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DATES COVERED (From - To) New Reprint - 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Cleaved-Coupled Nanowire Lasers W911NF-07-1-0314 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 7D10AI 6. AUTHORS 5d. PROJECT NUMBER Hanwei Gao, Anthony Fu, Sean C. Andrews, Peidong Yang 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAMES AND ADDRESSES 8. PERFORMING ORGANIZATION REPORT NUMBER University of California - Berkeley Sponsored Projects Office 2150 Shattuck Avenue, Suite 300 Berkeley, CA 94704 -5940 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS 10. SPONSOR/MONITOR'S ACRONYM(S) (ES) ARO U.S. Army Research Office 11. SPONSOR/MONITOR'S REPORT P.O. Box 12211 NUMBER(S) Research Triangle Park, NC 27709-2211 53042-EL-DRP.26 12. DISTRIBUTION AVAILIBILITY STATEMENT Approved for public release; distribution is unlimited. 13. SUPPLEMENTARY NOTES The views, opinions and/or findings contained in this report are those of the author(s) and should not contrued as an official Department of the Army position, policy or decision, unless so designated by other documentation. 14. ABSTRACT The miniaturization of optoelectronic devices is essential for the continued success of photonic technologies. Nanowires have been identified as potential building blocks that mimic conventional photonic components such as interconnects, waveguides, and optical cavities at the nanoscale. Semiconductor nanowires with high optical gain offer promising solutions for lasers with small footprints and low power consumption. Although much effort has been directed toward controlling their size, shape, and composition, most nanowire lasers currently suffer from emitting at multiple frequencies simultaneously, arising from the longitudinal modes native to simple Fabry–Pérot 15. SUBJECT TERMS Nano Lasers, uv wavelegnth, nanowire 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 15. NUMBER 19a. NAME OF RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE ABSTRACT OF PAGES Peidong Yang UU UU UU UU 19b. TELEPHONE NUMBER 510-643-1545 Standard Form 298 (Rev 8/98) Prescribed by ANSI Std. Z39.18 Report Title Cleaved-Coupled Nanowire Lasers ABSTRACT The miniaturization of optoelectronic devices is essential for the continued success of photonic technologies. Nanowires have been identified as potential building blocks that mimic conventional photonic components such as interconnects, waveguides, and optical cavities at the nanoscale. Semiconductor nanowires with high optical gain offer promising solutions for lasers with small footprints and low power consumption. Although much effort has been directed toward controlling their size, shape, and composition, most nanowire lasers currently suffer from emitting at multiple frequencies simultaneously, arising from the longitudinal modes native to simple Fabry–Pérot cavities. Cleaved-coupled cavities, two Fabry–Pérot cavities that are axially coupled through an air gap, are a promising architecture to produce single-frequency emission. The miniaturization of this concept, however, imposes a restriction on the dimensions of the intercavity gaps because severe optical losses are incurred when the cross- sectional dimensions of cavities become comparable to the lasing wavelength. Here we theoretically investigate and experimentally demonstrate spectral manipulation of lasing modes by creating cleaved-coupled cavities in gallium nitride (GaN) nanowires. Lasing operation at a single UV wavelength at room temperature was achieved using nanoscale gaps to create the smallest cleaved-coupled cavities to date. Besides the reduced number of lasing modes, the cleaved-coupled nanowires also operate with a lower threshold gain than that of the individual component nanowires. Good agreement was found between the measured lasing spectra and the predicted spectral modes obtained by simulating optical coupling properties. This agreement between theory and experiment presents design principles to rationally control the lasing modes in cleaved-coupled nanowire lasers. REPORT DOCUMENTATION PAGE (SF298) (Continuation Sheet) Continuation for Block 13 ARO Report Number 53042.26-EL-DRP Cleaved-Coupled Nanowire Lasers ... Block 13: Supplementary Note © 2013 . Published in Proceedings National Academy of Sciences, Vol. Ed. 0 110, (3) (2013), (, (3). DoD Components reserve a royalty-free, nonexclusive and irrevocable right to reproduce, publish, or otherwise use the work for Federal purposes, and to authroize others to do so (DODGARS §32.36). The views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy or decision, unless so designated by other documentation. Approved for public release; distribution is unlimited. Cleaved-coupled nanowire lasers HanweiGaoa,b,1,AnthonyFua,b,1,SeanC.Andrewsa,b,andPeidongYanga,b,c,2 DepartmentsofaChemistryandcMaterialsScienceandEngineering,UniversityofCalifornia,Berkeley,CA94720;andbMaterialsSciencesDivision,Lawrence BerkeleyNationalLaboratory,Berkeley,CA94720 EditedbyGeorgeC.Schatz,NorthwesternUniversity,Evanston,IL,andapprovedDecember5,2012(receivedforreviewOctober8,2012) The miniaturization of optoelectronic devices is essential for the axially through an air gap, known as the cleaved-coupled cavity continuedsuccessofphotonictechnologies.Nanowireshavebeen (19–22).Toachievethisgeometryinnanowires,thetwocavities identified as potential building blocks that mimic conventional canbedefinedbycuttingasinglenanowire,whichensuresthatthe photonic components such as interconnects, waveguides, and twocavitiesareaxiallyaligned.Thisapproacheliminatestheneed optical cavities at the nanoscale. Semiconductor nanowires with to position two separate nanowires next to each other with high optical gain offer promising solutions for lasers with small nanoscaleprecision,afeatthatisrequiredbythelateralcoupling footprintsandlowpowerconsumption.Althoughmuchefforthas scheme. However, applying this axial coupling concept to nano- been directed towardcontrollingtheir size, shape,and composi- wires introduces a new complication: the range of gap widths is tion, most nanowire lasers currently suffer from emitting at limitedbecausediffractionlossesatthegapincreasewiththere- multiplefrequenciessimultaneously,arisingfromthelongitudinal ductionofthecavity’scross-sectionaldimensions.Inthiswork,we modesnativetosimpleFabry–Pérotcavities.Cleaved-coupledcav- use design principles derived from finite-element method simu- ities,twoFabry–Pérotcavitiesthatareaxiallycoupledthroughan lations and transfer matrix methods to experimentally demon- airgap,areapromisingarchitecturetoproducesingle-frequency strate single-mode lasing in cleaved-coupled nanowires. The emission. The miniaturization of this concept, however, imposes modelingandopticalmeasurementsshowthatagapwidthsmaller a restriction on the dimensions of the intercavity gaps because thanλ/2isparamountforeffectiveopticalcoupling,whichelimi- AL severeopticallossesareincurredwhenthecross-sectionaldimen- nates the applicability of the rule of λ/2 to cleaved-coupled na- YSICES sions of cavities become comparable to the lasing wavelength. nowires (23). A gap at this scale provides the complementary HC PN Hspeercetrwaelmthaenoipreutliactaiollynionfvleasstiinggatmeoadnedsebxypcerreimateinngtacllleyadveemd-ocnosutpraletde btheeneinfidtsivoidfusianlgcleo-mmpoodneelnatsinnagnaotwailroews.eSruthchrenshanooldscgaaliengthapanscthaantboef PLIEDSCIE cavities in gallium nitride (GaN) nanowires. Lasing operation at defined precisely using readily available fabrication techniques. AP asingleUVwavelengthatroomtemperaturewasachievedusing Because they require no positioning of the nanowires, cleaved- nanoscalegapstocreatethesmallestcleaved-coupledcavitiesto coupled cavities constructed out of single nanowires allow us to date. Besides the reduced number of lasing modes, the cleaved- achievereliableandreproduciblecontrolofthelasingmodes. couplednanowiresalsooperatewithalowerthresholdgainthan thatoftheindividualcomponentnanowires.Goodagreementwas ResultsandDiscussion found between the measured lasing spectra and the predicted Cleaved-couplednanowireswereobtainedbydefiningtheoptical spectralmodesobtainedbysimulatingopticalcouplingproperties. cavitiesonsingle-crystallinegalliumnitride(GaN)nanowiresus- Thisagreementbetweentheoryandexperimentpresentsdesign ingfocusedionbeammilling(FIB;Fig.1AandMethods).Ame- principlestorationallycontrolthelasingmodesincleaved-coupled tallicprotectionlayerwasusedtopreventthedegradationofthe nanowirelasers. luminescent properties of the nanowires during the ion beam milling. Photoluminescence measurements showed negligible As miniaturizedlasersseearapidincreaseinapplicationsfor differencesintheopticalqualityofthenanowiresbeforeandafter digitized communication and signal processing, the mono- fabrication. This fabrication technique provides precise control chromaticityofthelasingoutputbecomesanimportantfigureof overtwocriticalparametersforspectralmanipulationofthelasing merit(1).Laseremissionatmultiplefrequenciescanleadtoboth modes:cavitylengthsandintercavitygapwidths(asnarrowas30 temporalpulsebroadeningandfalsesignalingbecauseofgroup- nm). The smooth-end facets and gap facets obtained from FIB velocitydispersion(2).Theseproblemsareavoidedbycontrolling millingalsocontributetothelowdiffractionlossofthecavities. thelasertooscillateatasinglefrequency.Single-modelasingis MultipleFabry–Pérotmodesareobservedinthelasingspectraof obtainedwhenthespectralspacingbetweenthemodes,thefree theindividualnanowireswithlengthsof3.86μmand5.14μm(Fig. spectralrange,islargerthanthebandwidthoftheopticalgain(3– 1BandMethods).Incontrast,whenthesetwocavitiesarealigned 5). Although they are intriguing miniaturized lasers (6–11), in- axially with a 40-nm intercavity gap, single-frequency lasing is dividual semiconductor nanowires would need to be as short as generated from the 9-μm (4:3) cleaved-coupled nanowire cavity acoupleofmicronstolaseatasingleopticalfrequencybecauseof (Fig. 1B). [The notation x μm (y:z) describes a cleaved-coupled theirrelativelybroadgainprofile(>10nmatroomtemperature) cavitywithatotallengthofxμm,andy:zistheratiobetweenthe (12,13).Withthelowreflectivityoftheendfacets(14),suchshort lengthsofthetwocomponentnanowires.]Inadditiontothere- nanowires are inefficient resonators and may not have a lasing duced number of lasing modes, the lasing transition occurs at thresholdthatcanbereachedwiththelimitedgainofthematerial a lower pump intensity in the cleaved-coupled nanowires (Fig. (15,16);withthisinmind,couplingnanowirecavitiesisaprom- 1C).Therelationshipbetweentheoutputintensityandthepump isingroutetoproducesingle-modeoperation.Previousreportsof intensity was modeled and fitted using a rate equation analysis laterallycouplednanowiresrequiredmicromanipulationtocreate a coupling structure. This form of evanescent wave coupling is highly sensitive to geometric parameters, such as internanowire Authorcontributions:H.G.,A.F.,andP.Y.designedresearch;H.G.,A.F.,andS.C.A.per- distances,lengthsofthecoupledsegments,andperimetersofthe formedresearch;H.G.,A.F.,S.C.A.,andP.Y.wrotethepaper. nanowireloops(17,18).Therelianceonmicromanipulation,with Theauthorsdeclarenoconflictofinterest. itsinnateimprecision,limitsthecontroloverthecouplingprop- ThisarticleisaPNASDirectSubmission. erties,introducessurfacecontaminationthatalterscavitymodes, 1H.G.andA.F.contributedequallytothiswork. and restrictsthe miniaturization of the overall dimensionof the 2Towhomcorrespondenceshouldbeaddressed.E-mail:[email protected]. devices.Analternativephotonicarchitecturetoincreasethefree Thisarticlecontainssupportinginformationonlineatwww.pnas.org/lookup/suppl/doi:10. spectralrangeistheradiativecouplingoftwoFabry–Pérotcavities 1073/pnas.1217335110/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1217335110 PNAS | January15,2013 | vol.110 | no.3 | 865–869 Fig.1. Single-frequencylasingin9-μm(4:3)cleaved-couplednanowires.(A)SEMimagesshowingtheaxiallycoupledGaNnanowiresonaSisubstrate with250-nm–thickthermaloxide.Thetwo-componentnanowiresare∼100nminradiusandcoupledviaanintercavitygap∼40nmwide.(B)Single- wavelengthlasingisobservedfromthecoupledcavity(blueline),andeachcomponentnanowirelasesatmultiplewavelengthswhentheyareseparated. (C)Clearlasingtransitionscanbeseenfromthepower-dependentmeasurements.Thepumpintensityandtheoutputintensityarebothnormalizedto thevaluesatthethresholdofthecleaved-couplednanowires.Thedashedlineswerefittedusingarateequationanalysis(SIAppendix,sectionS11).(D) Outputspectra ofthecleaved-couplednanowires show cleansingle-wavelengthlasing at differentexcitation intensitiescorrespondingtothe open diamondsinC. (SIAppendix).Thereductioninthelasingthresholdbytheaddi- excitationintensities(21),possiblyduetoband-gaprenormaliza- tion of active material is pronounced because the suboptimal tion(24,25). reflectivity of the nanowires’ end facets makes them inherently In macroscopiccleaved-coupledcavitylasers,largeintercavity inefficientresonators.Thesetwoadvantagescannotbeachieved gapwidthscanbeusedforeffectivecoupling.Atacertainwave- simultaneously in single Fabry–Pérot nanowire cavities or using length,thetransmittanceTandthereflectanceRattheintercavity somepreviouslyreportednanowirecouplingschemes(18)where gapvaryperiodicallywiththegapwidthasexpectedinaFabry– alargerfree-spectralrangeisaccompaniedbyahigherthreshold Pérotcavitywithinfinitecross-sectionaldimensions(SIAppendix). gain. The cleaved-coupled nanowires exhibit stable single-mode The coupling strength, quantified by the coupling constant T/R, operation over a large range of pump intensities (Fig. 1D). At repeatsasthegapwidthischangedbymultiplesofλ/2,whichis pump intensities far above the lasing threshold, a small satellite known as the rule of λ/2 (23). Therefore, traditional cleaved- peak appears at a longer wavelength. Such mode-hopping is coupledcavities,whicharemadeofsubmillimeter-scalecrystals, usually observed when the gain profile red-shifts under high can be fabricated with micrometer-scale gaps (26, 27). This 866 | www.pnas.org/cgi/doi/10.1073/pnas.1217335110 Gaoetal. geometrictolerancecannotbeappliedtocleaved-couplednano- and5.14-μmcavitiesappearwhenthegapisexpandedto∼300nm wirelaserswithcross-sectionscomparabletothelasingwavelength (Fig.3,Left,greenline).Fromthesimulatedresults(Fig.2),the becausethefinitecross-sectionsofthecavitiesinduceseveredif- transmittancethrougha300-nmgapismuchsmallerthanthere- fractionlossesattheintercavitygaps.Usingfinite-elementmeth- flectance, and the optical loss reaches saturation; therefore, the ods (COMSOL 4.2 software), the optical properties of the gaps couplingbetweenthenanowiresbecomesweakenoughthateach betweennanowireswerecalculatedfrom3D,full-wavesimulations component nanowire behaves as an independent lasing cavity. (SIAppendix).Atafixedwavelengthof370nm,thetransmittance Theseresultsfurtherconfirmthedesignprinciplesobtainedfrom throughthegapdecreasesmonotonicallywithanincreaseingap thesimulations.Althoughopticallosscanbeneglectedinthede- width (Fig. 2A); consequently, the periodic behavior of the cou- signofmacroscalecleaved-coupledcavitylasers,theimportanceof pling constant is highly damped, and significant optical loss is thisphenomenonemergesduringminiaturizationofthecleaved- observed(Fig.2B).Boththecouplingconstantandtheopticalloss coupledcavitytodimensionscomparabletothewavelength;itis are key factors for the effectiveness of a gap in coupling the the key parameter that dictatesthe designofnanoscale cleaved- nanowirecavities.Whenthegapwidthismuchsmallerthanthe coupledcavities.Amoredetaileddiscussionontherelevantthe- operating wavelength (e.g., 20 nm), the coupling constant is so oretical analysis of the effect of gap widths on the threshold largethatthephysicalgapbecomesopticallyinvisible.Asthegap modulationcanbefoundinSIAppendix. widens,theintensityofthefieldscatteredbythegaptotheoutside Thespectralmodulationofmodesobservedincleaved-coupled ofthenanowirewaveguidesincreasesinthesimulatedfieldmaps nanowire lasers can be predicted using transfer matrix methods. (Fig. 2C), which corresponds to a dramatic increase in optical AlthoughtheVerniereffectprovidesanintuitiveexplanationfor lossesatwidergaps.Whenthegapwidthisfurtherincreasedbe- the mode modulation, it does not account for the phase of the yond300nm,thecouplingconstantapproacheszeroandtheop- coupledmodes.Modeswithwavelengthssharedbytheuncoupled ticallossstabilizesatabout0.8,indicatingthatthetwonanowire componentnanowiresmaynotnecessarilylasewhenthenanowires cavities are optically decoupled. To maintain effective coupling, arecoupledbecauseofthephasedelayofTrelativetoRatthegap thegapwidthbetweenaxiallycouplednanowiresneedstobe∼30– (SIAppendix).Amorerigorousanalysiscanbedoneusingtransfer L A 1ca0n0bnemo,bwthaeinreedl.owopticallossandamoderatecouplingconstant mtharetrsihxolmdegtahiond(sSItoApppreenddicixt)t(h2e8)n.eTwhismaondaelystiacanldmtohdeeirlmreaskpeesctuivsee HYSICCES PN witEhxvpaerryiminegngtaapl wmidetahssurceomnfiernmtsthoenprceledaicvteido-ncsofurpolmedsimnaunlaotwioirness. soifmthuelaotipotnicsa.lTphreopcearltcieuslaotbedtaieniegdenfvroamluetshefofirn9it-eμ-mele(m4:e3n)tcmouetphloedd PLIEDSCIE Though 9-μm (4:3) coupled nanowires with a 60-nm gap can nanowireswitha40-nmgapshowsignificantmodulationofthe AP producesingle-frequencylasing,multimodeoperationisobserved threshold gain among different lasing modes (Fig. 4, blue dia- when the gap width was increased to 150 nm (Fig. 3, Left, red monds).WithinthebandwidthoftheGaNgainprofile,onlyone line).Althoughthestrengthofthemodesuppressionisreduced, modewiththelowestthresholdgainisoutstanding.Incontrast, spectralmodulationofthemodeintensitiesisstillobservablewith modes predicted for single nanowires have nearly equal thresh- a 150-nm gap, which is in contrast to the well-defined lasing oldgain,andmultiplemodesareexpectedintheirlasingoutput. modes from traditional Fabry–Pérot cavities. Additional peaks Besides single-mode operation, the calculation also predicts correspondingtotheFabry–Pérotmodesoftheindividual3.86-μm the relationship between the lasing thresholds of the coupled Fig.2. Opticalpropertiesofintercavitygapsdependupongeometricfactors.(AandB)Numericallysimulatedopticalpropertiesofthegapbetween100-nm radiusGaNnanowireswithtriangularcross-sectionsonglasssubstratesatthewavelengthof370nm.(C)Simulatedelectricfieldmapswithgapwidthsof20, 100,150, and200 nm.TheTM00guidedmodewasinjectedfromthe topedge oftheimages. Thewhite dashedlines indicatethe boundariesof the nanowires.Significantdiffractionlosscanbeseenatgapwidthslargerthan100nm. Gaoetal. PNAS | January15,2013 | vol.110 | no.3 | 867 Ourworkoffersapromisingandpracticalroutetoimprovethe qualityoflasingfromsemiconductornanowires.Alongwithsim- ple geometric designs and precise fabrication techniques, the agreement between the theoretical predictions and the experi- mentalobservationsallowsrationaldesignofthecleaved-coupled cavities in nanowires. Though single-frequency lasing is demon- stratedhereinGaNnanowires,theprinciplesforselectingmodes using thisarchitecture shouldnot be restrictedto a specific material,operatingwavelength,orpumpingscheme.Theideaofaxial coupling can also be extended to cleaved-coupled cavities con- taining more than two nanowires to achieve more complicated modulation of the lasing modes (29). Although the wavelength- scale cross-sectional dimensions of nanowires induce severe op- ticallossesatintercavitygaps,ourtheoreticalanalysispredictsa rangeofgapwidthsthatcanproducesingle-modeoperationand can be reliably achieved using available nanofabrication techniques. Though focused ion beam milling was used in this work, there should be no fundamental limitations with using other lithographical techniques with comparable spatial resolution to create the cleaved-coupled cavity structures in nanowires. The cleaved-couplednanowire lasersdemonstrated here are suitable Fig.3. Lasingspectrafrom9-μm(4:3)couplednanowireswithdifferentgap for miniaturization, highly reproducible by using theoretically widths. Though single-mode operation is observed with the 60-nm gap, predicted design principles, and can be integrated into lithogra- aless-effectivethresholdmodulationwitha150-nmgapresultsinmultiple phy-basedsemiconductorprocessing.Thehighlymonochromatic lasingmodes.Foraverywideintercavitygap(300nm),thelasingspectrum lightfromcleaved-couplednanowirelasersisanticipatedtopro- containsthemodesofbothcomponentnanowires,whichareindicatedby videultracompactphotonsourcesforlaser-basedremotesensing, theGaussianpeakfittingshowninthegraycurves.(Right)Corresponding opticaldatastorage,andlong-distanceopticalcommunication. SEMimagesofthegaps. Methods nanowires and the component nanowires. For the modes of Growth of GaN Nanowires and Fabrication of Cleaved-Coupled Nanowire Lasers.GaNnanowiresweresynthesizedusingnickel-catalyzedchemicalva- cleaved-coupledcavities,bothcomponentnanowiresprovidethe portransportonc-planesapphiresubstratesinahot-wallfurnace(8).The optical gain; therefore, the modal gain required for cleaved- furnacewasheldat1,030–1,050°CtofacilitatethereactionbetweenNH3gas coupled nanowires to reach lasing transitions is expected to be andgalliummetal(99.9995%metalsbasis;SigmaAldrich).Usingamicroma- lowerthanthatforeachindividualnanowire(Fig.4,redsquares nipulator,singleGaNnanowiresweretransferredontosiliconsubstrateswith and green triangles). The calculated threshold gain agrees with a250-nm–thickthermaloxidelayer.A100-nmmetalprotectionlayerwas the experimental results(Fig. 1C)and confirmsthetwo benefits then deposited on the samples by sputtering tungsten for 30 s with the (i.e., lower threshold and fewer lasing modes) of the cleaved- shutterclosed(forthepurposeofcleaningthesputteringtarget),followed couplednanowirelasers.Moreover,witha40-nmgapwidth,the by5minwiththeshutteropenedat200WDCina9-mtorrArenvironment. Protectednanowiresweremilledusingafocusedionbeam(FEIStata235 threshold of the outstanding mode of the coupled cavities is slightlylargerthanthethresholdofa9-μmsinglenanowire(Fig. DualBeamFIB),whichdefinedthedimensionsofthecoupledcavitieswith gapsasnarrowas30nm.NanowiresweremilledusingaGabeamcurrentof 4, gray circles). This small difference further highlights the im- 10pA,andthemillingtimesforindividual1-μm-longcutsvariedbetween1 portanceofmaintaininganarrowgapforminimizingdiffraction lossessuchthatsingle-wavelengthoperationincouplednanowires doesnotsacrificetheopticalefficiencyofthelaserresonator. The analytical model for mode calculations allows rational designofcleaved-couplednanowiresfortheselectionofdesirable modes. Integer or fractional ratios between the lengths of the component nanowires make a significant difference in the free spectral range of the coupled nanowires. Following the Vernier effect,couplednanowires with integerratios would producethe free spectral range of the shorter nanowire. The lasing spectra confirmthat9-μm(1:1)and9-μm(2:1)couplednanowiresshow amodulationinthethresholdgainthatfollowstheresonancesin the shorter cavities (Fig. 5). In the cases where the depth of threshold modulation between neighboring modes is not large enough,satellitepeaksappearedbetweenneighboringfavorable modes,whichfurtherreducethemodespacingandincreasethe number of modes in the lasing spectra (SI Appendix). Alterna- tively, fractional ratios lead to a modulation in the threshold gain at low-frequency spectral periodicities by a beating effect (SI Appendix). Such mode modulation can result in one favor- ablemodethathasathresholdgainlowerthanallothermodes Fig. 4. Lasing modes calculated based on transfer matrix methods. A within the spectral window of the gain profile; therefore, a smallerabsolutevaluealongtheyaxisindicatesalowerlasingthreshold.A spectrallymodulatedthresholdcanbeseenforthecleaved-couplednano- fractional ratio between the lengths of the component nano- wirewitha40-nmgap,whereassinglecavitiesexhibitflatthresholdprofiles. wires is critical for achieving single-frequency operation in The spectral range shaded in purple represents the nominal optical gain cleaved-coupled nanowire lasers. regioninGaN. 868 | www.pnas.org/cgi/doi/10.1073/pnas.1217335110 Gaoetal. Fig.5. Measuredlasingspectraandcalculatedmodesofcleaved-couplednanowireswithintegerratiosbetweenthelengthsofthecomponentnanowires. Goodagreementisfoundbetweentheexperimentallasingspectra(bluelines)andtheoreticalpredictions(bluediamonds)forboth(A)9-μm(1:1)and(B) 9-μm(2:1)couplednanowires.Thefreespectralrangesofthesecouplednanowirescoincidewiththoseoftheshortercomponentnanowires(redsquares). and2s,subjecttothefocusingconditions.Thedwelltimeandpercentage ME600opticalmicroscope)androutedviaabundledopticalfibertoaUV- overlapforeverycutwas1μsand99%,respectively.Formaximumpositional visible spectroscopy spectrometer (Princeton Instruments/Acton) equipped L A aimccaugreacwyaosfrtehceormdeildlinagtlainsecawnitshpereedspeocft0t.o3tshbeenfoarneowcuitrse,waerseingmleadGea.Fioonl- cwhiathrgae-1co,2u0p0l-egdrodoevvei/cme.mThgeractionmgpbalraizsoendaotf3th00enlamsinagndpraoplieqrutiidesNb2e-ctowoeleedn HYSICCES lowingmilling,theprotectionlayerwasremovedwithhydrogenperoxide PN (30% w/w; Sigma Aldrich) at 80 °C for 7–10 min and then washed with cuosiunpgletdheamndicsrionmglaennipaunlaotwoirretosisnepFaigra.t1ewthaescmoaudpelewdinthantohweisraems.edeviceby LIEDSCIE deionized water. The micromanipulator was then used to remove excess P P nanowirepieces,leavingbehindthecompletedcleaved-couplednanowires. A ACKNOWLEDGMENTS.WethankDr.JoelHenzieforhelpscanningelectron microscope imaging, and Sarah Brittman for useful discussions during MeasurementsofLasingSpectra.Opticalmeasurementswereperformedusing preparation of the manuscript. The simulation part of this work was the frequency-quadrupled 266-nm output from a Nd:YAG laser (Spectra supported by the Defense Advanced Research Planning Agency, and the Physics;8-nspulsewidth,10-Hzrepetitionrate).Usinganirisdiaphragmand experimentalpartwassupportedbytheDepartmentofEnergy.Thiswork afocusinglens,a200-μmGaussianbeamspotwasobtainedandusedtoexcite madeuseoftheimagingandthenanofabricationfacilitiesintheMolecular individualdevicesuniformly.Theoutputpoweroftheexcitationsourcewas Foundry and the National Center for Electron Microscopy at Lawrence adjustedusingaQ-switchandmonitoredwithanexternalenergymeterand Berkeley National Laboratory, the fabrication tools in the Marvell Nano- aphotodetector(Newport818J-09).Emissionfromnanowireswascollected fabrication Laboratory, and the computing clusters in the Molecular with a dark-field microscope objective (Nikon 50×, N.A. 0.55, in a Nikon GraphicsandComputationFacilityattheUniversityofCalifornia,Berkeley. 1. 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