-6%8*( ."9*.*-*"/ 6/*7&34*5: 0' .6/*$) #"$)&-03 5)&4*4 $POTUSVDUJPO PG BO JOUFSGFSFODFmMUFSTUBCJMJ[FE EJPEF MBTFS GPS FYQFSJNFOUT XJUI VMUSBDPME TUSPOUJVN BUPNT *7"/ ,0,)"/074,:* JO DPMMBCPSBUJPO XJUI UIF .BY1MBODL*OTUJUVUF GPS 2VBOUVN 0QUJDT VOEFS TVQFSWJTJPO PG 1SPG %S *NNBOVFM #MPDI BOE %S 4FCBTUJBO #MBUU .VOJDI #"$)&-03"3#&*5 "/ %&3 -6%8*(."9*.*-*"/46/*7&34*55 ./$)&/ ,POTUSVLUJPO FJOFT JOUFSGFSFO[mMUFSTUBCJMJTJFSUFO %JPEFOMBTFST GÊS &YQFSJNFOUF NJU VMUSBLBMUFO 4USPOUJVNBUPNFO WPSHFMFHU WPO *7"/ ,0,)"/074,:* .ºODIFO EFO +VMJ Abstract *O UIJT #BDIFMPS UIFTJT XF SFQPSU PO UIF DPOTUSVDUJPO PG BO JOUFSGFSFODFɯMUFSTUBCJMJ[FE FY UFSOBM DBWJUZ EJPEF MBTFS BU B XBWFMFOHUI PG ON GPS VTF JO FYQFSJNFOUT XJUI VMUSBDPME TUSPOUJVN BUPNT 5IJT XPSL DPOUBJOT B TUFQCZTUFQ FYQMBOBUJPO PG UIF MBTFS DPOTUSVDUJPO JODMVEJOH BEWJDF GPS JOTUBMMJOH FBDI MBTFS DPNQPOFOU 'VSUIFSNPSF XF EFTDSJCF DPOUSPM TZTUFNT BOE XBWFMFOHUI TFMFDUJPO NFDIBOJTNT UIBU FOBCMF TUBCMF TJOHMFNPEF PQFSBUJPO PG UIF MBTFS 0QUJNJ[BUJPO PG UIF MBTFS PVUQVU QPXFS JUT XBWFMFOHUI UVOJOH BOE B EFUFSNJ OBUJPO PG JUT MJOFXJEUI BSF EJTDVTTFE 8F BMTP NBLF TVHHFTUJPOT GPS QPTTJCMF JNQSPWFNFOUT JO GVUVSF JUFSBUJPOT PG UIF EFTJHO i Contents ii Contents 1Introduction 1 2FundamentalProcessesinaLaser 2 -JHIU.BUUFS *OUFSBDUJPO -JHIU "NQMJɯDBUJPO 4FNJDPOEVDUPS -BTFST 4FNJDPOEVDUPST 4FNJDPOEVDUPS -BTFS %JPEF 3FTPOBUPS 3LaserConstruction 9 %FTJHO 0WFSWJFX *OUFSGFSFODF 'JMUFS &MFDUSJDBM $POUSPM 1BSUT 5FNQFSBUVSF $POUSPM 4ZTUFN 1JF[PFMFDUSJDBMMZ 5VOBCMF 3FTPOBUPS .FDIBOJDBM %FTJHO PG BO &$%- $PMMJNBUPS "MJHOJOH UIF &YUFOEFE $BWJUZ 4OpticalSetup 24 "OBNPSQIJD 1SJTN 1BJS 0QUJDBM %FWJDFT 0QUJDBM 4FUVQ 5LaserProperties 31 0VUQVU 1PXFS 8BWFMFOHUI 4FMFDUJPO .PEF)PQ'SFF 5VOJOH 3BOHF -JOFXJEUI 6Conclusion 42 References 42 Acknowledgements 46 List of Tables iii List of Tables 5IFSNJTUPS 5), List of Figures iv List of Figures -JHIUNBUUFS JOUFSBDUJPO QSPDFTTFT JO B UXPMFWFM TZTUFN " TDIFNBUJD PG B GPSXBSECJBTFE QO KVODUJPO " TDIFNBUJD PG B TFNJDPOEVDUPS MBTFS EJPEF JO B GPSN PG B GPSXBSECJBTFE QO KVODUJPO 5IF QSPQBHBUJPO PG B QMBOF XBWF CFUXFFO UXP NJSSPST JO UIF HBJO NFEJVN &YUFSOBM DBWJUZ EJPEF MBTFS EFTJHO 'BCSZ1§SPU UZQF JOUFSGFSFODF ɯMUFS XJUI B TBOEXJDI EFTJHO 5FNQFSBUVSF DPOUSPM TZTUFN 5FNQFSBUVSF WFSTVT SFTJTUBODF GPS 5), 5XP DPOEVDUPST JO B UFNQFSBUVSF HSBEJFOU " TFSJFT PG BMUFSOBUJOH O BOE QUZQF TFNJDPOEVDUPS FMFNFOUT 5IF EFTJHO PG B DPNNFSDJBM 1FMUJFS EFWJDF 1JF[PFMFDUSJD FɮFDU JO B RVBSU[ DSZTUBM 1JF[P SJOH BDUVBUPS " % TDIFNBUJD PG UIF &$%-T NFDIBOJDBM EFTJHO "TTFNCMZQJF[P UP PVUQVU DPVQMFS "TTFNCMZ UIFSNJTUPS JOUP UIF DBWJUZ IPVTJOH $PMMJNBUPS "MJHOJOH PG UIF FYUFSOBM DBWJUZ #FBN TIBQF JO UIF GBSɯFME "OBNPSQIJD QSJTN QBJS DPOɯHVSBUJPO 5SBOTNJTTJPO BOE JTPMBUJPO QSPɯMFT GPS *057-1 'BSBEBZ UBOEFN JTP MBUPS " TDIFNBUJD PG BO 'BSBEBZ JTPMBUPS 1PMBSJ[JOH CFBN TQMJUUFS DVCF 'JCFS HVJEF GSPN UXP QPJOUT PG WJFX " TDIFNBUJD PG UIF PQUJDBM TFUVQ PO UIF CSFBE CPBSE 5ISFTIPME DVSSFOU PQUJNJ[BUJPO VTJOH B GVODUJPO HFOFSBUPS -JHIUDVSSFOU DIBSBDUFSJTUJDT PG UIF MBTFS BU WBSJPVT UFNQFSBUVSFT 5ISFTIPME DVSSFOU BU WBSJPVT UFNQFSBUVSFT 5SBOTNJTTJPO QSPɯMF PG UIF CBOEQBTT PG UIF ɯMUFS PQUJNJ[FE GPS USBOTNJT TJPO BU ON 'JMUFS XBWFMFOHUI UVOJOH SBOHF JOWFTUJHBUFE GPS EJɮFSFOU PQFSBUJOH UFN QFSBUVSFT 5FNQFSBUVSF XBWFMFOHUI UVOJOH List of Figures v " TDIFNBUJD TFUVQ GPS B CFBU TJHOBM #FBU TJHOBM XJUI 5PQUJDB #FBU TJHOBM XJUI .PHMBCT Chapter 1 Introduction 1 Chapter 1 Introduction 5IF QIZTJDBM QSJODJQMF PG MJHIU BNQMJɯDBUJPO CZ TUJNVMBUFE FNJTTJPO XBT QSFEJDUFE CZ "M CFSU &JOTUFJO JO *O UIF ɯSTU MBTFS XBT DPOTUSVDUFE CZ $ ) 5PXOFT / ( #BTPW BOE " . 1SPLIPSPW < > /PX MBTFST BSF VTFE JO BO FOPSNPVT WBSJFUZ PG EFWJDFT PQFSBUJOH JO EJɮ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ɯMUFSTUBCJMJ[FE FYUFSOBM DBWJUZ EJPEF MBTFS &$%- <Ʀ> XJUI FNJT TJPO BU ON 5IF MBTFS JT JOUFOEFE UP CF VTFE BT QBSU PG BO VMUSBDPME BUPN FYQFSJNFOU CBTFE PO TUSPOUJVN BUPNT 5IFSFGPSF UIJT QBSUJDVMBS XBWFMFOHUI XBT DIPTFO TP BT UP 1 3 CF BCMF UP BEESFTT UIF 40 11 USBOTJUJPO JO TUSPOUJVN <> 5IF OFX JOUFSGFSFODFɯMUFS − TUBCJMJ[FE &$%- XPVME QPUFOUJBMMZ SFQMBDF UIF TUSPOUJVN MBCƫT POMZ ON MBTFS XJUI -JUUSPX DPOɯHVSBUJPO * XBT UBTLFE XJUI DPOTUSVDUJPO BOE DIBSBDUFSJ[BUJPO PG UIJT MBTFS 5IJT #BDIFMPSƫ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ɯMUFSTUBCJMJ[FE MBTFS TIPVME CF CVJMU DPOTJEFS QSPCMFNT FO DPVOUFSFE XJUI UIF TFUVQ BOE QSPQPTF QPTTJCMF TPMVUJPOT *O UIF GVSUIFS $IBQUFS XF FYQMPSF UIF PQUJDBM FMFNFOUT OFFEFE GPS UIF PQUJDBM TFUVQ 5IF TDIFNBUJD PG TFMGEFTJHOFE PQUJDBM TFUVQ JT BMTP QSFTFOUFE 5IF QSPQFSUJFT PG UIF MBTFS BSF EFTDSJCFE JO UIF ɯOBM $IBQUFS 5IF MBTFS QSPWJEFT PVUQVU QPXFS PG VQ UP N8 BU B NBYJNVN DVSSFOU PG N" "EEJUJPOBMMZ XF JOWFTUJHBUF IPX UIF PQFSBUJOH UFNQFSBUVSF JOɰVFODFT UIF TQFDUSBM QSPQFSUJFT PG UIF MBTFS BOE UIF UISFTI PME DVSSFOU DPOEJUJPO 5IF LFZ UP XBWFMFOHUI UVOJOH PG UIF MBTFS JT UIF BGPSFNFOUJPOFE JOUFSGFSFODFɯMUFS 5IFSFGPSF XF FYQFSJNFOUBMMZ JOWFTUJHBUF JUT CBOEQBTT TIBQF BOE UIF XBWFMFOHUI UVOBCJMJUZ SBOHF BU WBSJPVT UFNQFSBUVSFT .PSFPWFS XF EFTDSJCF UIF EJɮFS FOU UVOJOH NFDIBOJTNT PG UIF MBTFS XIJDI BMMPX VT UP BDIJFWF TJOHMF NPEF PQFSBUJPO BU BSCJUSBSZ XBWFMFOHUI XJUIJO UIF UVOJOH SBOHF 5IF GVMM XJEUI BU IBMG NBYJNVN XBT BMTP EFUFSNJOFE VTJOH BO PQUJDBM IFUFSPEZOF NFUIPE CFBU TJHOBM NFBTVSFNFOU Chapter 2 Fundamental Processes in a Laser 2 Chapter 2 Fundamental Processes in a Laser *O UIF ɯSTU $IBQUFS XF EFTDSJCF UIF GVOEBNFOUBM MBXT PG MBTFS BDUJPO 8F CFHJO XJUI UIF JOUSPEVDUJPO PG UISFF QSPDFTTFT JO XIJDI FOFSHZ DPOWFSTJPO DBO PDDVS 5IFO XF MPPL BU TPNF QSPQFSUJFT PG TFNJDPOEVDUPS EJPEF MBTFST 'JOBMMZ UIF UISFTIPME DPOEJUJPO JT EJT DVTTFE 2.1 Light-Matter Interaction 5IJT 4FDUJPO CFHJOT XJUI B TIPSU SFWJFX PG MJHIUNBUUFS JOUFSBDUJPO QSPDFTTFT -FU VT DPO TJEFS B NFEJVN DPOTJTUJOH PG UXPMFWFM RVBOUVN TZTUFNT XJUI B HSPVOE TUBUF XJUI FOFSHZ E1 BOE BO FYDJUFE TUBUF XJUI FOFSHZ E2 8F UBLF UIF OVNCFS PG BUPNT JO UIF HSPVOE TUBUF UP CF N1 BOE UIF OVNCFS PG BUPNT JO UIF FYDJUFE TUBUF UP CF N2 5IF QPQVMBUJPO SBUJP JO UIF UXP TUBUFT JT HJWFO CZ UIF #PMU[NBOO EJTUSJCVUJPO <> N2 g2 E1 E2 = exp − , N g k T 1 1 ! B " XIFSF g1 BOE g2 SFQSFTFOU UIF EFHFOFSBDZ UIF OVNCFS PG TUBUFT XJUI UIF TBNF FOFSHZ PG UIF HSPVOE BOE FYDJUFE TUBUFT SFTQFDUJWFMZ BOE kB JT UIF #PMU[NBOO DPOTUBOU 5IFSF BSF UISFF QSPDFTTFT SFMFWBOU GPS VOEFSTUBOEJOH UIF PQFSBUJOH QSJODJQMF PG B MBTFS BCTPSQUJPO TQPOUBOFPVT FNJTTJPO BOE TUJNVMBUFE FNJTTJPO <> *O UIF GPMMPXJOH XF EF TDSJCF UIFTF QSPDFTTFT JO EFUBJM VTJOH &JOTUFJOƫT NPEFM 'JH 8IFO SFTPOBOU SBEJBUJPO JT JODJEFOU PO UIF NFEJVN BO BUPN DBO CF USBOTGFSSFE GSPN UIF HSPVOE UP UIF FYDJUFE TUBUF 5IJT UZQF PG USBOTJUJPO JT DBMMFE BCTPSQUJPO BOE JUT SBUF JT HJWFO CZ dN1 = B12N1ρ(ν), dt − ! "ab XIFSF B12 JT DBMMFE &JOTUFJOƫT BCTPSQUJPO DPFɱDJFOU BOE ρ(ν) JT UIF FOFSHZ EFOTJUZ XIJDI EFTDSJCFT UIF BNPVOU PG DPOUJOVPVTMZ FNJUUFE FOFSHZ CZ BUPNT BU UFNQFSB UVSF T BOE JT HJWFO CZ 1MBODLƫT MBX <> 8πhν3 1 ρ(ν)= . c3 ehν/kB T 1 − 4QPOUBOFPVT FNJTTJPO PDDVST XIFO BO BUPN KVNQT EPXO GSPN UIF FYDJUFE TUBUF UP Chapter 2 Fundamental Processes in a Laser 3 1 2 3 Fig. 2.1 Light-matter interaction processes in a two-level system: 1 - absorption, 2 - spontaneous emission, 3 - stimulated emission. UIF HSPVOE TUBUF XIJMF FNJUUJOH B QIPUPO PG FOFSHZ E2 E1 5IF SBUF PG EFDSFBTF − PG UIF FYJUFE TUBUF QPQVMBUJPO DBO CF XSJUUFO BT dN2 = A21N2, dt − ! "sp XIFSF A21 JT &JOTUFJOƫT DPFɱDJFOU EFTDSJCJOH UIF SBUF PG TQPOUBOFPVT FNJTTJPO *O UIF DBTF PG TUJNVMBUFE FNJTTJPO BUPNT JO UIF FYDJUFE TUBUF BSF TUJNVMBUFE UP NBLF B USBOTJUJPO UP UIF HSPVOE TUBUF CZ BO JODJEFOU QIPUPO 5IJT QSPDFTT MFBET UP UIF FNJTTJPO PG B TFDPOE QIPUPO 5IF SBUF PG UIJT QSPDFTT JT EFTDSJCFE CZ dN2 = B21N2ρ(ν), dt − ! "st XIFSF B21 JT UIF &JOTUFJOƫT DPFɱDJFOU EFTDSJCJOH UIF SBUF PG TUJNVMBUFE FNJTTJPO 5IF TVN PG BUPN OVNCFST JO CPUI TUBUFT NVTU CF DPOTUBOU XIJDI MFBET UP dN dN 1 = 2 , dt − dt BOE A21N2 =(B12N1 B21N2) ρ(ν). − "QQMZJOH &R POF DBO EFSJWF &JOTUFJOƫT SFMBUJPOT 3 A21 8πhν = , 3 B21 c g1B12 = g2B21. Chapter 2 Fundamental Processes in a Laser 4 2.2 Light Amplification -FU VT DPOTJEFS OPX B MJHIU XBWF QBTTJOH UISPVHI BO BDUJWF NFEJVN "DDPSEJOH UP &R UIJT QSPDFTT DBVTFT TUJNVMBUFE FNJTTJPO BOE BCTPSQUJPO JO UIF BDUJWF NFEJVN *G UIF SBUF PG TUJNVMBUFE FNJTTJPO FYDFFET UIF SBUF PG BCTPSQUJPO UIF XBWF XJMM HSPX JO JSSBEJBODF QPXFS QFS VOJU BSFB *O B TNBMM QBUI FMFNFOU dz UIF DIBOHF JO JSSBEJBODF JT QSPQPSUJPOBM UP UIF EJɮFSFODF CFUXFFO UIF SBUF PG TUJNVMBUFE