AFRL-RY-WP-TP-2013-0028 GAIN COUPLING VECSELs (POSTPRINT) Robert Bedford Optoelectronic Technology Branch Aerospace Components & Subsystems Division Chris Hessenius, Jerome Moloney, and Mahmoud Fallahi Univerity of Arizona Nathan Terry United States Air Force Academy JANUARY 2013 Interim Approved for public release; distribution unlimited. See additional restrictions described on inside pages ©2011 SPIE STINFO COPY AIR FORCE RESEARCH LABORATORY SENSORS DIRECTORATE WRIGHT-PATTERSON AIR FORCE BASE, OH 45433-7304 AIR FORCE MATERIEL COMMAND UNITED STATES AIR FORCE Form Approved REPORT DOCUMENTATION PAGE OMB No. 0704-0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YY) 2. REPORT TYPE 3. DATES COVERED (From - To) January 2013 Technical Paper 1 October 2009 – 11 January 2011 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER GAIN COUPLING VECSELs (POSTPRINT) In-house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62204F 6. AUTHOR(S) 5d. PROJECT NUMBER Robert Bedford (AFRL/RYDH) 2002 Chris Hessenius, Jerome Moloney, and Mahmoud Fallahi (University of Arizona) 5e. TASK NUMBER Nathan Terry (United States Air Force Academy) IH 5f. WORK UNIT NUMBER Y053 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Optoelectronic Technology Branch Aerospace Components & Subsystems Division University of Arizona AFRL-RY-WP-TP-2013-0028 Air Force Research Laboratory, Sensors Directorate United States Air Force Academy Wright-Patterson Air Force Base, OH 45433-7320 Air Force Materiel Command, United States Air Force 9. SPONSORING/MONITORING AGENCY NAME(S) AND 10. SPONSORING/MONITORING ADDRESS(ES) AGENCY ACRONYM(S) Air Force Office of Scientific Air Force Research Laboratory Research AFOSR AFRL/RYDH Sensors Directorate 875 North Randolph Street, Suite 11. SPONSORING/MONITORING Wright-Patterson Air Force Base, OH 45433-7320 325, Room 3112 AGENCY REPORT NUMBER(S) Air Force Materiel Command Arlington, VA 22203-1768 AFRL-RY-WP-TP-2013-0028 United States Air Force 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited. 13. SUPPLEMENTARY NOTES Journal article published in Proc. SPIE 7945, 794508-1-9, 2011. ©2011 SPIE. The U.S. Government is joint author of the work and has the right to use, modify, reproduce, release, perform, display or disclose the work. PAO Case Number 88ABW-2012-6713, Clearance Date 28 December 2012. Report contains color. 14. ABSTRACT Vertical external cavity surface emitting lasers (VECSELs) provide a flexible platform in order to explore curious laser designs and systems as their high-power, high-brightness make them attractive for many applications, and their flexibility eases this exploration. In considering the methods of coupling VECSELs as well as their potential uses, we begin by reporting on the development of a gain coupled VECSEL for use in optical switching. In particular, two VECSEL cavities share a common gain region; the competition for a common set of carriers dictate how these cavities interact. The easiest manifestation to realize gain coupling is to utilize a linear cavity as well as a v-cavity, built around a single half-VCSEL chip. The cavity gain/loss of each cavity can be controlled independently through use of birefringent filters, allowing us to explore the design space, which can be divided up into coarse behavior, easy to analyze through comparing the two uncoupled lasers, and a fine behavior, where one cavity will affect the other and each cavity can laser simultaneously, sometimes at dramatically different wavelengths. These two regions may be explained with simple rate equations, and it will be shown that if prepared properly, spontaneous emission plays a large role in balancing out the two laser cavities within the fine regime, while may be completely neglected in the coarse regime. 15. SUBJECT TERMS Semiconductor, lasers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON (Monitor) OF ABSTRACT: OF PAGES a. REPORT b. ABSTRACT c. THIS PAGE Robert Bedford Unclassified Unclassified Unclassified SAR 12 19b. TELEPHONE NUMBER (Include Area Code) N/A Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39-18 Gain coupling VECSELs Robert G. Bedforda, Chris Hesseniusc, Nathan Terryb, Jerome Moloneyc, and Mahmoud Fallahic aAir Force Research Laboratory, Wright-Patterson Air Force Base, Ohio bDepartment of Physics, United States Air Force Academy, Colorado cCollege of Optical Sciences, University of Arizona, Tucson, Arizona ABSTRACT Vertical external cavity surface emitting lasers (VECSELs) provide a laser design platform in order to explore a variety of systems, and their flexibility eases this exploration. Moreover, their high-brightness operation makes them attractive for many applications. In considering the methods of coupling VECSELs as well as their potential uses, we begin by reporting on the development of a gain coupled VECSEL for use in optical switching. In particular, two VECSEL cavities share a common gain region; the competition for a common set of carriers dictate how these cavities interact. The easiest manifestation to realize gain coupling is to utilize a linear cavity as well as a v-cavity, built around a single half-vertical cavity surface-emitting laser (VCSEL) chip. The cavity gain/loss of each cavity can be controlled independently through use of birefringent filters, allowing us to explore the design space, which can be divided up into coarse behavior, easy to analyze through comparing the two uncoupled lasers, and a fine behavior, where one cavity will affect the other and each cavity can lase simultaneously, sometimes at dramatically different wavelengths. These two regions may be explained with simple rate equations, and it will be shown that if prepared properly, spontaneous emission plays a large role in balancing the two laser cavities within the fine regime, while may be completely neglected in the coarse regime. 1. INTRODUCTION Manyoftoday’sapplicationsrequirehigh-brightnesslightsourcesinordertoimprovepowerconsumption,obtain longerrangeandhigherspatialresolutionforremotesensing. Smaller,moreenvironmentallyrobustsourcesare required for laser radar applications to maintain portability and/or be able to handle adverse environments (aircrafts,forexample). Thehighgainsreadilyachievedbysemiconductormaterialsmakethemanattractive The ability to integrate additional functionality to existing laser technology provides a potential advantage because such a laser platform may satisfy multiple applications, or be utilized durring “off-times” in another capacity. High brightness semiconductor lasers with wavelength switching capability are of great interest in a range of applications including free-space wavelength-multiplexed optical communication. Optically-pumped vertical external cavity surface emitting lasers (VECSEL) have proven to be very reliable in achieving multi- watt high brightness emission in a linear or v-cavity configuration.1–3 The insertion of a birefringent filter in a VECSELcavityallowsnarrowlinewidth,widelytunableemission.2,4 The“open-cavity”natureoftheVECSEL alsoallowsadditionalnon-linearelementstobeincorporated,suchassemiconductorsaturableabsorbermirrors (SESAMs),5 or nonlinear crystals for wavelength conversion.6 In this paper we report for the first time gain coupling, switching, and dual wavelength operation in VECSELs by combining a linear-cavity and a v-cavity VECSEL sharing the same gain region. We present unique behaviors such as high-power optical switching and tunabledual-wavelengthemission. Experimentalresultsand supportingmodelingresultsarereported. This manuscript is laid out in the following manner. We first introduce a generic understanding of an arbitrarysystemofVECSELsinSection2,whereinitispossibletocouplemultipleopticalcavitiesandmultiple chips,alloperatinginconcert. Section3addressesthemostbasiccomponentofthegenericsystem: twooptical cavities sharing a single gain, with only gain (and not photons) coupling the two cavities. We analyze specific regimes of this system operation. We first identify the “coarse” regime in Section 3.1 where the operation may be adequately predicted through analysis of the uncoupled laser cavities, and where we can change the system Furtherauthorinformation(RGB):e-mail: [email protected] Vertical External Cavity Surface Emitting Lasers (VECSELs), edited by Ursula Keller, Proc. of SPIE Vol. 7919, 791906 · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.873864 Proc. of SPIE Vol. 7919 791906-1 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited. suchthatoneofthecavitieslases,andtheothermaintainszerooutput. Wefollowthiswithslightlymorerigor in Section 3.2, identifying a unique behavior near where the two cavities have similar thresholds, which allows simultaneous lasing utilizing the same gain medium, even at vastly different wavelengths. In Section 3.3 we explorehowthecavitylasingswitchingoccurs,andtheoretically,howwemaymodifyandcontroltheswitching dynamics. Finally, we summarize our conclusions concerning this first step in VECSEL system dynamics in Section4. 2. GENERIC VECSEL SYSTEMS DuetotheaforementionedopennatureoftheVECSELsystem,itispossibletocombinegainchipsinmuchthe same way one may add a nonlinear wavelength conversion filter or a SESAM. More peculiarly, it is possible to combine multiple laser cavities, only coupled through the gain material. In principal, we may expand the laser cavitytoasystemofopticalcavitiesandgainelements,whichmaynaturallyleadtonewbehavior. Inthe“slow” regime(time-scalesmuchlongerthanthephotonlifetime),wechosetoignorealltermsrelativetoN andarrive b atageneralizeI gain-element,J cavitysetofcoupledordinarydifferentialequations: d Ω N (cid:2)J Γ(j) N = w P − i −v g i S(j) (1) dt i (¯hωpVw) i τi g ij=1Γ˜(ij) dS(j) = −S(j) +v S(j)(cid:2)I Γ(j)g (2) dt τ(j) g i i p i=1 In these equations, N is the carrier density in chip i, and S(j) is the photon density in optical cavity j. i Ω /(¯hω V ) is the number of carriers produced per unit power, and we have assumed this is the same for w p w all chips. The carrier lifetime of the ith chip is given by τ∗, while the photon lifetime is τ(j) for the jth cavity i p in the system. The gain for each chip is g, the group velocity is v . The mode/gain overlap of cavity j with i g gainchipiisgivenbyΓ(j). Finally,theratioofoverlapsinEquation1accountsforchipsthatmayseemultiple i passesinacavityaswellasthecontributionofeachchip’sRPGenhancement. In this case, we can imagine one VECSEL cavity being the nonlinear element within another VECSEL cavity, and the nonlinearities between these two can potentially provide a rich capability that, as yet, remains predominantlyunexplored. 3. GAIN-COUPLING CAVITIES: 2 CAVITIES, 1 GAIN Equations 1and 2lend themselves toexceedingly complicated systems, and it becomes advantageous tounder- stand the building blocks of the VECSEL system. The simplest case, containing a single chip and two cavities, ispicturedschematicallyinFigure1a. Inthiscase,Equations1and2becomeasetofthreecoupledequations: (cid:4) (cid:5) ddtN = P(cid:3)− Nτ −g(cid:3) Γr1S(1)+2Γr2S(2) (3) d S(1) S(1) = − +g(cid:3)Γ(1)S(1) (4) dt τ(1) p d S(2) S(2) = − +g(cid:3)Γ(2)S(2). (5) dt τ(2) p WehaveintroducedP(cid:3) andg(cid:3),tosimplifynotation,equivalenttoΩ /¯hω V andv ,respectively,Inthescenario w p w g describedbyEquations3-5,thereareonlythreeregimesthatonemayfindthemselves: ∗Typically, carrier lifetime is separated into the constituent effects of non-radiative, spontaneous, and Auger effects, whereτi−1≡Ai+BiNi+CiNi2 Proc. of SPIE Vol. 7919 791906-2 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited. cavity 1 linear cavity N(p 1 )(t) “V” cavity S( 1 )(t) tuning filter cavity 2 NN(( 22 ))((tt)) S( 2 )(t) bp N (t) N (t) 1 1 g (t) g (t) 11 1 N(w 1 )(t) double-pass P (1 )(t) “phantom gain” g( 1 )(t) gain chip a) b) Figure1.a)Physicalset-upoftwo-cavitysystem,showingtwocavityfilters. b)Canonicalschematicofcoupledlasers. (cid:4) (cid:5) (cid:4) (cid:5) −1 −1 Below threshold: g(cid:3)< Γ(1)τ(1) andg(cid:3)< Γ(2)τ(2) representaparticularlyuninterestingregime. Both p p S(1) andS(2) tendtowardzero. (cid:4) (cid:5) (cid:4) (cid:5) −1 −1 Cavity 1 above threshold: If Γ(1)τ(1) < Γ(2)τ(2) , then at the point the material gain reaches the p p (cid:4) (cid:5) −1 lossofcavity1,itclampssuchthatg(cid:3)= Γ(1)τ(1) . AtpumppowersabovethispointtheS(1) increases p monotonically,andS(2) remainszero. (cid:4) (cid:5) (cid:4) (cid:5) −1 −1 Cavity 2 above threshold: If Γ(1)τ(1) > Γ(2)τ(2) , then at the point the material gain reaches the p p (cid:4) (cid:5) −1 lossofcavity2,itclampssuchthatg(cid:3)= Γ(2)τ(2) . AtpumppowersabovethispointtheS(2) increases p monotonically,andS(1) remainszero. Figure 1a shows how we can couple the lasers in such a way that Equations 3-5 adequately describe the system. In particular, linear cavities or v-cavities have been built around semiconductor gain for years. In the linear cavity (“cavity 1” in this case) places the semiconductor at one of two cavity mirrors. In this case, the mode passes through the gain twice in one round trip. However, in the v-cavity (labeled “cavity 2”), the gain chipactsasafoldinthecavity,composedoftwoexternalmirrors. Inthiscase,thelightpropagatesthroughthe gain four times in a single round trip, accounting for the factor of 2 in front of the stimulated emission term in Equation3. Inacanonicaldepictionofthisprocess,Figure1bshowshoweachofthesecavitiesinteractwiththe gain. The“phantomgain”isdepictedasasecondpieceofgaininthev-cavity,withthesamecarrierdensityand gain as the primary gain. The modal gain overlap between the two cavities is also different. The mode overlap Γistypicallygivenastheproductofmultipleoverlaps: Γ≡Γ Γ Γ Γ , z T p R where Γ is the temporal longitudinal overlap of the geometric cavity with the active region (semiconductor z between the DBR and air), Γ is the fraction of the quantum well within the active region, Γ is the RPG p R enhancementterm,7 andfinallyΓ isthemodeoverlapwiththepumpingregion. TheΓ Γ productisthenthe T z p temporallongitudinaloverlapofthequantumwellswiththegeometriccavity. Withthisunderstanding,foraparticularcavitywheretheoverlapsandlifetimesarefixed,onlytwoofofthe abovecaseswilltakeplace: eitherthesystemwillbebelowthreshold,orexclusivelycavity1orcavity2willlase, Proc. of SPIE Vol. 7919 791906-3 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited. 18 3000 6 16 2000 linear cavity ( fit) 14 v cavity ( fit) -1m) 1000 pump threshold (W) 110268 material gain & g (co --210000000 242N (cm)tr -3000 4 -4000 2 -5000 0 960 965 970 975 980 985 800 850 900 950 1000 1050 1100 wavelength (nm) wavelength (nm) a) b) Figure2.a)Experimentalthresholdofuncoupledlasersfordifferentbirefringentfilterwavelengthsettings. b)Computed spectralgaincurves, andnumericallyfitgain/carrierrelationparameters. Error-barsgivethestandarddeviationofthe logarithmicfittotheactualcomputedrelation. depending on which cavity has a lower loss overlap ratio. To present more interesting possibilities, and direct controloverthesystem,itispossibletoincludeabirefringentfilterintoeachcavity,andtunethecavityoverlap ofeachcavityindependently,changingboththegainandtheoverlapintegralofeachcavityindependently. The VECSEL gain chip used in the experiment is designed for emission around 975 nm. The active region consistsof14InGaAscompressivestrainedquantumwells8nmthicksurroundedbyGaAsPstraincompensation layersandAlGaAspump-absorbingbarriers. A99.9%DBRstackmadeof25pairsofAl0.2Ga0.8As/AlAsisgrown on the top of the active region and a single layer quarter-wave low-reflection coating of SiO2 is applied to the surfaceofthechiptoenhancethe975nmsignal. Cavity1consistsofasingleoutputcoupler(OC)andbirefringentfilterpositionedatBrewstersanglewitha cavitylengthof16cmanda350μmmodesizediameterontheVECSELchip. Cavity2isfoldedattheVECSEL chipandhasahighlyreflective(HR)flatmirroratoneendanda96%reflective,30cmradiusofcurvatureOC at the other end. The 3 cm separation between the HR flat mirror and the chip and 25 cm between the chip andtheOCresultsinamodediameterof∼360μm,whichissimilartothatofcavity1. Cavity1hasanatural (1) (2) photonlifetimeof(τ )of18.75ns,whileincavity2, τ =9.27ns. p p 3.1 Coarse Tuning Characteristics Utilizing the birefringent filters, it is possible to change the uncoupled threshold of the two separate cavities. ThisdataisdepictedinFigure2a. Inordertobestunderstandthefunctionaldependanceofthethresholdwith wavelength,wecanfirstpredictthewavelengthnatureofthegeometriccavityresponse. Reference7derivesthe relative confinement factor that results in a 1+sinc function for normal incidence, whos argument is π2t/λ on resonance, where t is an individual quantum well thickness. In resonance Γ can approach 2. As we tune off r resonance,itfallsofas ∼sinc. The other main wavelength-dependent term is the gain, which we also allow to vary with wavelength. Fig- ure 2b shows how the gain shifts at a constant temperature as a function of carrier density. In this case, we takeasimplelogarithmicgainapproximation,andallowthetransparentcarrierdensitytovaryasafunctionof wavelength. Explicitly,thisis writtenas: (cid:6) (cid:7) N g(N;λ)=g0ln . N (λ) tr Proc. of SPIE Vol. 7919 791906-4 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited. Cavity-1 Output Power Cavity-2 Output Power 985 985 2.880 20 long wavelength curve 15 short wavelength curve 980 980 2.160 10 m) m) cavity-2 wavelength (n997705 cavity-2 wavelength (n997705 10..4742000 (nm)(cid:104)(cid:60)(cid:104)(cid:3)(cid:16)(cid:15) -1-0505 965 965 -15 0 -20 960 965 970 975 980 985 960 965 970 975 980 985 -25 965 970 975 980 985 a) cavity-1 wavelength (nm) b) cavity-1 wavelength (nm) c) cavity-1 wavelength (nm) Figure 3. a) Experimental power out of cavity 1 as a function of the birefringent filter wavelength of each cavity. b) Experimental power out of cavity 2 as a function of the birefringent filter wavelength of each cavity. The uncoupled cavity boundaries are shown in blue in (a) and (b). c) The difference in operation wavelengths of each cavity near the equithresholdboundaries. We maintain this approximation as suitable based on a gain calculation packaged SimuLase, using an 8×8 kp- modelandincludingmany-bodyCoulombeffects,andutilizethistofitourgain/carrierrelation. Empirically,we determinedtheslopeofthegaincoefficientg0 doesnotvaryappreciablywithwavelength,andalldependanceis in the N term. The transparency carrier density has nominally a linear dependance with wavelength over the tr fittedregionofinterest(∼950-980nm). Using the wavelength dependance in Γ and g, we can fit the experimental threshold data in Figure 2a to r determine the slope of N verses wavelength, as well as the RPG enhancement. We ignore thermal effects, our tr predictionatmuchlargerpumppowersshouldbesuspect. Wethereforechosetoweighthepointsnearthelowest thresholdthegreatest,asthisrangehasthemostdataallatsomewhatthesamepower. Ourfittoexperimental dataisdepictedinFigure2abythelines. Themajorityofthecurvatureofthisfunctionisduetothevariation of Γ with respect to wavelength. The gain/carrier relation’s wavelength dependance offers comparatively little r influence,althoughthe asymmetryinFigure 2aisdue solelytothis effect. Becauseweunderstandthatwhenonelaserthresholdisbelowtheother,thatcavitylases,effectivelyclamping thegainatthresholdandforbiddingtheothercavitytolase,wecanutilizethebirefringentfiltersineachcavity to select the the cavity loss (and therefore threshold). For a given pair of wavelength settings, we predict the coupled effect by referring to Figure 2a, determining which cavity is lasing, repeating this approach for every combinationoffiltersettings. Althoughtedious,itispossibletousethetwofilterstoacquiredataovertwodimensions(oneforeachfilter wavelength), taking data for each cavity output to confirm this scheme. The power of each cavity is plotted in thesetwobirefringentfilterwavelengthsettingsinFigure3a-b. Wecanimmediatelyseethetworegionsidentified by our original theoretical framework. Moreover, the region separating the two regions are identified over the boundary where Γ(2)τ(2) = Γ(1)τ(1), where we can turn either of the lasers completely off. This boundary, p p identified numerically in blue in Figure 3 and 3b (from fits in Figure 2a) is unstable and not achievable in practice due to noises in real systems. However, the analysis utilizing uncoupled analysis to the coupled cavity powerresultsshowagreementisquitegood. ThissystemalsoisinterestingbecauseisitpossibletooperateneartheΓ(2)τ(2)=Γ(1)τ(1) boundaryfortwo p p cavity settings over a broad wavelength region. For example, in the upper left of Figure 3, λ1 ∼963 nm, while λ2 ∼985 nm. A switch from one to the other results in a lasing wavelength change of 22 nm with almost no change in the cavity. Likewise, in the lower right of Figure 3 represents a switch of almost 24 nm. Conversely, thediagonalfromlowerlefttoupperrightrepresentswavelengthsofeachcavitythatarealmostidenticaltoeach other(∼2nmswitches). Thisboundarywavelengthdifferenceincavity1andcavity2isplottedinFigure3c. Proc. of SPIE Vol. 7919 791906-5 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited. 985 ccaavviittyy 12 (cid:104)1=971nm 2.0 980 2.0 c) 110...505 output power cavity-2 wavelength (nm)999966770505 output power (W) 0011....0505 ccaavviittyy 12 de)) cc ccaaaavvvviittiiyyttyy 12 12 (cid:104)(cid:104)1=1=996682nnmm 22111100000...........50500055000output power output power 965 970 975 980 985 950 952 954 956 958 960 962 964 966 968 970 972 974 952 954 956 958 960 962 964 966 968 970 972 a) cavity-1 wavelength (nm) b) wavelength (nm) wavelength of v-cavity (nm) Figure4.a)RegionasinFigure2,butjustidentifyingregionwheretwochipslasersimultaneously. b)Outputpowerof eachuncoupledcavityasafunctionofbirefringenttuningfilterwavelength. c-e)Outputpowerofeachcoupled cavityas afunctionofbirefringenttuningfilterfordifferentbirefringentfiltersettings. 3.2 Fine Tuning Characteristics While in the previous section, we stated the boundary is unstable and not suitable to observe in experimental systems,weseeinpracticethatbothlaserscanlasesimultaneously. Figure4aisacomplimentaryplottoFigure3 where we identify the region in red where both cavities have non-zero outputs. Equations 3-5 do not predict this,leavingustomodify our theorytoaccountforthe effect. We previously admit to arrive at Equations 3-5 through the use of numerous approximations, including neglecting the barrier carriers, thermal effects, incoherent terms, and the fast varying effects. To better explain the equithreshold region, we judiciously reintroduce spontaneous emission, primarily because of its effect near threshold, although the contribution well above threshold is typically negligible. Rewriting Equations 4-5 to includespontaneousemissiongives: d S(1) S(1) = − +g(cid:3)Γ(1)S(1)+β(1)BN2 (6) dt τ(1) p d S(2) S(2) = − +g(cid:3)Γ(2)S(2)+β(2)BN2, (7) dt τ(2) p where β(j) is the jth cavity mode cross-section with the spontaneous emission radiation, B is the spontaneous emission coefficient, a contribution to τ in Equation 3. Using this, we can redefine the boundary between the twomodesas: (cid:8) (cid:9) 1 β(2)S(2) 1 −g(cid:3)Γ(1)= −g(cid:3)Γ(2) , (8) τ(1) β(1)S(1) τ(2) p p andisnolongerindependentofphotondensity. Figure 4b represents the uncoupled “tuning curves” (output power) as a function of the birefringent filter wavelength for each cavity. This is the most common data presented when discussing VECSEL tuning.8,9 The three dotted lines in these tuning curves represent the settings for the filter in cavity 1 shown in Figures 4c-e. In these plots, the output in each cavity is shown as a function of the filter wavelength setting within cavity 2. Theseplotsaretheequivalentofsingleverticaltracesofthetwo-dimensionalplotsshowninFigure3,including the boundary regime in which both cavities have non-zero outputs. The width of the non-zero regime can be changed,dependingontherelativechangeofthethresholdasafunctionofwavelength. Becausetheslopedoes not change significantly as a function of wavelength, Figure 4b shows us that because the ∂P/∂λ is smaller on Proc. of SPIE Vol. 7919 791906-6 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited. ) u. a. ( r e pow (cid:104)1=967.3nm (cid:104)=968.4nm (cid:104)2=968.4nm ut 2 p ut o (cid:104)2=968.4nm (cid:104)1=968.6nm (cid:104)1=970.0nm 0 20 40 60 80 0 20 40 60 80 0 20 40 60 time ((cid:43)s) time ((cid:43)s) time ((cid:43)s) a) b) c) Figure5.Plotofexperimentaloutputpowerversustimefordifferentcavitytunings. Thelinearcavitywaschoppedinthe dual cavity configuration. a) Cavity tuned such that cavity switches from completely on to completely off b)-c) various tuningsuchthattheswitchingislesscomplete. Simulatedresultsareshownasdottedlines. theblue-sideofthetuningpeakthanontheredside,thenear-equithresholdregionisexpanded. Therearealso regions where we can tune completely through spectrum without turning off cavity 1. Two of these cases are showninFigures4d-e. 3.3 Dynamics To observe the transient response of the optical switch between the two cavities, both in the coarse and fine tuning regimes, we utilize silicon detectors with a 3-dB frequency of 200 MHz to simultaneously detect output from each cavity. These are coupled to a 500 MHz oscilloscope. An optical chopper is placed within cavity 1, periodicallyblockingandunblockinglasingfromoccurring. Cavity2istunedtoawavelengthprovidingahigher thresholdthancavity1,suchthatwhencavity1isblocked,cavity2buildsupandswitches“on”. Thechopper triggers the oscilloscope to acquire the build-up, not when cavity 1 is blocked, but rather when it is unblocked. WeseethreeexamplesofthisswitchinginFigure5. When spontaneous emission is included, the gain coupling can prevent one cavity running away and the other shutting off completely. Consider the case shown in Figures 5b and 5c where cavity 1 and cavity 2 are very near equithreshold spectral regions. Here we see cavity 1 is initially blocked and then unblocked at time t=0. The uncoupled threshold of cavity 1 is initially slightly lower and the photon density increases at the expense of the photon density of cavity 2. As the photon density of cavity 2 drops, the relative contribution of the spontaneous emission increases. Because spontaneous emission is an additive term to the photon equation, it can be considered as a mechanism for reducing the threshold gain of cavity 2, thus lowering the uncoupled thresholdofcavity2belowthatofcavity1andeffectivelyreducingthephotondensityofcavity1. Thiscycleis dampedbythe photonlifetime allowingboth cavities tooperate simultaneously. Thiseffectivereduction inthe thresholdisofcourse,verysmall,whichiswhythiseffectisimportantonlywhenthetwouncoupledthresholds areveryclose. The significant oscillations seen in Figure 5b-c are not seen in the numerical solution to Equation 3 and Equations 6-7, where the dotted-line numerical simulations shown in Figure 5. Near threshold, the relative cavity loss, caused by misalignments, for example, become extremely important. Small fluctuations caused by vibrationandaircurrentscanmanifestinvastchangespoweroutofthelaser,selectingonecavityovertheother. Proc. of SPIE Vol. 7919 791906-7 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited. 120 τ(2) = 9.27ns τ(1) = 18.75ns p p τ(1)=41.02ns p 100 class-B, class-A 1014 -3sity (cm) μg time (s) 6800 τp(1)=1 c8l.a7s5sn-sB, class-A on den1013 τ(1) = 0.020ns τp(2) = 9.2 7ns witchin 40 ot p s τ(1)=05.86ns h p p τ(2) = 0.021ns class-B, class-A τp(1) = 1.87ns p τp(2) = 0.928ns 20 τ(1)=00.12ns p τp(1) = 18.75ns 0 class-B, class-A 1012 10-1 100 101 102 100 101 102 0 10 20 30 40 50 60 70 a) time (μs) b) time (μs) c) Σnτp(n) (ns) Figure 6. Photon dynamics for various combinations of photon lifetimes. a) Holding τp(2) constant, and changing τp(1) through the carrier lifetime. b) Holding τp(1) constant while changing τp(2) through various photon lifetimes. c) Cavity switchingtimeasafunctionofnetphotonlifetime,holdingτp(1) constantatseveralvalues. Thislastplotshowsthatthe linearrelationholds,althoughtheremustbeaneffectiveoffsetforeveryvalueofτp(1). Experimentally, we take particular care to ensure there is no photon coupling directly from one cavity to the other, as this may cause laser instabilities, which could also cause such “noises”. This direct coupling could be duetoinadvertentsemiconductorsurfaceimperfectioninducedscattering. However,becausebirefringentfilters areineachcavity,anyphotonsscatteredfromonecavitytotheotherareimmediatelyremovedfromthecavity providedthetwofiltersareatdifferent,nonharmonic,wavelengths. WeseetheoscillationinFigure5b-cforall settingsofwavelengthsalongtheboundaryidentifiedinFigure4a. TounderstandthelimitationsofsuchaswitchasdepictedinFigure5,welookatthecaseofa“pure”class-A laser. Inthissystem,theturn-ontimeisderivedas: (cid:10) (cid:11) τ I T = p ln ss , (9) b r−1 I◦ where τ is the photon lifetime, r is the normalized ratio of round trip gain to loss, (presumed to be greater p than unity), and Iss and I◦ is the saturation power density and initial noise power density, respectively.10 This derivation is predicated on the fact that the optical gain of the material remains high until the laser hits some saturation level, at which time the gain begins to drop quickly, and causes the power to cease increasing exponentially. While not strictly applicable in this case, Equation 9 maintains qualitative agreement with experiments. InaVECSELswitch,webuildupfromspontaneousemission,thereforeln(Iss/I◦)∼17. Innearequithreshod regions, (r−1)∼10−3, which results in a relatively slow coupled-cavity switch, significantly greater than 1 μs. We simulate the switching time by allowing the cavity to settle down with cavity 1 “blocked” (significantly increasingthecavityloss). Thereforecavity2isallowedtolase,reachingasteady-statevalue. Attime t=0,we numerically “unblock” cavity 1 (returning its cavity loss to the normal value), which is slightly lower than that ofcavity1. Atypicalcomputed“switch”canbeseeinFigure6,wherethecavitieshaveverysimilarthresholds. Figure6a shows a switch where cavity 2 starts out in a lasing mode, and cavity 1 begins at near zero (just spontaneous emission). When cavity 1 is unblocked (at time t=0), photons begin building up, depleting carriers and thus Proc. of SPIE Vol. 7919 791906-8 Downloaded from SPIE Digital Library on 17 Jun 2011 to 134.131.125.50. Terms of Use: http://spiedl.org/terms Approved for public release; distribution unlimited.