
the optimum transmission is found at T 5%. The parasitic roundtrip loss determined
from the fits yield 10(4)% for the bidirec≈tional and L =16(6)% for the unidirectional
case.
For both the bidirectional(empty cavity only containingNd:YVO ) and the unidirectional
4
(additionalTGGandhalf-waveplate)operationwemeasuredthemaximumoutputpowerasa
functionoftheoutputcouplertransmission,seeFig.2.InbothcasesaT =5%mirrordelivers
the maximum fundamentaloutput power Pw . By equating the single-pass gain with the total
round-triplossL =L +L =L +T forboththebi-andunidirectionalcases,whereL
tot out
isthesumoftheparasiticround-triplosses,wefind
G
Pw =PsatT (cid:20)T +0L −1(cid:21) (1)
similarlyto[15],whereP isthesaturationpower,G thesmall-signalgainandL thesumof
sat 0
theparasiticround-triplosses.Althoughthisanalysisessentiallyreliesonplanewaves,itcanbe
mappedtothemorerealisticcaseoftop-hatpumpbeamsandgaussianlasercavityeigenmodes,
aspresentindiode-pumpedsolid-statelasers,see[5]andreferencestherein.Aleast-squaresfit
to (1) yieldsL =10(4)%forthe parasitic loss in the bidirectionalcase. In [5] we foundthe
lossinanemptyfour-mirrorbow-tiecavityofmirrorsfromthesamebatchtobesmallerthan
1%.Weattributetheremaining9(4)%mainlytoaberrationscausedbythethermallensinthe
Nd:YVO .
4
Intheunidirectionalcase,thefittingprocedureyieldsL =16(6)%.Comparedtothebidi-
rectionalcase,thedifferenceofL =6(7)%canbeattributedtotheinsertionoftheTGG
Faraday
crystalandthewaveplate.Indeed,thermaldepolarizationandtheaccompanyinglossisawell-
knowneffectinTGG.Itimposesstringentlimitsonpowerscalingofunidirectionalringlasers
and Faraday isolators[16]. We observe a dependence of the optimum half-wave plate angle
on the circulating intracavity power,which is strong evidenceof this effect. From the fit, we
furthermoreobtainthevaluesP =170(50)WandG =0.27(5)forunidirectionaloperation,
sat 0
whichareimportantfortheoptimizationofintracavitydoubling,seeSection3.
For the now-optimized unidirectional infrared setup, we measure the output power as a
function of the absorbed pump power P , see Figure3. As the optimization is performed
abs
at the maximum absorbed pump power P 32.5W, the laser emission only starts at
abs,max
≈
P 28W. After reachingthreshold, the outputpower is unstable and displaysa hysteresis
abs
≈
featurebetweenP =29Wand30W.Aftercrossingthehysteresisregion,thelaseremissionis
abs
stableandonlyweaklydependsonP .Thisbehavioristypicalforhigh-powersolid-statelaser
abs
designsandhasbeenreportedin[17].Asdiscussedbefore,thermaldepolarizationintheTGG
issignificantandcanleadtoachangeofthelasingdirectionandoccasionalbistablebehavior
whenincreasingthepumppower.Thus,theangleofthehalf-waveplatehadtobeadjustedfor
everydatapointpresentedhere.WekeepthepumppowerconstantatP 32.5Winthe
abs,max
≈
remainderofthearticle.
Fig. 3. (Color online) Infrared unidirectional output power Pw as a function of the ab-
sorbed pump power P .Thesetup isoptimized for themaximal absorbed pump power
abs
Pabs,max=32.5W.TheoscillationthresholdisfoundatPabs 28W.Thedatashowshys-
≈
teresisbetweenPabs=29Wand30W,asindicatedbythearrowsforincreasingordecreas-
ingpumppower.Thisbehavioristypicalforhigh-power designs.Afterasuddenrisethe
output power increases only slowlyuntil it eventually reaches themaximum of 2.5W at
P .Linesareguidestotheeyeonly.
abs,max
3. Efficientintracavitysecond-harmonicgeneration
Efficientfrequencydoublingofinfraredlaserscanbeestablishedusingperiodically-polednon-
linearcrystalsinanexternalcavity.Usingthismethodatafundamentalwavelengthof1342nm,
adoublingefficiencyofP2w /Pw =86%hasbeenobtainedinourfirst-generationsetup[5],and
serves as a benchmark.However,a more direct approachfollowed here is intracavity second
harmonicgeneration(ICSHG),whichrequiresonlyonecavityandthusrepresentsanimportant
simplification.
For the analysis of the output power of ICSHG lasers, the ouput coupling loss L =T
out
discussed in Section2 needs to be replaced by h P, where h is the single-pass doublingeffi-
ciency, and P the circulatingintracavity power. Similar to the one foundby R.G. Smith[18],
thesolutionfortheSHoutputpowerintheunidirectionalcasereads
P G 2
P2w = saxt 0(cid:20)q(x −z )2+x −(x +z )(cid:21) , (2)
wherex =h P (4G ) 1 andz =L(4G ) 1 are thedimensionlessoutputcouplingandloss
sat 0 − 0 −
parameters.Aspointedoutin[18],itisinterestingtonotethatthevaluefortheoptimumoutput
coupling L =√G L L is the same for both linear and non-linear output coupling
out,opt 0
−
mechanisms,anddeliversthesameamountofoutputpower.However,theround-tripparasitic
lossL willcontainanadditionalcontributionfromtheinsertionofthenonlinearmedium,such
thatP2w /Pw <1foranyrealisticsystem.UsingthefitvaluesfromSection2,wemaximize(2)
bychoosinganoptimumsingle-passdoublingefficiencyh =0.10(5)%.W 1.
opt −
Toevaluateh ,werefertotheBoyd-Kleinmantheoryforfocusedgaussianbeams[19],
2w 3d2L
h (T)= ij h[a ,b (T)], (3)
pe 0c4nw ,i(T)n2w ,j(T)×
wheree isthevacuumpermittivity,cthespeedoflightinvacuum,d isthei,j-thelementof
0 ij
thematerial’snonlineartensor,nw ,i(T)thematerial’srefractiveindexalongtheiaxisatangular
frequencyw andtemperatureT,andLthenonlinearmaterial’slength.d needstobereplaced
ij
byd =2d p 1forperiodicallypoled(pp)materials.Thefunction
eff ii −
a a 2
1 − 0eib (T)t
h[a ,a 0,b (T)]= 4a (cid:12)(cid:12) Z 1+it dt (cid:12)(cid:12) , (4)
(cid:12) a a (cid:12)
(cid:12)− − 0 (cid:12)
(cid:12) (cid:12)
isthedimensionlessBoyd-Kleinmanfunction[1(cid:12)9].a =L(2z ) (cid:12)1 anda =z (2z ) 1 arethe
R − 0 0 R −
focusingandoffsetparameters,respectively.z istheRayleighlength,andz istheoffsetofthe
R 0
beamfocuswithrespecttothenonlinearmedium’scenter.Thephase-matchingparameterreads
b (T)=4p zRl −1 nw ,i(T) n2w ,j(T) l [2L (T)]−1 ,wherel isthevacuumwavelength.
TheL (T)termon×ly(cid:8)occursfo−rperiodica−llypoledmate(cid:9)rials,whereL (T)isthepolingperiod,
andthetemperaturedependenceresultsfromthermalexpansion.
In the intracavity-doubling setup, we replace the output coupling mirror M by a high-
2
reflectivitymirror,cf.Figure1.Thenonlinear,periodically-poledpotassiumtitanylphosphate
crystal(ppKTP)isinsertedbetweentheconcavemirrorsM andM .ToaccountfortheppKTP
3 4
refractiveindex,thedistanceM M isincreasedto 106mm.Thenonlinearcrystalhasouter
3 4
≈
dimensionsof 1 6 18mm3 and is antireflectioncoated at 1342nm and 671nm. Its poling
period L =17.6×1µm×is chosen for phase matching at 23.5 C according to the temperature-
◦
dependentSellmeierequationsfrom[20,21].However,inapreviousstudywefoundthephase-
matching temperature at 33.2 C[5]. This deviation can be explained by uncertainties on the
◦
reported Sellmeier equations, and the manufacturing tolerance on the ppKTP poling period.
The nonlinearcoefficientd =14.5pm.V 1 foundforthe crystalin ourpreliminarystudyis
33 −
14%lowerthanthehighestliteraturevaluereportedsofar[22],probablyduetopolingimper-
fections[5].Usingthiscrystalfornonlinearoutputcoupling,wecaneasilyobtainasingle-pass
efficiency h >h , such that design considerations are relaxed, and we are able to tune to
opt
h bychangingthephase-matchingtemperature.Fortemperaturestabilization,thecrystalis
opt
wrappedinindiumfoilandmountedinatemperature-controlledcopperblock.Thefrequency-
doubledlightistransmittedthroughmirrorM .
3
In Fig.4 we present the measurement of the second-harmonic output power as a function
of the phase-matching temperature of the ppKTP crystal. We find a maximum of 2.1W of
output power at T =36 C, and a second maximum of 1.9W at T =31 C. As expected
pm ◦ pm ◦
from Eq.(2), at the perfectphase matchingtemperatureh >h , and the outputpower only
opt
amountsto1.6W.TheFWHMofthetemperature-tuningcurveamountsto22K.Ascompared
tothemaximuminfraredpowerpresentedintheformersection,weobtainamaximumdoubling
efficiencyof88%.Theexcellentmodequalityofthesecond-harmoniclightisconfirmedbya
single-modefibercouplingefficiencylargerthan80%.
Togaindeeperinsightinourdata,weemploytheICSHGtheory(Eqs.(2)-(4)).Weinclude
theadditionalparasiticintracavitylossduetothepresenceoftheetalonandthenonlinearcrys-
tal,whichamountstoL =0.6(1)%.Thus,thetheorypredictsamaximumSHoutputpower
add
Fig. 4. (Color online) Output power as a function of the phase-matching temperature
(points, blue lines are a guide to the eye only). The data shows a double-peak structure
of1.9W/2.1Wofoutputpowerslightlyoffoftheoptimumphase-matchingtemperature
of 33.2 C (central vertical line). A simpletheoretical model presented inthe text (dash-
◦
dottedpurpleline)describesthedatawellinthecentralhigh-conversionregion,usingthe
known temperature dependence of the single-pass doubling efficiency, which is propor-
tionaltothedimensionlessBoyd-Kleinmanfunctionh(T)[dashedgoldline,Eq.(4)].The
dashed vertical line indicates the perfect phase-matching temperature of Tpm =33.2◦C,
whereb (Tpm) 0.Theverticallineswitharrowsindicatethetemperatureregionswhere
≃
self-modelockingoccurs,cf.Section4.
of2.1W,asisfoundexperimentally.ThevalueofL iscompatibletothesumoftheppKTP
add
insertionlossmeasuredindependently[5]andthe calculatedwalk-offlossforthe etalon[23].
FromanABCD-matrixformalismweobtainthecavityeigenmode,yieldingz =11.5mmand
R
z =3mm. At perfect phase matching, we obtain h=0.40, yielding a SH output power of
0
1.6W, which is in excellentagreementwith our findings. This gives us further confidencein
our previously measured value of d [5]. The temperature-dependentKTP refractive indices
33
andthethermalexpansioncoefficientofthepolingperiodwerepresentedin[20,21].We ad-
justb byanadditiveconstantinordertoaccountforthemeasuredphasematchingcondition
b (T=33.2 C)=0,asjustifiedbefore.Thetheory(solidpurplelineinFig.4)describesthedata
◦
wellinthecentralhighconversionregion,andyieldsthecharacteristicdouble-peakstructure.
Outside of the central region, the circulating intracavity power rises significantly and the
power-dependent thermal depolarization loss would need to be accounted for in our simple
model.Ascomparedtothetheory,thedatadisplayslessevidenceofdips.Thiscanbeexplained
byathermalsmearingeffectduetoresidualabsorptionintheppKTPatlargepowers,yielding
a spatial dependenceof the phase-matchingparameter b (T). Outside of the region indicated
bythesolidverticallines,thelaserisinmode-locked(pulsed)operation,andwedonotexpect
ourmodeltobeapplicable.
4. Tuningbehaviorandnonlinear-Kerr-lensmodelocking
Forcoursetuningandsingle-longitudinal-mode(SLM)operation,thelaserwasequippedwith
anuncoatedetalonof0.5mmlength,yieldinga freespectralrangeof210GHz.We notethat
thissingle,weakly-selectiveetalonissufficientforthispurposeduetotheselfsuppressionof
axialmodehoppinginintracavity-frequency-doubledlasers[24,25].
The tuning range of the frequency-doubledlaser is characterized and compared to the in-
fraredlaserinFig.5.Apartfromhavingthesameshapeandfeatures,itisstrikingtonotethat
theoutputpowerofthefrequency-doubledlaseramountstoalmostthesamevalueasthenon-
doubledlaserovertheentireemissionspectrum.AsdiscussedinSection3,thenonlinearoutput
couplingisclosetotheoptimumlevelovertheentireemissionwavelengthrange.Thegainline
center,wheretheoutputpowerismaximal,isfoundataround671.1nm,resultingin2.2Wof
fundamentaland2.1Wofsecond-harmonicoutput.Atthelithium-Dlinewavelengththeoutput
poweramountsto 1.8W. Beingclose to the gainlinecenter,thisresultcomparesfavorably
≈
tothevalueobtainedin[4],wheretheauthorsusedanetalonfortuningwhichpotentiallypro-
duces significantlyhigher tilt loss[23, 26]. Comparingthe emitted power of the doubledand
non-doubledlasersacrosstheemissionspectra,wetypicallyobtainmorethan80%ofthepower
at 671nm,demonstratinga veryefficientfrequencydoublingprocess.Forthe absolutemaxi-
mum values, we obtain P2w /Pw =88%. It is even possible to obtain emission further away
from resonance, where the non-ICSHG lasers cease to oscillate. Our first-generation source
presented in[5] displays an output spectrum that is significantly more plateau-like (gold tri-
anglesin Fig.5), which we attribute to the presenceof a second,moreselective etalon in the
cavity.Attheexpenseofahigherinsertionlossbaseline,ripplesintheemissionspectrumhave
significantlylessinfluenceonthetuningbehaviorofthissetup.Theidenticalgapsinallofthe
emission spectra presentedhere (A,B,Cin Fig.5) can be explainedby absorptionfromwater
vapor,aswecomparethelaserspectratoawatervaporabsorptionspectrumobtainedfromthe
HITRANdatabase[27].ThewaterabsorptionpeakscoincidewiththefeaturesA,BandC.
Fig.5.(Coloronline,linesareguidesfortheeyeonly)Single-frequencyoutputspectraof
the infraredlaser presented inSection2(blue circles),theintracavity-frequency-doubled
laser (purple squares) and the infrared source presented in[5] (gold triangles). For easy
comparison, all wavelengths are given in vacuum values. The vertical lines denote the
positions of the lithium-D line resonances. The green line shows a water vapor absorp-
tionspectrumfortypicalparameters(23 C,60%rel.humidity).Thewavelengthregions
◦
marked A,B,C where stable, powerful operation of the lasers can not be established co-
incidewithabsorptionpeaksofwatermolecules.Thelevelofoutputpoweroftheinfrared
laserandthefrequency-doubledlaserarecloselyspaced,provingthatthenonlinearcrystal
introducesweakadditionalpassivelossinthelasercavity,whereasthedegreeofnonlinear
outputcouplingisatitsoptimumvalue.
Intracavity-frequency-doubledlaserstendtomode-lockedoperationwhenthedoublingcrys-
talis mismatchedfromtheoptimumphase matchingcondition[28, 29].Thiseffect,resulting
from an intensity-dependent phase shift of the fundamental beam passing the non-matched
crystal,iscommonlytermednonlinear-Kerr-lens-orc (2):c (2) modelocking.Althoughithas
beenobservedinthe1064-nm-Nd:YVO -ppKTPsystembefore[30],wereport,tothebestof
4
ourknowledge,thefirstobservationat1342nm.Weobservetheeffectwhendetuningfromthe
optimumphase-matchingtemperaturetobelowT =29 CandaboveT =45 C.Ascanning
low ◦ high ◦
Fabry-Perotspectrumanalyzershowsnodiscerniblesingle-orfew-modebackgroundoncethe
thresholdtomode-lockedoperationiscrossed.Weuseafastdetectorandaspectrumanalyzer
to measurethebeatfrequencybetweenneighboringmodes.Thissimplemethodto determine
thelasercavityfreespectralrangeyieldsavalueof345(1)MHz.
It is remarkablethatthe modelockingarises when tuningthe phase-matchingtemperature
to colder-than-optimalvalues. In analogy to standard Kerr-lens mode locking, the c (2) :c (2)
processrequiresanadditionalintracavityelementwhichmodifiestheround-tripgainorlossas
afunctionofthepower-dependentcavitymodesize.Thiscanberealizedbythegainmedium,
cf. Fig.1. As we presentedin Section2, the pump-to-cavitymode overlaphas been carefully
optimizedinthecwregime.However,anABCD-matrix-basedcavitymodecalculationreveals
thatthebeamwaistintheNd:YVO onlychangesmonotonouslywhencrossingoverfromneg-
4
ativetopositivefocalpowersintheppKTP.Thus,theinducedchangeingainorlossshouldbe
lessfavorablewheneverthelensingdepartsfromtheoptimizedvalue.Wenotethatinoursim-
pleanalysis,wedonottakeintoaccountdifferentKerr-likeandthermallensesthatmayoccur
intheintra-cavityelementsotherthanthelaserandnonlinearcrystals.Usingthetemperature-
dependentSellmeier equationsof [20, 21], we getdephasingparametersof b (T )=8.8(1)
low
andb (T )= 18.5(1),resultinginasingle-passefficiencyh (T)reducedtolessthan5%of
high
−
themaximumvalue.
Thelasercanbetunedcontinuouslyusingapiezoelectrictransducer(PZT),uponwhichmir-
rorM isgluedupon.Thisallowsmode-hopefreescansofthe671-nmoutputfrequencyover
2
morethan6GHz.Fortheresonatedfundamentallightthisamountstoabouttentimesthelaser
cavityfreespectralrange,atypicalbehaviorofICSHGlaserswithself-suppressedmodehop-
ping[24, 25]. We performDoppler-freesaturatedabsorptionspectroscopyon a lithium vapor
cell described previously in[5], see Fig.6. In Fig.6(a) we show a sample scan over the full
Doppler-broadenedlithium-6D1line.Theground-statehyperfinestructureisclearlyresolved.
Wephase-modulatetheprobebeamat20MHzusinganelectro-opticmodulator,andthenuse
a commerciallock-inamplifier to generate a dispersive error signalas presentedin Fig.6(b).
We can access all D-line transitions of both naturally abundantlithium isotopes, and the full
groundstatehyperfinestructureisresolved.
Fig. 6. (Color online) Doppler-free saturated absorption spectroscopy of the lithium D-
lines.(a)Samplescanovertheentire6LiD1Doppler-broadenedabsorptionpeak.Theinset
showsthesub-Dopplerfeatures.SimilarspectraareobtainedforalllithiumDlines.(b)Er-
rorsignalsofalllithiumD-linetransitions,generatedbyphasemodulationspectroscopy.
Thesesignalsprovideanexcellentreferenceforfrequency-lockingofthelaser.
The laser linewidth was estimated by slowly scanning the emission frequency over the
D1-lineoflithium-6.Fromtheobservedpeak-to-peaknoiseinthelinearpartoftheerrorsignal
weobtainanupperlimitof1MHzforthelaserlinewidth.Forfrequency-lockingthelaser,we