Investigation of the Nitrogen Laser

oe _ ta . 1 . ‘ INVESTIGATION OFTHEshenLASERASAPUMP FOR INTERFERENCE TUNED DXB LASER SPECTROSCOPY by : . Philip Tboht RESEARCH PROJECT | Submittedtothe Department 9fElectrical Engincering on?Computer Sciences, Univereitd ofCalifornia, Berkeley, in : . partial satisfaction ofthe fequirements for the degree of Master ofSciences, Plan’ IT. Approval.fortheReportandfevprehensive Exeninetion: COMMETTER olEh. __Research Adviser : n (Date) | INVESTIGATION OFTHENITROGEN LASER ASAPUMP FORINTERFERENCETUNED"|LASERSPECTROSCOPY by| | Philip e RESEARCH1Submitted tothe Department ofBlectrical Engineering sa? Computer Sciences, University ofCalifornia, Berkeley, in partial satisfaction ofthe quirenents for the degree of Master ofSciences, Plan‘ II. Approval for the Report and Gomprehensive Exaniuation: 4 7 : conmmnen _.7F Lhe___Research Adviser fr & % SiS : 2 (Date) , a | } Acknowledgement | .Forhismanyconstructive ooioseae andsuggestions relatingtothiereportandtoLife-In-General 1amindebted toProf.S.B.Schwara. Iwouldliketoacknowledge alsothesnivatuadle assistance oftwosenior membersofourgraduatestudentgroup,‘paDeTemple andRodThorne,who . Kindly provided answers toayendless questions, Finally, Iamappreciative ofthefinancial support provided bytileU.S.Governnent. . | t { { 1 | | >| | a. | : i i Contents i (1)Introduction ; (2)TheInterference-Tuned Distndbaled FeedbackDyeLaser2,1TheDistributed Feedback} Laser 2.2TheInterference Tuningfetes 2.3TheResults ofShank, Bjérkholm andKogelnik (3)Determinants oftheSpectralwiataleranInterference TimedDyeLaser 3.2Spatial Divergence | 3.2 Amplitude Variation1 3.3SpatialIncoherence | 3.4 Spectral Width 3.5 Summary 3.6 Evaluation ofthe Nitrogen Laser (4)Experimental Nitrogen Laser Researgh 4,1Physical Description of[apparatus 4.2Performance cnaracteriatios 4.3TheCavity Experiment ! (5)Conclusion | 5.1Interpretation ofExperitenta Results5.2Improving Spatialcoheresos 5-3 Proposal for anOscillatdr-Amplifier Nitrogen Pump references 1 | | ! , (1)Introduction i Among those characteristios which delimit theusefulness ofan absorption spectrometer, threestandoleasbeingmostsignificant: (1) rangeoftuneability, (2)spectral resolution, and(3)brilliance. A typical laboratory absorption spectrométer has atuning range ofseveral thousand angstroms andaspectral resolution of1£,thelight sourceusuallyemployedisatungstenvteeelhavingabrillianceofatmost 100W/on@-sr overthevisible portionjof thespectrum. Light fromthe tungsten source ispassed through smoochrometer andthebrilliance of theresulting sampleprobebeam,wichneassumetohaveaspeotralwidth of14,isthusabout30m/om’-er. | Foragiven light source, aniimprovement inspectral resolution maybeboughtonlyattheexpenseofbpilliance, forasthespectrometer slit ismade narrower, less light gets|through. One isthus led toseekamorebrilliantsourceofnel Thebrightestconventional light source known iethearolamp. Although|the emission spectrum ofanarc lampishighlyirregular,fractionalafererentiat absorptiontechniques make itpossible tousesuch asource torspectroscopy. Nevertheless, arc lampsprovidelessthananorderofmagnitude improvement inbrilliance. For example, aPEK 110 aro lamp has atotal brilliance inthe visible of only 250W/om@-sr. Itisinteresting tocomparelthese brilliance figures with those typicaloflasers.Aspointedoutbyreint,a4mW6328&heliumneon laserwithabeamof1mmradiusandalarangulardivergence hasa vrilliance of10°W/cm®-sr.Horeover|thesingle-mode helium-neon laserismonochromatic. Judged onthe criteria ofbrilliance end resolution, the heliumneon laser rates very well apotential spectrometer light source. Unfortunately, itsrangeoftulesbility isonly.01a t ‘ ! { 5 ‘ Tuneableparametriccookhadmanyproblemsassociated withthem, soitwasnotreally until thediscovery in1966ofthe tuneableorganicdyelaser®thatroadtand laserspectroscopy became apracticality. Solutions oforganic dyeshavebeenshown toexhibit gainoverseveralhundredangstroms,ofcmtto.01fortheheling-neonmixture. Inpartioular, thedye4Methyluabelliferone has#tuning range of17602.3guxtimm Atpresent, ‘organic dyelasers arepumped either byflashlamps, orbyother lasers. Continuous argon andpulsednitrogenlasers,forexample,haveveldeensuccessfully implemented as dyelaserpumps.Tuningofthedyeseeieaccomplished byreplacingone ofthe dye laser cavity mirrors with a rotateable diffraction grating. In thiswayonecangenerateawidelyenehighlybrilliantepectroscopicProbebeamhaving ©mpeotral widthof45ZLandbyusingseveral different dyes,theentire visible spectrum canuesaanned. Animprovement inthererolepepowerofthedyelaserspectrometer isthenextlogical step. Inorder toHeabidetostudy thefinestructure intheabsorption spectraofweaklyspring compounds, chemists wouldfind abroadly tuneable laser spectromqter with aresolution of10mito bequiteausefultool.Suchahighmpccannot,however,beobtained with adiffraction grating alone. AFabry-Perot interferometer must be inserted intothedyelasercavityashowinFig,1(a).Theinterferometer must,ofcourse, beshortenoughsondeonlyoneofitstransmission maxima falls within the dye's gain profile, which profile isdetermined bythe‘characteristios ofthegrating. |therwiss, laser oscillations can cecur atmorethanonewavelength andthepurpose ofhighresolution is defeated. ‘Thisprdesireable situation Wsdepicted inFigure 1(b)where the laser can oscillateattwosmi Ifaninterferometer has6 { i i i | M |Fe aeanie’g (a) Mcurved mirror D aye cell FPFabry-Perot etalon @diffractioneratingH i ~ .j f\.- A A)! LRA > > . BS) (b) 1organic dyegain —pfile without grating 2organic dye gain profile with grating 3tranmiosion peake ofFabry-Perot interferoneter | Figure 1. |! H : mirrorseparation of5mm,thewavetenth spacingbetweenitstransmission peaksis0.6iat6000A.Suchaninterferoneter,then, wouldbeadequate forthefine-tuning ofadyelaser.atypeoftuningsystemdescribed herehasbeeninvestigated bySoffer antiWoFarland} andbyBonch-Bruyevich etal? .t Theinconvenience oftheatovptuningtechnique isthatlongrange continuous tuningrequiresadjustmentsiboththegratingandtheinterfero-meter. For agiven setting ofthe diffraction grating, adjustment ofthe”interferometér tunesthelaseroverain0.6&.If,ontheotherhand, the grating isrotated without adjustmeht ofthe interferometer, laser oscillation occurs only atdisorete steps infrequency; the tuning isnot continuous. OnesolutiontothetuningmopttomistoreplacetheFabry-Perot device with ascanning interfer-ometer which continuously scans back and forthacrossthespectralwiéthofthepiffrection grating.A®thegrating isrotated, the spectral window displayed onanoscilloscope connected to thedetector andthescanning circuit translates through thespectrum, This scheme issketched inFigure 2. i Another approach todyelaser! tuning which dispenses altogether withgratings,interferometers, andevel,cavitymirrorsistheuseof distributed feedback. Whereas the*fgedbhok necessary foroscillation in aconventional laserisprovidedbyonymirrors,thefeedbackina distributed feedback tax (DFB) laser is} aethe mame suggests, distributed along thelength oftheactive medium. qnonescheme®, thedistributed feedback is generated inadye solution}by the interference pattern caused bytwopumping laser beams which areinoident onthedyefromdifferent angles. Byadjusting these angles itis|possible totune thedyelaser inacontinuousfashéénoveralargevalethespectrum.Moreover,the ‘7 | beStKea /, | | |[6 +—.{ oS SG xy | i D | DC dye o¢6llstcresting nterferometer Gdiffractién grating S sample ce/1Ddetector| Ooscilloscope SGsweepsenprator y |. ‘igure2. | | 1 q \ : spectralWidthoftheDFBdyelasericanbemadeassmallas10mA.FAllofthesefactorssuggestthatsnabeverternoe-ene distributed feedback (ITDFB)dyelaserisideallydusteaforhigh¥esolution spectroscopy. iAtpresent,theonlypumping=thathasbeenusedforan ITDFB dye laser isthe frequency-doublea, pulsed ruby laser. Inthis reportthepossibility ofusingthemapanitrogenlaserasanalternative pumping source isinvestigated. Theobvious advantage ofthenitrogen laser isitslowcost;whereasrubyrodsarebaimyexpensive, nitrogen is essentiallyfree.Asecondadvantageheethenitrogenlaseralready operates inthe ultraviolet portion of‘the spectrum where dye pumping is mostefficient, sothereisnoneedseslfrequencydoublinghardwareandits associated problens. Thedisadvantage ofthenitrogen laser isthelackofspatialandspectralcoherenceinofoutput.Asweshallsee,itturns out that this incoherence severely limits the usefulness ofthe pulsed nitrogenlaserasapumpfortheITDFBbyelaser. InthefirstsectionofthispowediscussDFBlasersand inparticular, interference-tuned DFB lasers. The next section deals withthosefactorswhichdeterminetheroawidthoftheITDFBlaser,and thefeasibility ofusingthenitrogeneeasapugpisevaluated. Semmadgy‘testese=Sy Experimental work with anitrogen laser ispresented in thefourthsection.Finally,incacti(5),anexplanation forthelask ofcoherence inthenitrogen laser output isgiven, andasuggestion foran improvedpumpingsystemisput7 | | to | 7 (2)Desoription oftheInterference-Tuhed Distributed-Feedback DyeLaser { |2sTheDistributed FeedbackDyeJasse : op SUTeredCanidboninCulorIndesOfpefeastiog ;! Ifaspatially ‘feriodic varidtion ingain orindex ofrefraction isinducedalongthelengthofamacellcontainingagainmediumsuch~* asanorganic dye solution, itiefound that, when pumped byanappropraate source,thedyeoscillates inverynarfowfrequency bandsandthatthese‘bandsaremuchnarrowerthanthoseouldintheemissions ofadyelaser whichisallowed tosuperadiate. Thebertoais structure induced inthe ayethusprovides frequency-selective feedback sothatcavitymirrors, thesourcelb offeedback inconventional lasers, areentirely dispensedwith,Alaserinwhichfeedbackispeinthisfashioniscalled adistributed feedback (DFB) laser. Imanexperiment carried out‘byH.Kogelnik and¢.V.ShankofBellLaboratories? theindexofrefraltion of@gelatinsolutionof thedyerhodamine66waspermanantly sfotianty modulatedbyaholographic exposuretechniquesothatthespetian[prtogofthemodulationwas0.3jm.Whentheresultant DFBstructure wastransversely pumped with anultraviolet nitrogen laseratacbumydensityofabout10®watts/on?, theayelaseroscillated near6300£vithaspectral linewidth oflese then0.54, thisbeingtheresolution linitoftheirspectrometer. This linewidth istobecomparedwiththe4Ziinewiath, centeredat'5900A, characteristic ofasuperadiant rhodamine 6¢laser without DFBmder ‘thesamepumping conditions. Clearly thedistributed feedback hada strong frequency-selective effect. | . Thewavelengths Xjofthesdaestnainat reésohancesofthe DFBstructure maybeobtained from the[Bragg condition’ inreference to Fig.3, | 's=NC), a eee(2261) i M H . if 1 >~* dyelayer ' ‘ 1s— i Lne) a /on\, t standing wave/ O%) 4 ' Figure 3.Astanding wave.rhifitiing ‘theBraggcondition (1.1)with Nel. n(x) represents the spatial variation ofthe index ofrefraction ofthe dye layer having spatial period s.; Hl i | j i | n| _WherenisfheaverageindexofmohoftheDFBmediumandsis thespatiel period oftheDFBstructurg, TheBragg condition merely statesthatthespatialDPBprtbeanintegralmiltipleof“x.~= theresonantravétengti osmeasuredinithedyeOde).Ifsissufficiently small,thena)j§correspondingto“=onevalueofHwillfallwithin ‘the ‘dye's overall gain profile, sothat only one longitudinal mode can lase,sofa; KogelnikandShankdidfinaevidenceofhigherorder transverse modes intheir DFBriedium resulting fromthewaveguide effect ofperiodicreflectionsatthecowie Fora14jmgelatinthinkness, thespacing ofthese transvqrse modes vasabout 5i.These higherordermodesappeared,however,fswhen,thedyewaspumpedconsiderably beyond its threshold. Just above threshold, the DFB dye laseroutputisacleaneingleline.I./ - 2eTheInterference-Tuning Method| Intheexperiment described qbove, thespatial modulationinducedinthedyewaspermanantaria{dyelaserwasnon~tuneable. Tf,however, thempatial period #wasjsonehow madevariable, tunéability could beachieved. Amethod which allows for adjustment ofs,and henceoftheresonantwavelengthYjissetolsoreee tuning. Fig. 4shows athin dye layer being pumped bytwo ultraviolet plane wave_s ofthe same frequency (). |These plane waves différ in amplitude, phase, and in their angle offincidence upon the dye. The electric fields ofthé waves are polarized inthe z-direction which is out ofthe plane ofpaper inFig 4. THecombined. electric field ofthe . 3A — | | | || 4H 1 ‘Woeplanewavesinsidethedyeis| Eat)=A;eos&+kh.eosom (2.2.1) whereA,istheamplitudeofthei-thofawaveand { an ROR tj= Rew-w 4#, (2.2.2) q wherea4isthek-vector ofthei-thwateinthedye(hence theprime), and$jisthephase. | Theintensity oftheslectronimnetic fieldisgivenby | .BEE)==| | (2.2.3) { . é. 2 / 2 '= LAT cosfl+ALoSQ, if1 Ades (Gf)+eos(GP)&. Ifthisintensity isaveraged overtime‘theresult is, > 4 cs —Wk)=rlA+A,|2AAzcos(ap)|,(2.2.4)1. where| u 4.>. -2B=R-B 4(ROR)A +adands | (2.2.5) Alongthedyecellwherey=0we"| ‘ 1 5| ! a ‘ D-ob=CRix=Rex)%Lag. e+em==(2.26) -1 i According toSnell's Law, i o, . ’ . 1 MSW, =SWE . (2.2.7) i} I wheretheGand©,aretheanglesofinojdenceoftheplanewavesinsideandoutside thedye. Since k’=nk,wefind that, { , ne: , . - k,=R’sme, =|ksme, =Ky(2.2.8) ; Ra=—Ri : > a=—R&SWOE, FRex. Thus,theintensity oftheelectromagnetic fieldalongy=0is,from 1 QAM),| =|\* = . ud=[A+AL+2AA,cox(aB,(—d) |0| 24Qa k(sma esme)x rag. (22.10) ! / j Clearly thereisaperiodic vafiation ontheintensity ofthe [email protected] relationship between the pump intensity and the gain $fthe dye, the interfering plane waves cause aspatial modulation ofthe dye's gain. The spatial period 16 | 1 1 ofthemodulation isfoundfrom | . o8.(99=apd+20 (2.2.18) whichtellsusthat | 2.2612 g= <i “ ()¢Sel* Se.) whereteisthepumpfrequency, \ ep= Qn =|Q07 =, (2.2.13)R w Combining the expression (22.12) for »with (21,1) weobtain the fundamental equation for the wavelengthjof the ITDFB laser, | ra=Aanre. (2.2.14) (Se,+Se.) , H ‘mus, thedyelaser wavelength maybetined byadjusting theangle of indidenceofeitherplanewave.Thissn]emethodofinterference tuning. Forthespecial caseof:@“eGewehave } *Thenotationsin(x)=S,andcos(x)=|willbeusedfrequently. t 1 t EERE "0 | N= (mesce) : (2.2.15) If,inaddition, 4,=Ap=A,(2.2.9) ftakes onthesimple form| .adn«<&cost(Crsme)x +“t. (2.2.16) : 2am ! 2 1 2.3TheResultsofShank,Bjorkholm wtKogelnik. Intheearlypartof1971|interference-tuned distributed— feedback ayeleanerwasimplemented byanSheuk,J.E.Bjorkholm, andH.Kogelnik.© Thedyeused wasa3x1073 Msolution ofrhodamine 60in ethanol.ThepumpingschemeisshownafPig.5,takendirectlyfrom theirmemorandum. The3470{secoadnhrnonic of2pulsedrubylaser, afterbeingpassedthrough acylindricht lens,wassplitintotwonearly equalpartsbyabeamsplitter. Thesehyo‘beamswerethenmadetocrossinside»dyecellbydeflection fromahsustanre planemirrors.Theanglesofincidence ofthetwobeansupontnelayecellwerekeptroughlyequal. Withtherubypumping power justabovelthedyelaserthreshold of13ki,theITDFBdyelaserhadaspectralsinftdth oflessthan10mkendwas tumeable overarange of640i,thecekter oftherange lying at5900 2. Theangular tuning ratewas80T/acgrab withtheincidence angle@centering at‘about50°, | t 1 1 i 1 ' | . | ee e ® e ee * OUTPUT DYE MIRROR a fg ’ /{& OUTPUT TO TT LENSESss—“i~—sSCS aA. 0347 MIRRORNS tH PUMPLIGHT _ BEAM LyLe SPLITTER FIGURE 1 " _. (3)determinants oftheSpédtral Width bfatThterference-Tuned DyeLaser ‘Ththepréceeding“esviesnoetheinterference tuningmethod wefount that the time-avetaged intensity along the x-axis ofthe tno interfering planewavesshowninFig,drs ue=S{RoRaAcrNomafon*ost (2.299) ' Thespatial periodofthegainnoduatipa induced bythisintensity variation inadyemedium’ lyingalongthex-axis wasfoundtobe, so » . (2.2.12) swe, +SWE, For the idealized oase oftwo plane wavbs, the spatial period sis exactly defined; soisthewavelength oftheayelaser since, da=ams. | (2.161) z H | Inapractical interference-tuhed laser theplane waves are Sand replacedwithlaserbeams.Itseems~otoexpectthatthedeviationsofalaserbeamfromatrueplanewavemaycreateaspreadinthespatial i modulationperiod s.Such &spread would! manifest itself asaspectral broadening inthe dye laser radiation, Since weare interested inobtaining @very narrow dye laser emission line fof apectrascopic purposes, itisof great interest tolaiow how the characterjetics ofthe pumping laser beans influence the spectral width ofthe dye Jaser. Thosefactors differentiating 4practical pumping beamfroma plane wavewhich seemtobemost signifi¢ant inproducing aspread ins are(1)spatialdivergence,(2)aanvariation,(3)spatialincoherence,and(4)spectralspread.4pienewave,"course,beinginfiniteinextent, » 1 1 I hasnospatialdivergence, itssovtetaleisthesameeverywhere, gnditsk-veotor isperfectly well-defined bot} indirection andmagnitude (mono- chromatic).Aplanewavethushesnonertheabovementioned "problems." 1.SpatialDivergence LThedyecellemployed inan;PBdyelasermsthavesome finitelength.Ifthepumpingbeamsmareaspatialdivergence, theangles @,and 0,ofFig. 4will vary along the length ofthe cell, and . i thie variation will result in«spectral broadening ofthe dye laser line. | Let usassume, for example, that the pumping beams originate i frompointsourcessymetrically sonwithrespecttothedyecell asshown inFig. Gawhere thelength of|thedyecell ie22. The fractional variation insovertherengthofthecellmaybecalculated: i asfollows. From (Za) wehavere| 1s= 25 } (3.1.2)| where1 | S®=smlec@]+ six[e.)] (3.2.2) |secon! anda(x)anda(x)aretheangles shown jnFig.‘6b.Thefractional variation | t : insis, ' i B82 26 2Sred—Sot (3.1.3) Ss } . ‘ 4|5 Since f(x) hastheform shown inPig. Gé, wemaywrite, | 1 ! al |oe om,*)| °| (Ke,Ye) es] :|eNps ee % (a) oo ||m=—h iand Note —--—SFty “x—— BI LLa® pee LL om |Ses 7 (») l !|. , 1 I! | S@) (0) ah 4;doe | 2 | fo a | | |a. SO)- S(O.Ss EEE (3.1.4) i s | 1 From the geometry ofFig. 5bitisapparent that { te=ae F__.aliiKe=* (3.2.5)z Het+YS|ous)Yer where (xo,Jo) and(-xo,y,) arethecooxdinates ofthepoint pumping sourcesandxis|position alongtheala.Byappropriate powerseries expansions invedoitisassumedonly{thatQisemallcomparedtobothXoandyoitcanbeshownthat |H 2 a M9-SO.Lih- ae] one gS Ne Ly ° | 1 —- weeee aa ib ae —— ' %Pgthefractional apreadin«naslanaxinumvalueof 1:—io: oor eee Re eer,s as ° os=&.. H(3.1.7) moa . Ss née ' If, onthe other had, the point sources lie close tothe x-axis, the fractional spread] takes oniteminimum value, | | 2 as 1, Lo, ia (3.1.8) 8 aAa | IfpointsourcesweresetausedforpumpinganITDKBlaser, 1S typicaldimensions mightbe=1omwohroelmec e104,Ata wavelengthof6000f,aspectralwidth;0.64isimplied. 23. { —_i :i 1 {’ Laser beams liesomewhere inithedomain between plane waves and point sources. Ifalaser source ofbeam divergence %radians were placed at(xos¥)asshowninPig.VY,theofteptive gx.equivalent pointsourcewould liemuch farther awaythan thelasér itself. Theeffective r,in(3.1.9)(=Hwouldbe,| ilHl 1 fo%Ri(288) | Gas) TNA H andthe.fractional spreadinthedyeasherlinewouldbe,[dtmost, 2~ote del4s=ga aoSe | (3.1.10) ASS 1aE T-coe 'f I t Herewehavethefractional spectral width asafunction ofpumpbeam divergence .IfWearebuilding aspeofrometer, thisequation tells usthe maximum diyergenge tolerable foragiveh resolution. Theachievenent of .‘a10m[Penaat6000&requires 'pumpbeamdivergence ofless * heb .e a - =6axBOL%=Reso) =(|:4)x\L9xs0 x2anod. ‘ (3-1611) ! t where weassune thatGisoh I. Thedivergence specification! ofA..mradisnottoodifficult tomeetwithagaussian beamfrom,say,lanargonlaser.Thefarfieldi ate. divergence ofagaussian beamisdetermined by,Pation ofthewavelength totheradius ofthebeam waist, Wo: } | x=a» | (3.1.12) TWWy Bytrensforming anargonbeamwithseal,aWaistradiusof1omgong a. : |‘equivalent pointsource3| ew divergence a | pKA 1pumplaserandoptics :ayeoe NoStL,zQLwse |a | | | | | | | | ely H ne |1 || easilybe~tinwhichcasewewouldhave,1 -8 H a= F80x/0 LI!lols’ wed Bayea i ’ avaluewellseayethe2mradlimit.|Onanadmraddivergencefrom‘asuperadiantmiteaguxlaser suchasthenitrogenlaserissomewhatredifficult, thoughnotimpossible. Assohematised inFig8%theangular divergence ofthesuperadiant bean ofanitrogen laser withaplane mirrorlat oneendisroughly, a=sa | (3.1.23)Typically,Q=1tw=lomsoXemrad. Sinoethesuperadiant nitrgen poseroutput isspadially incoherent, itcannot becollimated into alow divergence bean asispossible with @gaussianbeanitheradiationfromafotntsource.Thisfactisillustratedinmig.be.‘There,thelens[osoceedsimcollimatingtheraysA,B and C,but rayeDand E,which were jparallel inside the laser, haveadivergencews]collimationwhichisbethesameorderasthedivergenceoftheoriginal beam. : Nevertheless, alonger nitrogen laser withasmaller cross section andjustenoughgaintosuperadiaté omaconceivably meetthemrad criterion. However, there are much more ‘ringent conditions onthe.pumpingbeamandthesearediscussedinCnextseotions. , ;| 1 { oie H | mii |irrorimage H actual laserifv_ | w }« w mirror i. || {° ee ae APa ee——————ny|VW 38 () E |Figure8,|| | || | 21. :‘ 2.Amplitude Variation |Forsimplicity, letusassume thatthepumping beams usedto pumptheITDFBadeoraresprerimelytessTheamplitudeofthe electric field atanypoint inagaussian beam is,bydefinition, a gaussian function ofthe distance oftat point from the beam aris. As afurther simplification, letusspprodimate thegaussian function by | thesingle lobe ofacosine function ofappropriate spatial period XQ Thisapproximation iswhowh inFig.9b.* . 1Wemayfates‘thisapproximted amplitudevanjetbenRinto our previous equations byreplacing A,and!ApofEquation! Gan)with\ ' too A,=A(t)=0,008(Ra2) - > RY (36201)?Ar=Ac®)=a,008Oa \ ‘ wheretheRo;pointiin thedirection of{the amplitude variation of i * thei-thbeam.rabagthex-axiswheretheayecellliswehave, Roz | ah=(Rkcose) RK, (3.2.20 ' >Rai =(Rocose) x! | | fet” ‘Theelectric field given bysubstituting these newA;into“(22.9{beybeequaledandtime-averaged Asbefore;,however,itismore \convenienttoomtheintensityoovatiol@29Wirectiy,substituting fortheAy.Theresulting time averagedyintencity oftheinterfering 1 beams isgiven by, after expanding all the cosine products, i \ { 1 . ee ee iN y . NorON BONY | : _ Oe DX]aeona |“ r\ soa (a) | | | | { |k.ar |3 Den 7 | 1Wey . Y | —ee | .<—_—— luge2-3 =>—_Z. | Py(») ee ettonmetion| irectangularvariation Figure9. | | | 1s73 | . | | | us|deeot(hiGe)| +acot(RCo) FEAR Fcos(aferleelCaC)x):+cos(abeke(Co-Ce)x) H |*cos(ab,—Re(Co+Co)x) 4cos@f=ky(G,-Cex) f|(3.2.3) where, from (2.2.10), { =k(SetS |* (3.2.4) aR, *Seu)o¢. ! Theresult showsthattherearefoursifmifioant* spatial modulation components inthedyeallhavingthesheamplitude. Thefourspatial . periodsaregivenbypermting thesienbinthefollowing expression, Ss 24 ¢)a 7 . 3.2.5 , R(SqtSe) +Re(Ce,£Ce.) Thefractionalseparationofthetwoolaseparatedperiodsis ‘ :as=(SAS) «igBe(Ato) 9.2.6ss|R\Se,+Se *Thespatial frequencies (wavenumbers) ofthefirst twoterms aretoo lowtomatter; thedyecouldneverlase]atawavelength theorderofk,.{ 1 3i .! Takingbothanglestobe45°,wearrivhatanexpression forthespectralbroadening ofanITDFBlaserduetoanhituae variations inthepumping beans: ii Aa. as=Gitt.n= Ss |sae 4c. ‘ f InordertoachieveaspectralwidthawtomKst6000Rweneed@valueof)wpgreaterthan ed‘ rw=CZ) 22(and%Di0¢ =6Oom.Withtheuseofcylindricallenses,/variationinthepumpingbeans across thedyecellmaybemadetoloolmichliketherectangular variation showninFig.9b.Theeffeotive Nvofthecosinewhichapproximates this vamiationover thecellmayeasily bemadegreater than60om,soweconclude thatamplitudevariationsofthisnatesthoughimportant,arenotcritical. Thecriterigydisouassed inthenext section, itturne out, is muchforecritical forthenitrogen aderpump.° H i . [ | : i i i. | ; | a | OE 31 | 2sSpatial Incoherence H Spatialincoherencetndanysituationinwhichthereisa lack ofphase correlation between the fields attwo points inspace. One typeofspatial incoherence whichhae|serious broadening effeotonthe spectralwidthoftheITDFBlaserisofmightbecalledk-vectorspread. The problem ofK-vector spread inapump beam isrelated tothe problem of divergence described above, butitisnotthesane‘thing,as willbeshown, Atanypointinaplanewave,the-K-vector isperfectly defined. Thesame#strueinagaussian beam,teateachpointinthebeam is exactly normal tothecurved phasé frodt andtheK-vector spread iszero atthatpoint.Forclarification ofapoint,comparetheEvector spread ofanincoherent source withthatofagaussian beanofidentical geometry asshown inFig-iO.. With thelincoherent source, there isak-vector = aRRGSAAofwin-l(9/0)radians,snarestecoherentsourcehas!sanesoeante|, © *i: |. 1 | i || ; 1 Vy 32 {| ® _--__ae a=0 i oe2 oS i= — ~ —— - h (a) oocherent gaussian beam yak oo ey . (b) incoherent source Figure 10. 3al | \ ' . ‘The effect of ak-vector spread on the ITDFB laser can be estimated with theaidofFig, 11. Each ofthe original beams shown inFig. 4is replaced with two beams ofthe same phase, but half the amplitude ofthe original beam, The kvectors ofthe new, beams are displaced bya’small amount JRfrom thekvectors ofFig. 4.{AsAR—>0, thesituation depicted inPig. 4and described inSection 2.2 isapproached exactly. Asbefore, all ; electric field vectors point along the p-axis, out ofthe plane ofpaper. ‘Tecombined electric field ofthefourbeamsshown’ inFig,T(ayie r > > } ‘ es --+ -E,(it)=A.cos(6)+MR)+Acos(0,- de?)| (3.3.2) 2 =.4Azeos(BrRR)+Aucoslt=ARR), z zm : where 1 | fe=RR-wt'gi. (3.3.2) Algebraic manipulation yields | 2 ~Ea)=-cos(a82))A,cob8,+A,cosh.) (343.3) ‘Theresultanttimeaveragedfield+‘becomes, i { { i ' aw Hl i‘. |4 rae|| 4 ina KO Bra) iBtZe \|msZKrak - _ -5AA}—___§—_———- -x (a) | |i i | ro to| ber Figure14.' | —— ——-dion afa 1Se [~* \ 4 fas | Z z | (») | ‘ ” r.| (3.344) WR)=feAA)“IA)+AA,X | .{Cos(OR)++cos(apr)++clapat}|, | where |* R= Re =RR) A+ag. (3.365) | Theintensity shows three significant lterms. FromPig.aitisevident that, |_Ry=wsinel 1 .Rex=Rsfos (3.3.6)@R),=(@R)sesQa. Thus, evalutated along thex-aris, thdthree significant terms are i ue)=eecascg,+4cor(ehraek,x)+cos(spr2ax)|. ’t (3.3.7) Tpeseparation inthespatialperiodsrthetwospatialsidebandsis AS&Bar(al.Ae (3.3.8) . R*(SejrSe.” andthetotalfraétional spreadinstoons, 1 aS.Mhak|.(3.3.9) : S RX Se+Ser { 1 } Ifwetake both angles tobe45°, theestimate forthespectral witth of de a nee the ITDFB laser line due tok-vector gpread i8 A_4saan! SUK=XSS =! (3.3.90). a Ri 1 whereXistheangleoftheinyweber, spresdshowninFig.8(((8).=>," | Usingthecriterion ef\40wk6BOGA,therequired valuefor -- iisabout 10-6radians. Foré"pure igaussiat beam, asnoted above, the k-vectorspregdiszeroradiansoftisnoproblem.Forasuperadiant nitrogen laser ofthetype stiown inFig, 8andredrawn inFig. 12,10-6 radiansofk-vectorspreadisanextreoety stringent specification. As showninFig.1,thek-vectorspreadbethenitrogenlaseris asMM | (3.3.21) | , :i | assu($) fee] —aWfognase I _ abene | <— D> : | . | igure!2.1ieeveotorspreadof|onelager. ‘ | | | * | whereWisthechannelwidthandDis|¢distancefromthelasertothepointofinterest.Sinceachannelmiofatleast1omisnecessaryto generate sufficient pumpiigpower’inabnitrogen laser,thevalueofDneeded tomeetthe10-6radianrequirdnent isbeimpractical. 10km,Alternatively,casingareasonablevaluefor-Dof3m,fefindthat©is3mradandthe spectral broadening ofthedyelineatoooRis184,onethirdthetotal gain width ofrhodamine 60, 3:4Spectral Width The spectral width ofthe ontput ofgcontinuous single mode laser iszero. Inacavity laser ofthei type that might beused topup an ITDFBlaser,severallongitudinal nodee!oscillateatoncesothelaseremissionconsistsofdiscretefrequencies seperebedbythewell-known spacing0/22.Aoneméterargonionlaser,forexanpib,hasabandwidth ofabout3gizand@longitudinal modespacingof150ns,|thas,therecanbeupto20orsolinesintheargonlaserspectrumevenlysprebaoverthe3glsbandwidth. Thespacingbetweenthefarthestseparatedfronlinesisthus arp (nd)=¥20QHOACRA . z=Ex3{(Hee) - -~asmA | , Gan ThepuleednitrogenTasercthasseveraldiscretecomponents initsemission spectrum, “but fora.wery different reason. Thesuperadiantnitrogenlaseroscillatesofseveralwalanerotationallinesofthenitrogenmolecule, whichlinesspanarangeofAen0.6& Ifomultiline laserisused.asanITDFBlaserpump,wewantto knowtheeffectofthesemultiple1ines|on theoverallspectral widthof theITDPBlaser,Forasimple_letusassumethatthepumping i a laser:has.onlytwolinesofequalamplifude. Thesitugtion isadequately illustrated inFig. 4except that now each."beam" ismade upoftwo plane waves separated infrequency by QAW here aad =Bare =are} %»~rp reOne (3.4.2) The total electric field of ‘the four interfering-plane waves is, asusual, inthez.direction, andHas‘asonalgiven.by —_—_—-— ee - “TT—+ _ --Elie)=$A,sesMP(worad)t| +5A,ws]8,(w-awyt{ ,| (3.4.3, +SALcs[Tap(w+aw)t] eAcori(w-awe] where | i‘—RE BR+K!. ©Gada) H Algebraicmanipulation yeidds | i _Ealat).=cos(awt)|Ayopsut)+A,eos(Yo|. Theintensity ofthefieldis | G45), a aey)|z—uli,s)=£weGou8)|APAL+DAA,X (8)=FGi)yfAe AA (3.446) a $208(4,¥,-2st)cosh %)gI. Ifthe optical portion ofthe intensity istime avaraged, the result is, Yo | . ut)sens&$2A&se.Gehrywhereabisgivenby(3.3.5).‘TheIthen,ofanon=seroDWis atemporalamplitude modulation attebquanoy (2.00)ofthespatial intensity distribution wefound earliér in(2.2.4). Nospread inthe DFBspatial period isproduced. srenkine fixedandisdetermined by (2.2.12). | The periodic spatial patter induced inthedyewill rise and fallasillustrated inFig.13.Astngaverage pumpintensity periodically falle below thedyelasing threshold, |thedyelaser output falls tosero.| Thus,thedye'sradiation isae modulated. Thepercentage of modulation isgreaterthan100%,thefeactamountdependingonthe specificdyethreshold.Ifweassumetthedyelaseris"cutoff"for half the time, then the duration ofajdye laser burst asshom inFig. 13 isgivenby. | |og A=2+ ET=—ey (3+4.8)ZzZaw |2eare wherewemadeuseof(3.4.2), and@fethemodulation period ofthedye output(seeFig.13).Inthecaseoftinenitrogen pump, Geguste|~~Bzprrosernds(36449) 2(Bx10'%)(.6x10"Thisduration,incidentally, isaongitotheopticalperiodof 10715seoandshortcomparedtothenhtrogenpulsedurationof10-8seo. Thefrequencyspreadof*Fpulseimpliedbyt,is, { 4| | Fe=Witt ore). iY 7, i _| | ' |; oy |S > VILL LT272A TLR (LV kT 4Be=)MU:AMMA a <<' |Ss Wire Tle dyelaseroutput ifstructurevariation ' t Figure 15.Correspondence atheamplitude modulated DFBdye structurecagaedtysallinepaapings | 42 \ 4 Aw,¥2ha/320)% |Hence,thefractionalspectralwidth|theITDFBdyelaseremidsiondue toasimplecaseofmultiline Pumping!is1 A= om =Yaw. .__ (364-12) » oa |@a Substituting from(3.4.2) aiidusing therelation —wy=2nd,oe'd xe? we obtain the result 17ray? = =< (3.4.12) --Od4=.Qar(x): Forthemultimodeargonalaserdescribedearlier,aaheand the dye linewidth becomes, e -~ SN= 2hr%_ &SOmA—i “k._,.p7Inthecaseoftheattrogen[taser, thingsaremchworse.Since xp wehave, | ay)=3Pr=SA. 3.4.13) 2 Thenumerical‘factorin(3.4.13);fromtheratioC3)£4andfrom . | theassumption that&=2.Itcannot4,reducedmuch‘below8.Thus,a inorder toachieve ourdesired 10mk dyelaser linewidth, thespectral width ofthe.nitrogen laser mst beheld toabout 1.2i. : i Evenifthenitrogen laser jisrestricted tooscillate ononlyoneofitsrotationallines,itstillfsafinitespectralwidthonaccount ofthe10nsecpulseduration.That“| Ads+=|longle.Cuise, and .s-—Sdp(why =EadGta)[(kAY] =+di)Gand .° - SaH mAs. *(3.4.14) ‘Thus, from thepoint ofview ofsinglediine operation, thenitrogen laser clearsthewirebyafactorofom| | 5Summary ofthe Spectral Broadening/Pactors InSections 3,1through 3.4/the spectral broadening ofthe ITDFB dye laser line was calculated for each offour pathological characteristics ofthepumping beams Usedfortuning. Theresults of thesecalculations maybesummarized dsfollows: _ —- jo.|i —SourceofBroadening | (ya) 1 eat, 1.spatial divergence sseefessseeeesee ASM X 2.amplitude variation....J.cssseeeees WOQAP/AvAR 3.spatial incoherence..+.peeerereeees COSURXD 4.spectral Widtheseeecefeseeeeedee ro'{dre/ de where I A,=angle ofdivergence i Q,=angleofk-vectorfread |Ame effective wavelength ofamplitude variation Ap©pump laser wavelength Be=pumplaserspectra} width andthesymbol"/»"istobeinterprptea asmeaning"isontheorderof.”i 1 : .. po “a | us .| | 3.6Evaluation oftheNitrogen Laser 2Punpihg SourceforInterference ‘Tuned _DyeLaser Spectroscopy | : InfSection(1)itwasaessahathatadesirableresolution foranITDPB laser spectrometer is10mA,since this represents an improvement ofatleastanorderofnefitaaeovertheresolution of conventional spectrometers. Atvisible wavelengths, a10miresolution oanbeachievedifthefractional spectrinspread4\/AoftheITDFBaye ager islees than 2x1075, Atransverse pumped superadtant nitrogen laser ofthetype commercially manufactured byAveo, Carver and other companies has the followingcharacteristics: | dp=BSTIA are#6{| %= 10% nod. . %=10°ned), Aspointed out inSection 3.2, aslong asthe cross-sectional area of the nitrogen beam is larger than the dyecell be aconsiderable margin, orifacylindricallensisusedto“oethebeaminonedirectionso . that the widened’ beam has aneven intensity over the dye cell, the problem of"amplitude variation isnotsignitichnt. Typically, wemaytake Daw=0“| ‘Thus, caloulated values for the four broadening factors are, 1.spatial divergence Ss =UKIO ‘ 2.amplitude variation ayn =6x0? 3.spatial inéoherence wn =txio? 4.spectral width Y= xIo! Mb7 ' : Sinceweareseekingafractionalefofleesthan2x10~®,evenifthe calculations ofSection (3)areoffvytwoorders ofmagnitude; itisclear thatthesuperadiant nitrogen laserodunotbeexpected toyielda10m dyelaserlineintheITDFBschemebedause ofitsoverwhelming failure to meetthe1076criteriononaccountoffenvectorspread,thethirdbroadening factor. Itwill berecalled from Section 3.3that thedyelaser linewidth islikelytobebroadened outtoroughly 18Abytheactionofk-vector spreadalone,Thespectralwidthtactsisalsowideofthemarkbyseveral ordersofmagnitude. ThefirsttwoPhotons,ontheotherhand,donot appear to pose any problem, ‘Asamovetowardsonek-vectorspreadandspectral width of’the nitrogen laser, areasongble approach istotry toreduce the gain.of the nitrogen laser and toput/the laser tube into aresonant cavity. Inthis way, atransition from the superadiant regime tothemore coherent cavity oscillator regime might beachieved. | t 47 | 4)Experimental Nitrogen Laser Reseach i Forpurposesofsnventiasting thepossililityofusingthe nitrogen laser asapumpforanITDFBidye lawer, astpansverse-field .\ “y pulsednitrogenlaserwasal : 1 ‘Bical Desoription of Nitrogen Laser Asketchofthenitrogen leartubeemployed isehownin |Fig.14.Thetwo,electrodes, eachsfinlength,-weremadefrom 1"0.D.polishedbrasstubingandwerepositioned withina2"I.D. | acrylic plastic tube so that the sepatation between the electrodes was 1p". Each electrode wassupported bythree 4"diametér brass studs which | protruded through theacrylic tube ajdwerecemented inplace. Copper sheets were then used tocomnect the $lectrodes via the studs tothe Various discharge circuit components. |Theendsofthesorplibttube xere fittedwith2"diameter circular winddwscutfrom4"thickCoxaing No.7740pyrexglasa.Thesewindowswhremountedperpendicularlytothe | axisofthelasertube.Twogasconnabttons weremadeinthesideof thetubeneartheendstoprovideforaflowofnitrogengas.‘thedischarge circuit consisted ofa30KVDC power supply, twocapacitor banke,andanBO&Goraltriggered sparkgap.AschematicAiagramofthedischargecircuitissheinFig.15.Theinductances . 1shown intheschematic diagran repr¢aent thedistributed inductance of the copper sheets which were used|in place of wires to connect the | discharge cirouit elenénts. Fromtranttission lineodloulations, thevalue | ofLwasfound tobeabout 30nH.Thelinductance ofthespark gapis 20nH. The capacitor banks C,and Cy Were composed ofSprague 30kV | 2500pFceramicunite.Thestatof.thesespecialpurposecapacitors, i | us o naea}cS—_a Zs2 Ne Figure (4.thenitrogen laser.tube. uf .| | ‘ i | ! | ‘ totriggersspett°° i R \(| & ui SG to L30kvDe C=20nF QsSak ()oTsupply | am - 2.200, 0000 000 u|u u i Ldistributea sndudtence Iqsparkgapinductahoe Rcharging resistor! 80spark gap { DYdischarge tube; FigureIS,Dischargeaschematio.‘1 2 Hi RADHAond6w.an T @Aco~soovor 24v.|lowkd|OZ 62K I.||TSQTK 4 Ne-47MW221 é 5mSALSnim2-9 A Wn0R oom v i ' 9.200 2NHIOl 2N497)i -ools AY,292. al oy TY ‘ i it ‘73 Bank's: vet| _*Ize ' TR-ISS | 4GP~\WAE6e | Ese | Pigure|G.Triggercircuiti . 5 | notshownintheschematic,isonAorderof2-4ni. ‘Thesparkgapwes‘ehegerehvyanEG&GTR-153trigger transformer driven by avariable frequency transistorised pulser. Thecompletetriggercircuitisshownwhe16.Itwasfoundthatthe i polarity ofthe voltage pulse triggering the gap was very critical. If theleads:fromthetriggertransformer tothegapwereconnected incorrectly, the gap simply did not’ fire at all. The correct polarity isshow inPig. 16, 2sPerformance Characteristics ‘The 30KVDC power supply eployed was capable ofdelivering amaximum average power of150W.Sihce the energy required tocharge capacitor bank C,for each pulse was a = 3.2~WyeCV=(2OMd Hox Y=1Bjeethemaximumrepetitaonratedwasaetodout8pps. Asmeasured byaCDCReto calorimeter, theenergy contained inedch laser pulse was0.50 #5mJ. Theefficiency ofthelaser, based onthe9JstoredinC,perpulse,“st005%. Thewavelength ofthenitrogen. laser emission isknown to be3371 4with aspectral width ofabput 0.6i.This width, aswasnoted previously, isdue to the fact that phe excited nitrogen gas lases on severalrotational transitions atoasesThedurationofthelaserpulse, asmeasured with anITTFi-114A biplahar photodiode connected toa Techtronix Type 519 dscilloscope, was|found tobe10nseg. The pulse occurred some 80nsec after the voltage across the nitrogen discharge began tobreak dom.The,Jigcharge voltage andlaser pulse ovcillogransareshowninFig17j°Bothtraceshave@timebaseof50nsec/cm andwere triggered bythe voltage rise show in(a), Atriple trace of thelaser pulse at5nsec/om isshown|in FigTe) Since the laser pulse lasttd 10nsec and contained anenergy 9f, 0.50 mJ, theaverage power output $fthe laser during thepulse was — i 2, : (a) Voltage across discharge tube. Vert: 10kV/om, ~ Base: 50nsec/cm. E- ‘ gai Z — - B| fo (b) Laser pulse. Vert: uncalibrated, an: Base: 50nsec/om i F i — —s; (c) Three superposed laserFE pulses. Vert: uncal, ~ Base: 5nsec/om — iF tFigure {]. — if y.] 383 | suo?fa“or =SON x Sinoe theyulse wasapproxingtely sinisoidal inshape, thepeakpower achieved during thepulsewas Hi Pose=HEPoe*78k: Theshapeofthelaserbeatleavingthelaserlasertube vasrectangular, thedimerisions being 1g"x2".Thedivergence ofthe eam inthe longer dimension was meashired tobe1Bmrad.TheoptimumsizeofsoulsbankCp,whichinoursetupcould nitybechangedinincrements of2.5iawasfoundtobe5nF.Theoptimanitrogen pressure was 20torr. Atheoretical upperlimitafthepoweravailablefromthe nitrogen laser at20torrcanbecalculated fromtheassuaption of100% inversion inthedischarge channel, i { . Bape Apdo 1 wheren,isthegasdensity,Vthewilofthechannel,and2thepulse duration. Forthelaser described abové wehave ny=4x10!7/om}, V=75om}, hY=7x10719 J,andQ=1078sec.ninePmax=26[x109W,Sincetheactual powerofthepulsewaé50KW,theaverdeepercentinversion was.025%. 1 | . | | i i 54. . 3.TheCavityExperiment | Inthe conclusion ofSection! (3) itwas pointed out that inorder toobtain thedesired 10nkspectral widthfromanitrogen pumped ITDFB dyelaser,theohargteristics ofthenitrogen beambatty beimproved. The purposeofthecavityexperiment wasteseeifthese“characteristics could beimvpovedbyreducingthegainofopnitrogen laserandbyputtingit into aresonant cavity. .Achoiceofthetypeofsesoatcavitytobeusedwasgoverned byconsideration ofthe volume ofthe Dptical mode that would fit inthe cavity. Toobtain asufficient amount) ofpower output for dye pumping, | @large mode volume isneeded, The diameter ofthe mode should beonthe orderof1cm,sincethislengthisspaofthedimensionsoftheinverted region intlsgap.<c. 4 oan . Ourfirstinclination wastofaneaHemispherical cavitywith &@gaussian beam diameter of1om, Itijmediately became apparent, however,thatsuchadesignwasimpracticalvechee,attheutraviotelwavelengthof3371A,thecalculated radius ofo|vetureforthecurved nirrop-of.the_hemispherical cawity-needed tooktre1ombeamdianiterwas simplytoolarge.Thiscanbedemonetepet asfollows.Thediamterofabeamformedinackemiephenical Pesonant cavityoflengthzandmirrorcurvature Risfen = Ya a)aoa | The condition for cavity stability is simply that Rbe greater than z.For | z=1th,thevalueofRneededtoovteinDelonis, . | |{ cso { | ardReTR26x(lene. =60km... \orz | Ifthewavelength were10pminstead of33714,Rwould comeouttoaround 100mwhichibwithintherealmofprabticality.Essentially,whetthe calculation for-R-teltins isthatthe!onlywayto,getobeandianeter oftheorder of1am&tUVwavelengths! istouseaplane-parallel cavity. Thisiewhatwe‘tried. | Aplane-parallel cavitywasforebya100%reflectorandone ofthreeavailble quartsbeamspittere Thesebeaneplitters, withlow-loss evaporated aluminum surfaces, hadireflectivities at33714of30%, 60%,and95%.Thegainofthentroemtubewasreducedsothattheouput _beam,aobserved byfluorescence rox}@moveable screen,onlyappeared . .whenthesecondmirroroftheplane-parallel cavity, thebeamsplitter, . .wasinplaceandwasperfectlystewed,Severaldifferent‘methodsof reducing the nitrogen gain were tried reductibn ofthe power supply7 voltage; adjustment of the nitrogen pzessure away from its optimum value; the addition ofhelium tothe discharge tube. With all ofthesé tethods, and trying all three bean-splitters, {heeuallest beam divergence that could beobtained wad 5mrad. Ifacolerent mode were forming inthe : cavity, wewould expect its divergencq tobe onthe order of 4o~X=anfa.03mrad.D ES 7 Thefailureofthecavity‘prertaenttoachievealowdivergence nitrogen beamwithitslow—k-vectorspreadcastsdoubtuponthe t a ee i] 7 ab .— - feasibility ofusingasingle-tube nitfogenlaserasapumpforahigh resolution ITDFEdye-lasergpectronetep Apossible explanation ofthelargedivergence obtained inpresented! inthenextsection alongwitha suggestion for improvement. i} : | . | | | “ 1 ! { | | | | | -t { | (5)Gonelusion | i 1.Interpretation of experimental results, ImSection 4.3 wefound thatjthe divergence ofthe ouput beam of 17 #50 omlong hitrogen cavity “laser uas|many times larger than what would be expected fronthediffraction ofacohbrent mode.Itappearsthatthelaserisoperating asamultipées, ope}iallyincoherent sourcecrather thanapacoherentsource.Thatis,byaa2secondplanemirrorandby _,Peduoing thegain, thelaser still behpves in’a superadiant manner but . ~ with »longereffective lengthandcorresponding decreased divergence. te ‘Thesituation isitiustrated inPig.18.Whenthegainofthe nitrogen mediumisreducedbelowacertainvalue,theamplification oftheoe noise generated atpoint Palong the pth A-B-C inFig. 18a, where only one mirror isused, isinsufficieat toproduce asignificant output power, "However, whenmirror2isadded.ag soyainFig.1%b,©longeranplifidation path appears along AUB~C-D‘and the ovbrall gain abong-this=path is sufficient toproduce anoutput ofsevbral kilowatts from the spontaneous noisegenerated atpoint | Tocompare theintensitjes ofthetwobeams depicted inFig. 1%, wemaywrites, | | {By=ooTa ee |ie where Listhelength ofthecavity, aistheexponential gaininintensity, andwehaveassumedthattheeaiusif unsaturated. Aroughestimate forthevalueofQcaitbemadefromanetperinentan resultofD.AyLeonaral71 HeYound that the small-signal (unsathrated) gain ofhic transverse-field nitrogen laser,whtninxas; comparable t)ours,was75db/a.Thatie, [; { { i oemirror1 | ° (a)Atwo-pass path inaone-nirror| superadiant laser, et SST 1. rs 4 a ae A ae mirrox1 |mifror2 (o)Athree-pass pathinatno-mirbor cavity.(Mirror 2ispartiallytrdnemitting.) i || Figure\8.| of a ~10bogEGO=|=75 ary . ae i - and I2¥s| —d=... &S000, a qa, ! eee ve 4 nd . ~ ~theextrapassmakesa,veryceaniaan difference.The obvious suggestion that ‘comes tomind istoreduce the gain ofthenitrogenmedium.stillfurther;thatonlypathswhichhave,say, 50ormore passes will have sufficient{gain to produce kilowatts ofoutput.Thenthedivergence ofthecoilbeamwouldbeimprovedoverthat showninFig.Ifabyafactorof25.jieourexperiment failedtoyield such alarge divergence reduction, wegoncluda that the population inversion ofthenitrogen discharge didnotlast|long enough toallow forduke long multipass amplification paths, ‘The best divergence obtained jwas 5nirad. For acavity oflength 50omandwidth 14£3om,thenumberlof passes implied bythdSdivergence figure is: ase Ww « 3| =12, Laea)to’) The time required for light tomake this number ofpasses through the cavity is. . H dL “ee (oBf v -~@= = 3=QOmsec. _ esof i Theconclusion,then; isthattherepayinversioninthelasertube onlylasts forroughly 20nsec, Thisfiguré isreasonable ontwoaccounts, First,20nseoisthetimescalefor“vevoltage breakdown andcurrent + —'pulae asevidenced bytheogcillograns ofFig. 1].Secondly,thelifetine | oftheupperstateofthe33714sft is40nsec,Oncea' nitrogen molecule ispumped tothe uppér state, itmust be"used" before itsLifetimeexpires. | | _ ee 7 ~ 2eImproving Spatial Coherence Le cats ~ ' Appargntly, according toourfponception ofamplification in we terms ofrays andpasses, thedivergence ofthenitrogen laser beam cannot deimproved bydecreasing thelengtir oftthecavity. Althougha shorter cavity allows formore passes, thegemmetric factor W/L isincreased by thesameamountandthesameoveralldivergence results.Thatis, 1 1 _ Ae = ow wy bat —~.~mh=a+_- . — | ° | Cc Rael 6 | i} H Another,perhapsworeremsonapproachtothequestionof nitrogen laser beam divergence istoask: what isthe divergence ofthe dominantsteadystatemodeoftheosnify,andhowlongdoesittakefor thetmodetobuildup.Thedivergence fasteadystatefieldconfiguration inaplane-parallel cavity islimited only bydiffraction and was shown in Section4.3tobeontheorderof.03rad.‘Thequestion ofthetimeit takesforamodetogrowandsaturatefeemediumwasinvestigated byFox andLi.t°Onegetstheimpression“Ireadingtheirpaperthatittakes roughly 200 single passes for amode tdbuild’ up inawell-aligned plane— parallel cavity ofreasonable dimeneios, aslong astheFresnell number is greaterthan5,Thus,itappearsthatpeertotheconclusion ofthe oversimplified rayanalysis, there ieahadvantage tobegained bya reduction incavity length. Ifitistrue that the inversion inthe nitrogenlaserlestsatleast20nseo,andifobneueisaoufficienttimefor themodalbuildup,adiffraction nessesbeamshouldbeobtainable from @cavityoflength ost.vat- -h= St =Ga}Oio) =Sem. n200 However,thepoweroutputofsuchaoncktnitrogenlaserwouldbemuchtoo lowtopumpanydyes.” | *At this point the reader may bewondering why the ruby pumping laser used byKogelnik and Shank (see Section 2.3) had such ahigh spatial coherence tobe able tomeet the criteria presented inSection 3.One reason isthat highpowerrubylssere oanbefitted intoveryshortcavities. Farnore important, however, isthe fact that the lifetime ofthe upper state of the lasing transition inruby isseveral milliseconds. Once achromium ion is excited, itiswilling towait millibns ofnanoseconds before it adds its quantum ofenergy tothe cavity modp. Secondly, ruby lasere are pumped byflashlamps. The duration ofaflashlpmp pulse isseveral thousand nano- seconds, much longer than the 20nseo phmping period inthe nitrogen discharge. Themodesinarubycavitylaser,meee plentyoftimetobuildup. { ssee . 5.3Proposalforawcsotntetop-tapritile NitrogenPump Wefoundthat,witha3omfeteanitrogenlasershouldbe capable ofproducing aspatially coherent beam. Inorder toobtain both ‘thepowerandthespatialcoherence nafaeaforITDFBdyelaserpumping, ashort 3om nitrogen laser could be ued as an oscillator to drive another nitrogen tubeemployed asanamplifier} Suchaconfiguration isshow in Pig. 19. Aslong asthe smplifier i $Hort eiough sothat itdoes not |superadiats onasingle pasa, theschepe ought toworkwithbothdischarge tubéstriggered atthesametime.Ifairepowerisneeded,onecoulduse alongeramplifier tubsiftrigger defying wereused. Bydelaying the firing ofthe amplifier discharge, the {amplifying population inversion isnotturnedonuntilthecoherentminepulsehashadtimetobuildup andisready todrive theamplifier. | Unfortunately, wehadtimedettner toexperimentally investigate the divergence characteristics ofshort discharge lasers, nor toimplement ‘adual tube apparatus. i) | 1 i | | { & { Il H i mi m2 | 0laseroscillator| A laser amplifier M1 full-reflecting plane mirror M2 partially transmitting plane mirror T triggering circuit ‘TDL trigger delay line | 1 | Figure(|.meOvskttaton-tnon Configuration. H ' ot References Ht } ta,Klein,"Optics"(Wiley,Newrol1970),pe129. 2p.p, Sorokin andJ.R.Lankard, IBMg.|Res. Develop. vol.10,pp.162- 163(1966). | { 3c.¥.Shank, A.Dienes, A.M.Trozzolo, J.A.Myer,Aupl.Phys,Letters, vol.16,pp.405-407 (1970). \ 43.u, Soffer andB.B.McFarland, Appl.{Phys. Letters vol10,pp.266- 267(1967). — Pha.Bonch-Bruyevich, N.N.Kostin,|V.A.Khodovoi, Opt.Spectry. vol.24,pp.547-548 (1968). i ®0.V.Shank, J.B.Bjorkholm, andH.Kogelnik, unpublished menorandum, Ty,KogeinikandC.V.Shank,Appl.rl.Lettersvol.18,pp.152-154 Gen}: 8 1 seeforexample A.Yariv, "Quantum Electronics" (Wiley, NewYork, 1967), . Pp.227. H . 1 9o.n.Leonard,Appl.Phys.Lettersmup-6(1965).10 ; | A.G. Fox and T.Li, IEEE J.Quantum Blectronics, QE-2, pp,774f (1966). | { . i