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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 FNJTTJPO BOE BCTPSQUJPO

dI(z)=[B21N2ρ(ν)E g(ν) α] I(z)dz,  ph − XFSF UIF TQFDUSBM GVODUJPO g(ν) EFTDSJCFT UIF GSFRVFODZ TQFDUSVN PG UIF TQPOUBOFPVTMZ FNJUUFE SBEJBUJPO BOE α JT BO BCTPSQUJPO DPFɱDJFOU 5IF JSSBEJBODF DBO BMTP CF QSFTFOUFE BT B QSPEVDU PG UIF FOFSHZ EFOTJUZ BOE UIF TQFFE PG MJHIU I = ρ(ν)c < > 'SPN &R    XF DBO SFXSJUF UIJT FYQSFTTJPO BT

2 dI g2 A21c = (N2 N1) I(z)g(ν) α I(z),  dz − g 8πν2 − # 1 $ BOE JOUFHSBUF PWFS z UP ɯOE (γ(ν) α)z I = I0e − ,  XIFSF γ(ν) JT UIF HBJO DPFɱDJFOU *G γ(ν) JT QPTJUJWF BOE MBSHFS UIFO α UIF JSSBEJBODF HSPXT FYQPOFOUJBMMZ XJUI EJTUBODF z

2.3 Semiconductor Lasers

*O UIJT 4FDUJPO XF HJWF BO PWFSWJFX PG TFNJDPOEVDUPS MBTFST 'JSTU XF EJTDVTT UIF NFBOJOH PG WBMFODF BOE DPOEVDUJPO CBOET GPS TFNJDPOEVDUPS EFWJDFT 5IFO XF NPWF PO UP UIF DPO DFQU PG B QO KVODUJPO 'JOBMMZ XF EFTDSJCF UIF SBEJBUJPO NFDIBOJTN PG B TFNJDPOEVDUPS MBTFS EJPEF BOE EJTDVTT JUT CBTJD QSPQFSUJFT

2.3.1 Semiconductors

&MFDUSPOT PDDVQZ RVBOUJ[FE FOFSHZ TUBUFT <> 'PS JOTUBODF JO BO BUPN XJUI BUPNJD OVN CFS Z FMFDUSPOT PDDVQZ UIF Z MPXFTU FOFSHZ TUBUFT -FU VT DPOTJEFS N BUPNT UIBU GPSN B TPMJE "DDPSEJOH UP UIF 1BVMJ QSJODJQMF FMFDUSPOT XJUI UIF TBNF RVBOUVN OVNCFST DBOOPU PDDVQZ UIF TBNF TQJO TUBUF %VF UP UIF JOUFSBDUJPO CFUXFFO UIF BUPNT CBOET BSF GPSNFE FBDI DPOUBJOJOH N UIF GBDUPS UXP CFDBVTF PG UIF FMFDUSPO TQJO FOFSHZ TUBUFT "U BCTP MVUF [FSP UFNQFSBUVSF UIF MBTU GVMMZ ɯMMFE CBOE JT DBMMFE UIF WBMFODF CBOE 5IF DPOEVDUJPO CBOE JT UIF ɯSTU FNQUZ CBOE JO TFNJDPOEVDUPST 5IFTF CBOET BSF TFQBSBUFE CZ BO FOFSHZ HBQ 5IF SFRVJSFE FOFSHZ UP BEE BO FMFDUSPO BU BCTPMVUF [FSP UFNQFSBUVSF JT HJWFO CZ UIF 'FSNJ FOFSHZ Ef  'PS TFNJDPOEVDUPST Ef JT MPDBUFE JO UIF CBOE HBQ 5IFSFGPSF UIF BEEFE FMFDUSPO BQQFBST JO UIF DPOEVDUJPO CBOE 8JUI BO JODSFBTF JO UFNQFSBUVSF UIF FMFDUSPOT DBO PWFSDPNF Eg CFDBVTF PG UIFSNBM FYDJUBUJPOT <> Chapter 2 Fundamental Processes in a Laser 5

p n - +

Ef eV

Ef

Electron energy

Position Fig. 2.2 Aschematicofaforward-biasedp-njunction.Thehorizontalaxisrepresentstheposition, and the vertical axis the electron energy. The energy difference between the Fermi ener- gies is given by eV ,whereV is the voltage due to the electrical field, and e is the electron charge.

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QO KVODUJPO -FU VT DPOTJEFS OPX XIBU XPVME IBQQFO XIFO BO OEPQFE BOE B QEPQFE SFHJPO BSF QVU JOUP B DPOUBDU &MFDUSPOT GSPN UIF OSFHJPO XJMM EJɮVTF JOUP UIF QSFHJPO XIFSF SFDPNCJOBUJPO XJUI UIF BCVOEBOU IPMFT DBO UBLF QMBDF 4JNJMBSMZ IPMFT GSPN UIF QSFHJPO XJMM EJɮVTF JOUP UIF OSFHJPO UP SFDPNCJOF XJUI UIF BCVOEBOU FMFDUSPOT 5IF BDDVNVMBUFE DIBSHF PO CPUI TJEFT HFOFSBUFT BO FMFDUSJD ɯFME BDSPTT UIF DPOUBDU BSFB *O UIJT XBZ UIF 'FSNJ MFWFMT MJOF VQ BOE BO FOFSHZ CBSSJFS JT QSPEVDFE "QQMZJOH B QPTJUJWF WPMUBHF UP UIF QSFHJPO DBVTFT B NJTBMJHONFOU PG UIF 'FSNJ MFWFMT JO UIF Q BOE OSFHJPOT 5IF QPUFOUJBM EJɮFSFODF CFUXFFO UIF 'FSNJ MFWFMT XJMM JODSFBTF 5IF JOKFDUJPO PG FMFD USPOT JOUP UIF DPOEVDUJPO CBOE BOE IPMFT JOUP UIF WBMFODF CBOE CZ BQQMZJOH JO FYUFSOBM FMFDUSJD ɯFME XJMM NBLF UIF EFQMFUJPO SFHJPO NPSF OBSSPX 5IJT QSPDFTT HFOFSBUFT TQPO UBOFPVT FNJTTJPO PG QIPUPOT CZ UIF FMFDUSPOIPMF SFDPNCJOBUJPO NFDIBOJTN BT TLFUDIFE JO 'JH 

2.3.2 Semiconductor Laser Diode

5IF MBTFS EJPEF JT B TFNJDPOEVDUPS EFWJDF B GFX IVOESFET PG µN MPOH BOE B GFX UFOT PG µN UIJDL TFF 'JH   5IF GVODUJPO PG B TFNJDPOEVDUPS MBTFS EJPEF JT CBTFE PO B Chapter 2 Fundamental Processes in a Laser 6

E

w

pn

- +

L d

Fig. 2.3 Aschematicofasemiconductorlaserdiodeinaformofaforward-biasedp-njunction.The active layer width is d, L is the cavity length,w is the laser diode width, and E represents a polarization.

GPSXBSECJBTFE QO KVODUJPO DPOTUSVDUFE GSPN B EJSFDUCBOEHBQ TFNJDPOEVDUPS NBUFSJBM 'JH   *O UIJT DBTF UIF QPTJUJWF UFSNJOBM PG UIF QPXFS TVQQMZ JT DPOOFDUFE UP UIF Q UZQF TJEF PG UIF TFNJDPOEVDUPS MBTFS EJPEF BOE UIF OFHBUJWF POF UP UIF OUZQF 8IFO B WPMUBHF JT BQQMJFE UP UIF MBTFS EJPEF UIF SBUF PG FMFDUSPOIPMF SFDPNCJOBUJPO QSPDFTTFT JODSFBTFT 5IJT QSPDFTT MFBET UP BO JODSFBTF PG UIF SBUF PG TUJNVMBUFE FNJTTJPO 5IF MJHIU JT HFOFSBUFE CZ TUJNVMBUFE FNJTTJPO JO B UIJO MBZFS DBMMFE UIF BDUJWF SFHJPO XIFSF UIF FMFDUSPOIPMF SFDPNCJOBUJPO UBLFT QMBDF 5IF BDUJWF SFHJPO BMTP IBT PQUJDBM MPTTFT TVDI BT NJSSPS MPTTFT PS GSFFDBSSJFS BCTPSQUJPO *O UIF GPMMPXJOH 4FDUJPO XF EJTDVTT TPNF CBTJD QSPQFSUJFT PG TFNJDPOEVDUPS 'BCSZ1§SPU EJPEF MBTFST TVDI BT PQUJDBM HBJO UISFTIPME DPOEJUJPO BOE CFBN QPMBSJ[BUJPO

2.3.3 Resonator

5P VOEFSTUBOE UIF QIZTJDT CFIJOE MJHIU QSPQBHBUJPO JO B MBTFS EJPEF DBWJUZ XF UBLF BT PVS NPEFM .BYXFMMƫT DPODFQU PG MJHIU BT BO FMFDUSPNBHOFUJD XBWF "DDPSEJOH UP UIJT NPEFM BO PTDJMMBUJOH FMFDUSJD ɯFME BOE BO PTDJMMBUJOH NBHOFUJD ɯFME BSF PSJFOUFE QFSQFOEJDVMBS UP FBDI PUIFS IBWJOH UIF TBNF GSFRVFODZ 5IF PSJFOUBUJPO PG UIF FMFDUSJD ɯFME WFDUPS E JO UIF QMBOF QFSQFOEJDVMBS UP UIF EJSFDUJPO PG UIF QSPQBHBUJPO EFTDSJCFT UIF QPMBSJ[BUJPO *G BMM UIF QIPUPOT IBWF UIF TBNF QPMBSJ[BUJPO UIF XBWF JT DBMMFE MJOFBSMZ QPMBSJ[FE 5IF MJOFBSMZ QPMBSJ[FE MJHIU QSPQBHBUJOH BMPOH UIF z BYJT XJUI BNQMJUVEF E0 XBWFOVNCFS k Chapter 2 Fundamental Processes in a Laser 7

gain medium

L Fig. 2.4 The propagation of a plane wave between two mirrors in the gain medium. The length L describes the distance between mirrors.

GSFRVFODZ ω BOE QIBTF φ DBO CF EFTDSJCFE BT < >

(ωt ikz+φ) Ez = E0e −

*O NPTU MBTFST UIF BDUJWF NFEJVN JO XIJDI MBTFS BDUJPO IBQQFOT JT JOTJEF BO PQUJDBM SFTPOBUPS -FU VT DPOTJEFS B QMBOF XBWF QSPQBHBUJOH JO B TFNJDPOEVDUPS MBTFS DBWJUZ PG MFOHUI L 'JH  DPOTJTUJOH PG UXP NJSSPST XJUI USBOTNJTTJPO DPFɱDJFOUT t1 t2 BOE SFɰFDUJPO DPFɱDJFOUT r1 r2 SFTQFDUJWFMZ 5IF ɯFME KVTU BGUFS UIF MFGU NJSSPS JT HJWFO CZ t1E0 5SBWFMJOH UISPVHI UIF DBWJUZ JUT QIBTF HSPXT VOUJM UIF TFDPOE NJSSPS JT SFBDIFE ikL ikL " QBSU PG r2t1E0e− XJMM CF SFɰFDUFE CBDL JOUP UIF DBWJUZ BOE B QBSU t2t1E0e− XJMM CF USBOTNJUUFE 5IF GPMMPXJOH QSPDFTT SFQFBUT BOE UIF ɯOBM USBOTNJUUFE FMFDUSJDBM ɯFME JT HJWFO CZ B TVQFSQPTJUJPO

ikL 3ikL 2 5ikL Et = t2t1E0e− + r1r2t1E0e− +(r1r2) t2t1E0e− + ..., 

BOE DBO CF DBMDVMBUFE BT B HFPNFUSJD TFSJFT

ikL 2 t1t2e− E0(1 R ) Et = E0 = − ,  1 r r e 2ikL 1 R2e iδ − 1 2 − − − 2 2 XIFSF R = r1r2 t1t2 =1 R BOE δ =2kL JT UIF BDDVNVMBUFE SPVOEUSJQ QIBTF TIJGU − 5IF ɯOBM USBOTNJTTJPO DBO CF DBMDVMBUFE BT

2 2 Et (1 R) 1 T = = − 2 δ = 2 δ ,  E0 (1 R)2 +4R sin 1+F sin ! " − 2 2 XIFSF F JT UIF ɯOFTTF EFɯOFE BT 4R F = .  (1 R)2 − 5IF USBOTNJTTJPO NBYJNB DPSSFTQPOE UP EJɮFSFOU PTDJMMBUJPO NPEFT XIPTF XBWFMFOHUI JT HJWFO CZ 2nL λm = ,  m Chapter 2 Fundamental Processes in a Laser 8

XIFSF n JT UIF SFGSBDUJWF JOEFY PG UIF DBWJUZ NFEJVN BOE m JT UIF NPEF OVNCFS

5ISFTIPME DPOEJUJPO 4QPOUBOFPVT FNJUUFE MJHIU QSPQBHBUJOH UP UIF SFɰFDUJPO NJSSPS JT BNQMJɯFE CZ TUJNVMBUFE FNJTTJPO JO UIF HBJO NFEJVN 8IFO UIF DBSSJFS EFOTJUZ JO UIF BDUJWF MBZFS PG B MBTFS EJPEF JT IJHI FOPVHI UP BMMPX QPQVMBUJPO JOWFSTJPO γ(ν) >α TUJNVMBUFE FNJTTJPO CFDPNFT EPNJOBOU PWFS MPTTFT 5IJT JOKFDUJPO DVSSFOU WBMVF JT LOPXO BT UIF UISFTIPME DVSSFOU #Z UIF UISFTIPME DPOEJUJPO UIF HBJO NVTU CF IJHIFS UIBO UIF UPUBM SPVOEUSJQ MPTT .BUIFNBUJDBMMZ UIJT SFRVJSFNFOU DBO CF XSJUUFO BT

2 2ikL R e− =1. 

5IF XBWFOVNCFS k PG B QMBOF XBWF DBO CF HFOFSBMMZ XSJUUFO BT k = β + i(γ α) XIFSF β − JT UIF QSPQBHBUJPO DPFɱDJFOU γ JT UIF HBJO PG NFEJVN QFS VOJU MFOHUI XIJDI JT QSPWJEFE CZ TUJNVMBUFE FNJTTJPOT BOE α JT UIF BCTPSQUJPO DPFɱDJFOU <> "QQMZJOH UIJT GPSN PG k UP UIF QSFWJPVT FRVBUJPO POF DBO SFXSJUF JU UP

2 2(γ α)L 2iβL R e − e− =1. 

8F EFɯOF UIF DPOɯOFNFOU GBDUPS Γ BT Γ=1 iβ  5IFO UIF UISFTIPME DPOEJUJPO JT HJWFO − γ CZ ln(R) Γγ = α .  − L -BTFS EJPEFT QSPWJEF NPEFT UIBU BSF QPMBSJ[FE QBSBMMFM UP KVODUJPO 5& BOE QFSQFOEJDVMBS UP UIF KVODUJPO 5. TFF 'JH   5& NPEFT BSF TUSPOHMZ HVJEFE BOE IBWF MPXFS JOUFSOBM MPTTFT " TFNJDPOEVDUPS MBTFS EJPEF VTVBMMZ IBWF IBT 5& QPMBSJ[BUJPO SBUJPT PG BU MFBTU  JO UIF DBTF XIFO UIF DVSSFOU JT XFMM BCPWF UISFTIPME <> Chapter 3 Laser Construction 9

Chapter 3

Laser Construction

*O UIF QSFWJPVT $IBQUFS XF EJTDVTTFE UIF CBTJD QSPQFSUJFT PG TJOHMFNPEF TFNJDPOEVDUPS MBTFST 5IF UZQJDBM FYUFSOBM DBWJUZ EJPEF MBTFS &$%- EFTJHOT TVDI BT UIF -JUUSPX BOE -JUUNBO.FUDBMG DPOɯHVSBUJPOT VTF EJɮSBDUJPO HSBUJOHT GPS XBWFMFOHUI UVOJOH < > *O UIJT $IBQUFS XF BSF HPJOH UP EJTDVTT BO BMUFSOBUJWF &$%- XIJDI PQFSBUFT XJUI B OBSSPX CBOEQBTT ɯMUFS BT UIF XBWFMFOHUITFMFDUJWF QBSU <Ʀ> 8F CFHJO XJUI BO JO USPEVDUJPO PG UIF DBWJUZ EFTJHO 5IFO XF NPWF PO UP SFWJFX UIF PQUJDT TFUVQ FMFDUSPOJD FMFNFOUT BOE UIF NFDIBOJDBM DPOTUSVDUJPO PG UIF JOUFSGFSFODFɯMUFSTUBCJMJ[FE &$%- 'VS UIFSNPSF XF DPOTJEFS QSPCMFNT FODPVOUFSFE XJUI UIF TFUVQ BOE QSPQPTF QPTTJCMF TPMV UJPOT 'JOBMMZ XF EFTDSJCF UIF PQUJDBM BMJHONFOU QSPDFEVSF GPS TJOHMFNPEF PQFSBUJPO

3.1 Design Overview

5IF CBTJD TFUVQ PG UIF FYUFSOBM DBWJUZ EJPEF MBTFS JT JMMVTUSBUFE JO 'JH  5IF MJHIU FNJUUFE CZ B MBTFS EJPEF -% XJUI BO BOUJSFɰFDUJPODPBUFE PVUQVU GBDFU JT DPMMJNBUFE CZ BO BTQIFSJD MFOT JO UIF DPMMJNBUPS $-  " QBSUJBMMZ SFɰFDUJOH NJSSPS PVUQVU DPVQMFS 0$ XJUI USBOTNJTTJPO PG  BOE SFɰFDUJPO PG  QSPWJEFT UIF GFFECBDL JOUP UIF EJPEF " IJHI TUBCJMJUZ PG UIF PQUJDBM GFFECBDL JT BDIJFWFE CZ QMBDJOH BO BTQIFSJD MFOT XJUI GPDBM MFOHUI f   NN BOE OVNFSJDBM BQFSUVSF NA   B TNBMM SPUBUJPO PG UIF NJSSPS XJMM OPU DBVTF UIF NJTBMJHONFOU JO GSPOU PG UIF PVUQVU DPVQMFS 0$ BU UIF GPDBM MFOHUI EJTUBODF 5IF QPTJUJPO PG UIF 0$ DBO CF UVOFE CZ B QJF[PFMFDUSJD USBOTEVDFS 1;5 GPS UIF QVSQPTF PG DBWJUZ MFOHUI WBSJBUJPO " OBSSPXCBOE IJHIUSBOTNJTTJPO JOUFSGFSFODF

OC

LD CL IF L1 PZT L2 Fig. 3.1 External cavity diode laser design. LD - laser diode, CL - collimator, IF - interference filter, L1 - aspheric lens, PZT - piezo-electric transducer, OC - output coupler, L2 - output colli- mation lens. Chapter 3 Laser Construction 10

ɯMUFS *' JT MPDBUFE CFUXFFO UIF -% BOE 0$ BOE QSPWJEFT XBWFMFOHUI UVOJOH " TFDPOE MFOT f   NN NA   TIPVME DPMMJNBUF UIF PVUQVU CFBN *O DPOUSBTU UP UIF -JUUSPX MBTFS EFTJHO SFɰFDUJPO BOE XBWFMFOHUI UVOJOH JO PVS DBTF BSF QFSGPSNFE CZ UXP EJɮFSFOU FMFNFOUT 0$ BOE *' <> 5IF MBTFS EJPEF DPMMJNBUJPO UVCF BOE DBWJUZ PQUJDT BSF QMBDFE JO BO BMVNJOVN IPVTJOH UP JTPMBUF UIFN GSPN UIF MBCPSBUPSZ FOWJSPONFOU

3.2 Interference Filter

5IF LFZ UP UIF XBWFMFOHUI UVOJOH PG UIF DBWJUZ JT BO JOUSBDBWJUZ JOUFSGFSFODF ɯMUFS *UT XBWFMFOHUI TFMFDUJWJUZ JT CBTFE PO NVMUJQMF SFɰFDUJPOT CFUXFFO UXP IJHIMZ SFɰFDUJWF GBDFUT XJUIJO JUT EJFMFDUSJD DPBUJOHT BOE CFIBWFT BT B UIJO 'BCSZ1§SPU §UBMPO " ɯMUFS PG UIJT LJOE NBZ CF DPOTUSVDUFE CZ EFQPTJUJOH UXP SFɰFDUJWF DPBUJOHT XJUI B UIJO HMBTT QMBUF CFUXFFO UIFN < > 5P VOEFSTUBOE XIBU IBQQFOT XIFO XF UJMU UIF ɯMUFS MFU VT DPOTJEFS UIF DIBSBDUFSJTUJDT PG UIF 'BCSZ1§SPU JOUFSGFSPNFUFS "T XF EJTDVTTFE JO $IBQUFS  JUT USBOT NJUUBODF JT HJWFO CZ UIF FRVBUJPO 1 T = 2 δ ,  1+F sin 2 2π XIFSF F JT UIF ɯOFTTF BOE δ = λ nd cos β JT UIF QIBTF TIJGU PG UIF JOUFSGFSPNFUFS XJUI UIF SFGSBDUJWF JOEFY n UIF UIJDLOFTT d BOE UIF BOHMF PG JODJEFODF β %VF UP UIF BOHMF PG JODJEFODF UIF PQUJDBM MFOHUI JODSFBTFT XJUI B GBDUPS cos β TFF 'JH   5IF JOUFSGFSFODF ɯMUFS IBT QFSJPEJD USBOTNJTTJPO QFBLT BU XBWFMFOHUIT HJWFO CZ 2nd cos β λ = = λ0 cos β,  m

XIFSF λ0 JT UIF XBWFMFOHUI DBVTJOH NBYJNVN USBOTNJTTJPO BU B OPSNBM BOHMF PG JODJEFODF BOE m JT BO JOUFHFS 6TJOH 4OFMMƫT MBX XF DBO SFXSJUF UIF USBOTNJUUFE XBWFMFOHUI PG UIF ɯMUFS BT TFF 'JH  

2 2 sin α λ = λ0 1 sin β = λ0 1 ,  − − n2 % & XIFSF α JT UIF JODJEFODF BOHMF PVUTJEF PG UIF ɯMUFS 5IF XBWFMFOHUI UVOJOH DBO CF BD DPNQMJTIFE CZ UJMUJOH UIF ɯMUFS XJUI SFTQFDU UP UIF JODJEFOU CFBN " EFSJWBUJPO PG UIFTF FRVBUJPOT DBO CF GPVOE JO 3FG <> 'VSUIFS JOGPSNBUJPO BCPVU PQUJDBM QSPQFSUJFT PG DPBUJOHT GPS JOUFSGFSFODF ɯMUFST DBO CF GPVOE JO 3FGT < >

3.3 Electrical Control Parts

5IF PQFSBUJPO PG B MBTFS EJPEF SFRVJSFT B IJHIMZ TUBCMF DVSSFOU DPOUSPMMFS BT XFMM BT BO BDUJWF DPOUSPM PG UIF MBTFS EJPEF UFNQFSBUVSF #FDBVTF PG UIJT JO BEEJUJPO UP B XFMM FOHJOFFSFE NFDIBOJDBM EFTJHO BOE PQUJDBM BMJHONFOU XF OFFE UP QSPWJEF BO FMFDUSPOJD TZTUFN UP FOTVSF QSFDJTF UVOBCJMJUZ BOE TUBCJMJUZ PG B MBTFS TZTUFN 5P EP UIJT XF DPNCJOF Chapter 3 Laser Construction 11

Fig. 3.2 Fabry-Pérot type interference filter with a sandwich design. The angle α is the incidence angle, β is a reflection angle in interferometer and n is the refractive index of glass.

UXP 1FMUJFS FMFNFOUT B TFOTJUJWF UIFSNJTUPS 5IPSMBCT 5), BOE BO FMFDUSPOJD DPOUSPM TZTUFN 5PQUJDB 4:4 %$  XJUI B UFNQFSBUVSF DPOUSPM NPEVMF %5$  BOE DVSSFOU DPOUSPMMFS %$$   5P CPUI QSPUFDU UIF MBTFS EJPEF BOE UP QSPWJEF DVSSFOU NPEVMBUJPO QPSUT BO BEEJUJPOBM QSPUFDUJPO CPBSE JT JOUFHSBUFE JOUP UIF IPVTJOH 5IF DJSDVJU JT CBTFE PO 3FG <> BOE JUT TDIFNBUJD JT BUUBDIFE JO "QQFOEJY " 8F VTF B NBMF QJO TVC% DPOOFDUPS DBCMF GPS UIF UFNQFSBUVSF DPOUSPMMFS BOE B GFNBMF TVC% DPOOFDUPS DBCMF GPS UIF DVSSFOU DPOUSPMMFS 5IF CPBSE PɮFST UIF GPMMPXJOH GFBUVSFT

 " DPNCJOBUJPO PG GPVS MPXQBTT ɯMUFST QSPUFDUT UIF MBTFS EJPEF GSPN WPMUBHF TQJLFT JO UIF QPXFS TVQQMZ

 4DIPUULZ EJPEFT QSPUFDU UIF MBTFS EJPEF JG UIF XSPOH JOQVU WPMUBHF QPMBSJUZ JT BQ QMJFE

 5FTU QPJOUT GPS B GPVSQPJOU NFBTVSFNFOU UP EFUFSNJOF UIF DVSSFOU SVOOJOH UISPVHI UIF MBTFS EJPEF 5IF GPJM SFTJTUPS VTFE IFSF IBT B SFTJTUBODF PG R   Ω BOE CZ NFBTVSJOH UIF WPMUBHF U UIF DVSSFOU DBO CF DBMDVMBUFE GSPN U V I = = 10 .  R Ω

 *G B QIPUPEJPEF JT JOUFHSBUFE JO UIF DBTF PG UIF MBTFS EJPEF JUT TJHOBM DBO CF BNQMJɯFE BOE DBO CF SFBE PVU GSPN BO 4." DPOOFDUPS 5IF QIPUPEJPEF BNQMJɯFS SFRVJSFT BO FYUFSOBM  7 QPXFS TVQQMZ

3.3.1 Temperature Control System

*O 'JH  XF JMMVTUSBUF UIF UISFF NBJO DPNQPOFOUT PG UIF UIFSNJTUPSDPOUSPMMFE TZTUFN XIJDI SFHVMBUF UIF UFNQFSBUVSF PG UIF DBWJUZ "  LΩ UIFSNJTUPS 5IPSMBCT 5), QSPWJEFT UIF FMFDUSJDBM GFFECBDL UP UIF 1FMUJFS EFWJDF WJB B UFNQFSBUVSF DPOUSPMMFS 5PQUJDB %5$   *O UIF GPMMPXJOH 4FDUJPO XF EJTDVTT IPX UIF UIFSNJTUPS DBO UBLF BOE QSPDFTT Chapter 3 Laser Construction 12

TH10K Unit to be cooled Temperature signal DTC 110 Cooling plate Cooler current Peltier device Fig. 3.3 Temperature control system consisting of Peltier device, TH10K thermistor, DTC 110 con- troller, cooling plate and the unit to be cooled.

UIF JOGPSNBUJPO BCPVU UIF UFNQFSBUVSF BOE XIBU JT UIF QIZTJDBM FɮFDU CFIJOE UIF 1FMUJFS EFWJDF

5IFSNJTUPS 5IFSNJTUPST BSF UIFSNBMMZ TFOTJUJWF SFTJTUPST BOE IBWF EFQFOEJOH PO UIF UZQF B OFHBUJWF /5$ PS B QPTJUJWF 15$ SFTJTUBODFUFNQFSBUVSF DPFɱDJFOU /5$T PɮFS NFDIBOJDBM UIFSNBM BOE FMFDUSJDBM TUBCJMJUZ UPHFUIFS XJUI B IJHI EFHSFF PG TFOTJ UJWJUZ <> 5IF SFMBUJPOTIJQ CFUXFFO UFNQFSBUVSF BOE SFTJTUBODF JT OPU MJOFBS " HPPE BQQSPYJNBUJPO UP FYQMBJO UIF DPSSFMBUJPO CFUXFFO UIF UFNQFSBUVSF BOE UIF UIFSNJTUPSƫT SFTJTUBODF JT QSPWJEFE CZ UIF 4UFJOIBSU)BSU FRVBUJPO <>

1 2 3 = A + B ln(R/R25 )+C ln (R/R25 ) D ln (R/R25 ),  T ◦ ◦ − ◦

XIFSF T JT UIF UFNQFSBUVSF R JT UIF NFBTVSFE UIFSNJTUPS SFTJTUBODF R25◦C JT UIF UIFS NJTUPS SFTJTUBODF BU UIF UFNQFSBUVSF 25◦C BOE A B BOE C BSF DPOTUBOUT 'VSUIFS JO GPSNBUJPO BCPVU UIFSNJTUPST BT UIFSNPNFUFST BOE IPX UIF DIBOHF JO SFTJTUBODF DBO CF DPOWFSUFE JOUP B GFFECBDL TJHOBM DBO CF GPVOE JO 3FG <> "O FQPYZDPBUFE  LΩ UIFSNJTUPS XJUI JOTVMBUFE MFBET JT TVJUBCMF GPS PVS QVSQPTFT *O UIF UFNQFSBUVSF SBOHF GSPN  ◦C UP  ◦C UIF 5), DBO CF NPEFMMFE XJUI UIF EBUB JO 5BC  <>

1 1 1 1 R25◦ (kΩ) A(K− ) B(K− ) C(K− D(K− ) 10 3.354 10 3 2.562 10 4 2.141 10 6 7.241 10 8 × − × − × − × −

Tab. 3.1 The data for thermistor (Thorlabs TH10K [22]): R25◦C is the thermistor resistance at 25◦C, and A, B and C are constants.

1FMUJFS FMFNFOU 5IF TFDPOE QBSU PG UIF UFNQFSBUVSF DPOUSPM TZTUFN JT B 1FMUJFS EFWJDF *UT KPC JT UP IFBU PS DPPM UIF DBWJUZ EFQFOEJOH PO UIF SFRVJSFE UFNQFSBUVSF 8F TUBSU XJUI UIF EJTDVTTJPO PG UIF 4FFCFDL FɮFDU BOE UIFO NPWF PO UP UIF DPNNFSDJBM 1FMUJFS EFWJDF BOE JUT BQQMJDBUJPO <> 5IF 4FFCFDL FɮFDU JT B UIFSNPFMFDUSJD QIFOPNFOPO UIBU EFTDSJCFT UIF HFOFSBUJPO PG BO FMFDUSJDBM WPMUBHF EVF UP B UFNQFSBUVSF EJɮFSFODF CFUXFFO UIF FOET PG B UIFSNPFMFDUSJD Chapter 3 Laser Construction 13

50

40

30

20

10 Temperature (°C) 0 10 20 30 Resistance (kΩ)

Fig. 3.4 Temperature versus resistance for TH10K.

Conductor A T1 T2 V

Conductor B

Fig. 3.5 Two conductors, A and B, in a temperature gradient T2 >T1. A net thermovoltage is mea- sured with a voltmeter.

EFWJDF 5IF 4FFCFDL WPMUBHF EFQFOET PO UIF NBUFSJBM 'PS B TNBMM UFNQFSBUVSF EJɮFSFODF ∆T UIF SFMBUJPOTIJQ CFUXFFO UIF WPMUBHF EJɮFSFODF ∆V BOE UIF UFNQFSBUVSF EJɮFSFODF JT BQQSPYJNBUFMZ MJOFBS <> ∆V = S∆T,  XIFSF S JT UIF 4FFCFDL DPFɱDJFOU 8IFO UXP DPOEVDUPST A BOE B IBWJOH EJɮFSFOU 4FF CFDL DPFɱDJFOUT BSF DPOOFDUFE BU UXP FOET BU UIF MPDBM UFNQFSBUVSF T1 BOE UIF PUIFS UXP FOET BSF BU UIF MPDBM UFNQFSBUVSF T2 UIF WPMUBHF EJɮFSFODF CFUXFFO UIFN DBO CF NFB TVSFE 'JH   5IJT TJNQMF EFWJDF JT DBMMFE B UIFSNPDPVQMF 5IJT FɮFDU PDDVST XIFOFWFS FMFDUSJDBM DVSSFOU ɰPXT UISPVHI UXP EJTTJNJMBS DPOEVDUPST %FQFOEJOH PO UIF EJSFDUJPO PG DVSSFOU ɰPX UIF TZTUFN PG UXP EJTTJNJMBS DPOEVDUPST XJMM FJUIFS BCTPSC PS SFMFBTF IFBU 8IFO ∆T = T2 T1 JT OPU FRVBM UP [FSP FBDI DPOEVDUPS QSPEVDFT B UIFSNPWPMUBHF 5IF − NBHOJUVEF PG UIF NFBTVSFE WPMUBHF EJɮFSFODF CFUXFFO UIF UXP DPOEVDUPST JT

V = V V = S ∆T S ∆T = S ∆T,  AB A − B A − B AB XIFSF S = S S JT UIF FɮFDUJWF 4FFCFDL DPFɱDJFOU PG UIF DPOEVDUPS QBJS #BTFE AB A − B PO LOPXO UFNQFSBUVSFT POF DBO BMTP QSFEJDU UIF WPMUBHF VAB Chapter 3 Laser Construction 14

N PNP

- + - + - + + - + - + -

U I

Fig. 3.6 Aseriesofalternatingn-andp-typesemiconductorelements.

Fig. 3.7 The design of a commercial Peltier device. Adopted from Ref. [26].

5IF 1FMUJFS FɮFDU JT UIF SFWFSTF QIFOPNFOPO PG UIF 4FFCFDL FɮFDU 5IF 1FMUJFS FMFNFOU DBO CF VTFE UP QVNQ IFBU CFUXFFO UXP KVODUJPOT XIFO B WPMUBHF JT BQQMJFE 5ZQJDBMMZ B TJOHMF 1FMUJFS FMFNFOU JT OPU TVɱDJFOU GPS UFDIOJDBM TPMVUJPOT CFDBVTF PG JUT TNBMM PVUQVU QPXFS 5P JODSFBTF JUT PVUQVU QPXFS DPNNFSDJBM 1FMUJFS EFWJDFT DPOTJTU PG NBOZ OUZQF BOE QUZQF TFNJDPOEVDUPS FMFNFOUT XIJDI BSF JOEJWJEVBMMZ DPOOFDUFE JO TFSJFT VTJOH IPU BOE DPME NFUBMMJD KVODUJPOT 'JH   "T B SFTVMU PG UIJT DIBSHF DBSSJFST ɰPX GSFFMZ JO CPUI EJSFDUJPOT BOE QSPWJEF B IFBU ɰPX JO UIF TBNF EJSFDUJPO <> " DPNQMFUF 1FMUJFS EFWJDF MPPLT MJLF B TBOEXJDI XJUI UXP DFSBNJD QMBUFT BOE B TFSJFT PG NBOZ QO QBJST 'JH   "T B DPOTFRVFODF PG UIJT BSDIJUFDUVSF B MBSHF TVSGBDF BSFB DBO CF BDIJFWFE 5IF BNPVOU PG IFBU QVNQFE GSPN POF TVSGBDF UP UIF PUIFS EFQFOET PO UIF BQQMJFE DVSSFOU UP UIF EFWJDF Chapter 3 Laser Construction 15

Fig. 3.8 Piezoelectric effect in a quartz crystal. The positively charged ions represent silicon and the negatively charged ions represent oxygen. Adopted from [27].

3.3.2 Piezoelectrically Tunable Resonator

4JODF UIF SFTPOBODF GSFRVFODJFT PG B DBWJUZ EFQFOE PO JUT MFOHUI UIFZ DBO CF DIBOHFE CZ JOTFSUJOH B MFOHUIWBSZJOH FMFNFOU MJLF B QJF[PFMFDUSJD BDUVBUPS <> 5IF QIFOPNFOPO UIBU UIF QSFTTVSF BQQMJFE UP B QJF[PFMFDUSJD NBUFSJBM DBO QSPEVDF BO FMFDUSJD QPUFOUJBM XBT ɯSTU EFUFDUFE JO  CZ +BDRVFT BOE 1JFSSF $VSJF <> *O TVDI B NBUFSJBM UIF GPSDF BMPOH BO BUPNJD BYJT DBVTFT B DIBSHF CBMBODF DIBOHF 'JH   5IJT JNCBMBODF SFTVMUT JO UIF GPSNBUJPO PG BO FMFDUSJD EJQPMF BOE BO FMFDUSJD ɯFME $POUSBSZ JG BO FMFDUSJD ɯFME JT BQQMJFE UP B QJF[PFMFDUSJD NBUFSJBM UIF DSZTUBM HFPNFUSZ XJMM CF EFGPSNFE 5IJT JOWFSTF QJF[P FMFDUSJD FɮFDU JT VTFE JO QJF[PFMFDUSJD BDUVBUPST XIPTF MFOHUI DBO CF DIBOHFE CZ BQQMZJOH B WPMUBHF 'PS B QIZTJDBM EFTDSJQUJPO PG UIF QJF[PFMFDUSJD FɮFDU B GFX CBTJD SFMBUJPOT IBWF UP CF DPO TJEFSFE <> " EJFMFDUSJD NBUFSJBM IBT UIF QSPQFSUZ UIBU BO BQQMJFE FMFDUSJDBM ɯFME Ej DBO QSPEVDF B DIBSHF TFQBSBUJPO XIJDI JT FYQMBJOFE CZ UIF QPMBSJ[BUJPO WFDUPS Pi = χijEj XIFSF χij JT UIF NBUFSJBMƫT TVTDFQUJCJMJUZ 5IF UPUBM TVSGBDF DIBSHF EFOTJUZ JT HJWFO CZ UIF EJFMFDUSJD EJTQMBDFNFOU WFDUPS

Di = Ei + Pi =(1+χij)Ei = ϵijEj (i, j =1, 2, 3).  1JF[PFMFDUSJD NBUFSJBMT DBO CF BMTP QPMBSJ[FE CZ BQQMZJOH NFDIBOJDBM QSFTTVSF )PPLƫT MBX GPS MJOFBS FMBTUJD NBUFSJBMT BMMPXT VT UP XSJUF UIF DPOWFSTF QJF[PFMFDUSJD FɮFDU BT

Sij = dkijEk, 

XIFSF Sij JT UIF TUSBJO UFOTPS BOE dijk JT B UIJSE SBOL UFOTPS DPOUBJOJOH UIF QJF[PFMFDUSJD DPFɱDJFOUT Chapter 3 Laser Construction 16

z

L

L

U

Fig. 3.9 Ring actuator length L changing with an applied voltage U.

5IFSF BSF NBOZ EJɮFSFOU QJF[PFMFDUSJD NBUFSJBMT XIJDI DBO CF VTFE GPS EJɮFSFOU BQ QMJDBUJPOT "U UIF FOE PG UIF T QJF[PFMFDUSJD QFSGPSNBODF XBT EJTDPWFSFE JO MFBE [JSDPOBUF UJUBOBUF 1;5  "U SPPN UFNQFSBUVSF JUT VOJU DFMM TIPXT B EJQPMF NPNFOU BOE IBT QJF[PFMFDUSJD QSPQFSUJFT %VF UP JUT IJHI QJF[PFMFDUSJD DPFɱDJFOU 1;5 JT UIF NPTU VTFE QJF[PFMFDUSJD NBUFSJBM <> 5IF EFTDSJCFE NBUFSJBMT DBO CF VTFE UP CVJME B SJOH QJF[PFMFDUSJD BDUVBUPS UIBU PQFSBUFT BDDPSEJOH UP UIF DPOWFSTF QJF[PFMFDUSJD FɮFDU 5IF MFOHUI DIBOHF ∆L PG B SJOH BDUVBUPS BMPOH UIF EJSFDUJPO PG UIF FMFDUSJD ɯFME 'JH  EFQFOET PO UIF BQQMJFE WPMUBHF U BOE UIF QJF[PFMFDUSJD DPFɱDJFOU

∆L = SzL = dzzEzL0 = dzzU, 

XIFSF dzz JT UIF QJF[PFMFDUSJD DPFɱDJFOU U JT UIF BQQMJFE WPMUBHF Ez JT UIF FMFDUSJD ɯFME JO UIF [EJSFDUJPO Sz JT B TUSBJO JO UIF [EJSFDUJPO BOE L JT UIF SJOH XJEUI

3.4 Mechanical Design of an ECDL

*O UIJT 4FDUJPO XF SFQPSU PO UIF NFDIBOJDBM EFTJHO PG PVS &$%- XIJDI XBT EFWFMPQFE BU .12 .BY 1MBODL *OTUJUVUF PG 2VBOUVN 0QUJDT  5IF 'JHVSF  TIPXT B % TDIFNBUJD PG UIF &$%- GSPN UXP QPJOUT PG WJFX XJUIPVU DPWFS  5P BWPJE BOZ DPOTUSVDUJPO QSPCMFNT JU JT BEWJTFE UP DPNQMFUF UIF BTTFNCMZ PG UIF &$%- TUFQ CZ TUFQ BDDPSEJOH UP UIF GPMMPXJOH JOTUSVDUJPOT

4POJDBUJPO "GUFS BSSJWJOH GSPN UIF NBDIJOF TIPQ UIF NFDIBOJDBM QBSUT BSF VTVBMMZ EJSUZ BOE GBUUZ XJUI TNBMM QBSUJDMFT TUJDLJOH JO UIF DPSOFST 4JODF UIF DBWJUZ XJMM CF MPDBUFE JO B WBDVVN FWFSZ QBSU NVTU CF DMFBOFE WFSZ XFMM 8F DMFBO UIF QBSUT VTJOH BO VMUSBTPOJD CBUI 4POPTXJTT 48  ) XJUI B GSFRVFODZ PG  L)[ <> *O UIJT CBUI UIF BJS CVCCMFT HSPX BOE DPMMBQTF XIJDI DBO SFNPWF PSHBOJD DPNQPVOET GSPN UIF TVSGBDF PG UIF NBUFSJBMT BOE JO UIJT XBZ DMFBO UIFN 5IF XIPMF DMFBOJOH QSPDFTT DBO CF DPNQMFUFE BDDPSEJOH UP 3FG <> Chapter 3 Laser Construction 17

 1VU UIF QBSUT JO UIF CBUI BOE TPOJDBUF UIFN BU  ◦C GPS  NJOVUFT

 "GUFS UIF TPOJDBUJPO ɰVTI FWFSZ TVSGBDF XJUI EFJPOJ[FE XBUFS BOE UIFO XJUI BDFUPOF BOE JTPQSPQBOPM

 5P SFNPWF UIF DIFNJDBM DPNQPOFOUT ɰVTI FWFSZ QBSU BHBJO XJUI EFJPOJ[FE XBUFS

 "GUFS DMFBOJOH ESZ BOE TUPSF BMM UIF QBSUT PO B DMFBO TVSGBDF FH BMVNJOVN GPJM

 5P BWPJE UIVNC QSJOUT BGUFS UIJT BMM QBSUT TIPVME CF UPVDIFE POMZ XJUI HMPWFT

$POTUSVDUJPO *O UIF OFYU TUFQ NBLF TVSF UIBU BMM UIF QBSUT BSF ESZ BOE SFBEZ UP VTF 8F CFHJO UIF BTTFNCMZ XJUI DBWJUZ BEKVTUNFOU *O UIF GPMMPXJOH UFYU BMM OVNCFST SFGFS UP 'JH  5IF DPMMJNBUPS JT TDSFXFE JOUP UIF GSPOU TJEF PG UIF TNBMM BMVNJOVN IPVTJOH   5IF JOUFSGFSFODF ɯMUFS JT NPVOUFE BOE TJUT PO B  NN PG MFOHUI TNBMM DZMJOESJDBM QJO XIJDI QSPWJEFT B TUBCMF NPVOU QPTJUJPO BOE BMMPXT UIF SPUBUJPO   *O UIJT XBZ UIF JODJEFODF BOHMF PG UIF CFBN DBO CF FBTJMZ DIBOHFE CZ IBOE 5P BDIJFWF B QSFDJTF BEKVTU NFOU VTF UIF TDSFX PO UIF NPVOU UPQ   5IF PQUJDBM GFFECBDL FMFNFOUT BSF IPVTFE JO UIF EJɮFSFOU FODMPTVSFT   5IF MFOT CFUXFFO UIFN JT QMBDFE JO UIF DJSDVMBS IPMF   5P BWPJE GSJDUJPO XIFO UIF MFOT SPUBUFT VTF B WJUPO 0SJOH PO UIF MFOT BOE QVU B TNBMM BNPVOU PG WBDVVN HSFBTF 0,4  BSPVOE JU CFGPSF JOTFSUJOH %JSFDUMZ VOEFS UIF DBWJUZ IPVTJOH BSF UXP 1FMUJFS FMFNFOUT   5P FOTVSF PQUJNBM UIFSNBM DPOEVDUJWJUZ UIFSNBM QBTUF TIPVME CF BQQMJFE BU FBDI 1FMUJFS FMFNFOU JOUFSGBDF 5IF 1FMUJFS FMFNFOUT UIFSNJT UPS BOE QJF[P BSF DPOOFDUFE UP UIF QSPUFDUJPO CPBSE   5P QMVH BOE VOQMVH UIF MBTFS XJUIPVU PQFOJOH UIF IPVTJOH UIF CBDLQMBUF XJUI WBDVVN GFFEUISPVHIT JT DPOTUSVDUFE  CFDBVTF PG UIF EFTJHO NJTUBLF UIF CBDL QMBUF SFRVJSFT B TNBMM IPMF ESJMMJOH GPS QJF[P DPOOFDUJPO  5P QSPUFDU UIF MBTFS GSPN NFDIBOJDBM WJCSBUJPOT UIF DBWJUZ IPVTJOH JT QMBDFE JO B WBDVVN DIBNCFS   5IF &$%- TFUVQ JT JTPMBUFE GSPN UIF PQUJDBM UBCMF CZ QMBDJOH JU PO B CSFBECPBSE

"TTFNCMJOH PVUDPVQMFS UP QJF[P *O PVS DBWJUZ EFTJHO UIF 1;5 SJOH NVTU CF HMVFE CZ TorrSealUP UIF PVUQVU DPVQMFS NJSSPS UP NBOJQVMBUF UIF DBWJUZ MFOHUI TFF 'JH   *O UIF GPMMPXJOH 4FDUJPO XF XJMM EFTDSJCF IPX UP EP UIJT PO UIF CFTU XBZ " HPPE TUSBUFHZ GPS UIJT QSPDFTT JT BMTP QSFTFOUFE JO 3FG <> 'JSTUMZ QMBDF UIF PVUQVU DPVQMFS NJSSPS PO B GFX MBZFST PG PQUJDBM QBQFS BOE DIFDL UIBU UIF QBSUJBMMZ SFɰFDUJOH TJEF QPJOUT VQ 4FDPOE NBLF TVSF UIBU UIF VQQFS TJEF JT WFSZ DMFBO 5IFO QMBDF UIF QJF[P PO UIF NJSSPS JO UIF DPSSFDU PSJFOUBUJPO 5P CF TVSF UIBU UIF HMVF DBO OPU FYQBOE UP UIF JOTJEF PG UIF QJF[P SJOH QVU POMZ GPVS TNBMM ESPQT PG HMVF JO UIF DPSOFST 'JOBMMZ HFOUMZ QMBDF B XFJHIU PO UIF UPQ PG UIF QJF[P UP EJTUSJCVUF UIF QSFTTVSF VOJGPSNMZ PO UIF BDUVBUPS CVU EP OPU EBNBHF UIF PVUQVU DPVQMFS  +VTU BGUFS ɯOJTIJOH UIF HMVJOH JU JT B HPPE JEFB UP DIFDL CZ FZF UIBU FWFSZUIJOH JT QBSBMMFM BOE JO HPPE DPOEJUJPO

"TTFNCMJOH 5IFSNJTUPS /PX XF EFTDSJCF UIF BTTFNCMZ PG UIJT UZQF PG UIFSNJTUPS 'PS CFTU BDDVSBDZ PG UFNQFSBUVSF DPOUSPM UIF UIFSNJTUPS IBT UP CF HMVFE DMPTF UP UIF VOJU UP Chapter 3 Laser Construction 18

Fig. 3.10 A 3-D schematic of the mechanical design: (1) - cavity housing, (2) - vacuum chamber, (3) - thermoplate, (4) - collimation tube, (5) - interference filter, (6) - piezo, (7) - out-coupler, (8) - protection board, (9) - window, (10) - cat eye lens, (11) - collimation lens, (12) - backplate with vacuum feedthroughs , (13) - two Peltier elements, (14) - thermistor. Chapter 3 Laser Construction 19

Fig. 3.11 The assembly of piezo to output coupler using TorrSeal glue.

CF DPPMFE *O PVS DBTF JU JT MPDBUFE JO UIF IPVTJOH PG UIF MBTFS 8F VTF &105&, ) UIFSNBMMZ DPOEVDUJWF FQPYZ XJUI B NJYJOH SBUJP PG  CZ XFJHIU 5IF IPMF GPS UIF UIFSNJTUPS TIPVME CF  NN JO EJBNFUFS BEEJUJPOBM ESJMMJOH NBZ CF SFRVJSFE  "GUFS CBLJOH JO UIF PWFO GPS POF IPVS BU  ◦C UIF HMVF TIPVME UVSO B EBSL SFE 'JH  

3.5 Collimator

*O UIF ɯSTU DIBQUFS XF EFTDSJCFE UIF TUSVDUVSF PG B MBTFS EJPEF &YUFSOBMDBWJUZ TFNJDPO EVDUPS MBTFST BSF DPNQBDU FBTJMZ QVNQFE BOE IBWF MPOH MJGFUJNFT <> *O PVS DBTF XF VTF B UVOBCMF 'BCSZ1§SPU MBTFS EJPEF &BHMFZBSE 1IPUPOJDT &:138& 405 XJUI QBSBNFUFST

 $BWJUZ MFOHUI LD = NN

4  3FɰFDUJWJUZ BU GSPOU GBDFU rff =3− 

 3FGSBDUJWF JOEFY GPS λ   ON BU  ◦C  n =4.52 < >

 3FDPNNFOEFE PQFSBUJOH UFNQFSBUVSF SBOHF JT GSPN  ◦C UP  ◦C

 "U  ◦C UIF EJPEF IBT B UVOJOH SBOHF GSPN  ON UP  ON

 5IF BCTPMVUF NBYJNVN DVSSFOU JT Imax = 140 N"

%VF UP UIF TNBMM TJ[F PG JUT BDUJWF MBZFS UIJT UZQF PG MBTFS EJPEF IBT B XJEFBOHMF SB EJBUJPO QBUUFSO 5IF FNJUUFE CFBN JT EJWFSHFOU BOE SFRVJSFT BTTPDJBUFE PQUJDT XIJDI Chapter 3 Laser Construction 20

Fig. 3.12 The assembly of the thermistor into the cavity housing. Chapter 3 Laser Construction 21

Fig. 3.13 Collimator from the back point of view.

QSPWJEF FɱDJFOU DPMMFDUJPO PG UIF SBEJBUJPO <> 5IJT DBO CF BDIJFWFE XJUI B DPMMJNBUPS XIJDI DPOWFSUT UIF EJWFSHFOU CFBN GSPN B MBTFS EJPEF JOUP B DPMMJNBUFE CFBN 8F VTF B DPMMJNBUPS XJUI BO BTQIFSJD MFOT <> )PXFWFS UIF CFBN QSPɯMF JT TUJMM FMMJQUJDBM BT B SFTVMU PG BTUJHNBUJTN 'PS PVS DBWJUZ BSDIJUFDUVSF XF EFDJEFE UP VTF UIF DPMMJNBUPS UZQF 4DI¢GUFS ,JSDIIPȷ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hapter 3 Laser Construction 22

3.6 Aligning the Extended Cavity

0ODF UIF MBTFSƫT NFDIBOJDBM TFUVQ JT DPOTUSVDUFE BOE BMM FMFDUSJDBM QBSUT BSF SFBEZ UP VTF XF DBO TUBSU XJUI UIF BMJHONFOU QSPDFEVSF 5IF 'JHVSF  TIPXT B QIPUP PG UIF &$%- GSPN UIF UPQ 5IF MBTFS CFBN TIPVME CF SFɰFDUFE GSPN UIF PVUQVU DPVQMFS EJSFDUMZ CBDL JOUP UIF TFNJDPOEVDUPS MBTFS EJPEF )BWJOH TVDDFTTGVMMZ BMJHOFE BOE DPMMJNBUFE UIF MBTFS EJPEF POF DBO QSPDFFE XJUI UIF QSPDFTT PG QMBDJOH UIF SFNBJOJOH PQUJDT JO UIF MBTFS IPVTJOH 5IF MFOT DMPTFTU UP UIF MBTFS EJPEF TIPVME CF BMJHOFE ɯSTU TJODF BDDFTT UP JUT NPVOUJOH QPTJUJPO JT SFTUSJDUFE CZ UIF IPVTJOH PG UIF MBTFS "GUFS BTTFNCMZ PG UIF PQUJDT UIF BMJHONFOU PG FBDI DPNQPOFOU TIPVME CF PQUJNJ[FE 'JSTU XJUIPVU UIF JOUFSGFSFODF ɯMUFS UIF ɯSTU MFOT TIPVME CF BMJHOFE TVDI UIBU UIF CFBN JT GPDVTFE PO UIF PVUQVU DPVQMFS 5P BDIJFWF MBTJOH UIF MBTFS EJPEF BOE MFOT QPTJUJPO NVTU CF QFSGFDU BMJHOFE *U JT IFMQGVM UP VTF B NJSSPSQMBUF UP SFɰFDU UIF MBTFS CFBN WFSUJDBMMZ PVU PG UIF IPVTJOH BOE UIFO UP GPDVT JU JO UIF GBSɯFME 4VDDFTTJWF BEKVTUNFOU PG UIF MFOT UP NBYJNJ[F UIF DBWJUZ USBOTNJTTJPO NBZ BMSFBEZ MFBE UP MBTJOH 4FDPOEMZ UIF PSJFOUBUJPO PG UIF PVUQVU DPVQMFS TIPVME CF PQUJNJ[FE CZ DIBOHJOH JUT QJUDI BOE ZBX WJB UIF BEKVTUNFOU TDSFXT PO UIF NPVOU " DPNCJOBUJPO PG UIFTF UXP TUFQT TIPVME SFTVMU JO PQUJDBM GFFECBDL BOE MBTJOH *O UIJT DBTF UIF MBTFS EJPEF TUBSUT MBTJOH BOE UIF PVUQVU QPXFS XJMM JODSFBTF ESBNBUJDBMMZ 'JOBMMZ UIF MBTU MFOT - TIPVME CF BEKVTUFE TVDI UIBU UIF CFBN JT DPMMJNBUFE JO UIF GBSɯFME Chapter 3 Laser Construction 23

Fig. 3.14 The external cavity from the top view. LD - laser diode, CL - collimator, IF - interference filter, L1 - aspheric lens, PZT - piezo-electric transducer, OC - output coupler, L2 - output collimation lens. Chapter 4 Optical Setup 24

Chapter 4

Optical Setup

5IF QSFWJPVT $IBQUFS EFBMU XJUI UIF MBTFS DPOTUSVDUJPO QSPDFEVSF *O UIF GPMMPXJOH $IBQ UFS XF FYQMPSF UIF PQUJDBM TFUVQ PVUTJEF PG UIF MBTFS DBWJUZ "T XF EJTDVTTFE JO $IBQUFS  UIF PVUQVU CFBN JT FMMJQUJDBM BOE OFFET UP CF SFTIBQFE UP NBUDI BT DMPTFMZ BT QPTTJCMF B TEM00 )FSNJUF(BVTTJBO NPEF 5IF MBTFS TPVSDF NVTU BMTP CF QSPUFDUFE GSPN CBDL SFɰFDUJPOT UIBU DBO EBNBHF UIF MBTFS EJPEF PS BEE OPJTF 'VSUIFSNPSF XF XBOU UP DIFDL UIF MBTFSƫT XBWFMFOHUI BOE TJNVMUBOFPVTMZ CF BCMF UP NFBTVSF UIF MBTFSƫT QSPQFSUJFT 5IJT $IBQUFS CFHJOT XJUI B EJTDVTTJPO PO CFBN TIBQJOH 5IFO XF HJWF BO PWFSWJFX PG PQUJDBM EFWJDFT XIJDI BSF DPNNPOMZ VTFE JO TJNJMBS PQUJDBM TFUVQT "GUFS UIJT UIF TFMGCVJMU PQUJDBM TFUVQ XJMM CF QSFTFOUFE

4.1 Anamorphic Prism Pair

5IF PVUQVU CFBN TIBQF DBO CF JOWFTUJHBUFE CZ B $$% BOE UIF TPGUXBSF RayCi 5IF PC TFSWFE CFBN QSPɯMF JO UIF GBSɯFME BQQSPYJNBUFMZ  N GSPN UIF MBTFS JT TIPXO JO 'JH  "DDPSEJOH UP B (BVTTJBO ɯU QSPWJEFE CZ UIF TPGUXBSF UIF NFBTVSFE CFBN FMMJQUJDJUZ JT a ε = b =3.58 TFF 'JH  XIFSF a BOE b SFQSFTFOU UIF NBKPS BOE UIF NJOPS BYFT PG BO FMMJQTF SFTQFDUJWFMZ 8F CFHJO XJUI UIF BOBMZTJT PG UXP HFOFSBM BQQSPBDIFT PG TIBQJOH UIF FMMJQUJDBM EJPEF MBTFS CFBN JOUP B DJSDVMBS POF 0OF XBZ JT UP VTF DZMJOESJDBM MFOTFT UIF PUIFS JT UP FNQMPZ BO BOBNPSQIJD QSJTN QBJS <> 5IF BEWBOUBHFT PG DZMJOESJDBM MFOTFT JO UIF GPSN PG B UFMFTDPQF PWFS QSJTNT BSF UIBU UIF CFBN JT OPU EJTQMBDFE GSPN JUT PSJHJOBM EJSFDUJPO BOE UIBU UXP DZMJOESJDBM MFOTFT DBO CF BEKVTUFE UP DPSSFDU BO BTUJHNBUJTN 6OGPSUVOBUFMZ GPS MBSHF NBHOJɯDBUJPOT UIF UFMFTDPQF MFOHUI CFDPNFT FYUSFNFMZ MPOH DPNQBSFE UP UIBU PG B QSJTN QBJS TZTUFN .PSFPWFS UIF QSJTNT BSF SFMBUJWFMZ FBTZ UP BMJHO 5IF NPTU DPNNPO QSJTN DPOɯHVSBUJPO JT UIF #SFXTUFS UFMFTDPQF BT TIPXO JO 'JH  5IF NBHOJɯDBUJPO M PG UIF QSJTN QBJS JT DBMDVMBUFE JO 3FG <> BOE JT HJWFO CZ

D cos A 2 M = = ,  d cos B ! " XIFSF A JT UIF BOHMF PG JODJEFODF BOE B JT UIF BOHMF PG SFGSBDUJPO " NPVOUFE QSJTN QBJS 5IPSMBCT 14#/4' QSPWJEFT UIF NBHOJɯDBUJPO PG M =3.50 XJUI B CFBN EJTQMBDFNFOU PG L   NN BOE JT UIF CFTU DIPJDF GPS UIF CFBN TIBQF JO PVS DBTF <> 5IJT PQUJDBM EFWJDF TIPVME CF NPVOUFE EJSFDUMZ BGUFS UIF MBTFS JO TVDI B XBZ Chapter 4 Optical Setup 25

b a

Fig. 4.1 Beam shape in the far-field taken by RayCi.Here,a is the major axis and b is the minor axis of an ellipse of the beam.

30o

n L d B A A

B D n

Fig. 4.2 Anamorphic prism pair configuration: n is the refractive index, A is the angle of incidence, B is the angle of refraction, L is the beam displacement, D is the input beam diameter and d is the output beam diameter. Chapter 4 Optical Setup 26

UIBU UIF CFBNƫT NBKPS BYJT XJMM CF SFEVDFE CZ B GBDUPS PG  TFF 'JH   *O UIJT XBZ UIF CFBN DBO CF SFTIBQFE JO UIF GBSɯFME UP BDIJFWF BO FMMJQUJDJUZ PG ε′ = ε/M =1.02

4.2 Optical Devices

*O UIJT 4FDUJPO XF QSFTFOU UIF PQUJDBM EFWJDFT XIJDI DPNQPTF UIF NBJO QBSU PG PVS PQUJDBM TFUVQ 5IFO XF NPWF PO UP UIF TUSVDUVSF PG PQUJDBM EFWJDFT TVDI BT B 'BSBEBZ JTPMBUPS B XBWF QMBUF BOE QPMBSJ[JOH CFBN TQMJUUFS BOE EJTDVTT UIFJS BQQMJDBUJPOT

1PMBSJ[FS "O FMFDUSPNBHOFUJD XBWF DBO CF NBEF MJOFBSMZ QPMBSJ[FE CZ VTJOH B QPMBSJ[FS " QPMBSJ[FS DBO CF DPOTUSVDUFE GSPN B QBSBMMFM HSJE PG UIJO XJSFT XJUI B UIJDLOFTT TNBMM DPNQBSFE UP UIF XBWFMFOHUI <> %VF UP UIF GBDU UIBU POMZ UIF FMFDUSJD ɯFME DPNQPOFOU QFSQFOEJDVMBS UP UIF XJSFT DBO CF USBOTNJUUFE TVDI B EFWJDF BDUT BT B QPMBSJ[FS "DDPSEJOH UP .BMVTƫT MBX <> XIFO UIF CFBN QBTTFT UISPVHI B QFSGFDU QPMBSJ[FS JUT JOUFOTJUZ XJMM CF SFEVDFE CZ cos2(φ) XIFSF φ JT UIF BOHMF CFUXFFO UIF CFBNƫT JOJUJBM QPMBSJ[BUJPO EJSFDUJPO BOE UIF BYJT PG UIF QPMBSJ[FS

*TPMBUPS 5P BWPJE VOXBOUFE CBDLSFɰFDUJPOT JOUP B MBTFS TPVSDF BO PQUJDBM JTPMBUPS TIPVME CF VTFE &WFO B WFSZ MPX MFWFM PG PQUJDBM CBDLSFɰFDUJPO JT TVɱDJFOU UP DBVTF JOTUBCJMJ UJFT QPXFS TQJLFT PS GSFRVFODZ TIJGUT JO TJOHMFGSFRVFODZ TFNJDPOEVDUPS MBTFST <> 5IF TPMVUJPO JT B 'BSBEBZ JTPMBUPS XIJDI JT DPOTJTUT PG B 'BSBEBZ SPUBUPS BO JOQVU BOE BO PVUQVU QPMBSJ[FS 5P VOEFSTUBOE IPX UIF JTPMBUPS TIPVME CF BMJHOFE QSPWJEJOH NBYJNVN GPSXBSE USBOTNJTTJPO BOE SFWFSTF JTPMBUJPO XF EFTDSJCF UIF QIZTJDBM FɮFDUT CFIJOE JUT GVODUJPO *O  .JDIBFM 'BSBEBZ EJTDPWFSFE UIBU UIF QPMBSJ[BUJPO PG MJHIU DBO CF SPUBUFE JO B NBHOFUJD ɯFME BQQMJFE UP B NBHOFUPPQUJD NBUFSJBM <> 5IJT FɮFDU LOPXO BT UIF 'BSBEBZ FɮFDU PDDVST XIFO B NBHOFUJD ɯFME JT JOEVDFE JO UIF TBNF EJSFDUJPO BT UIF QBUI PG UIF MJHIU %JɮFSFOU JOEJDFT PG SFGSBDUJPO GPS UIF MFGU BOE SJHIU DJSDVMBSMZ QPMBSJ[FE MJHIU NFBOT UIBU UIFTF SBZT QSPQBHBUF BU EJɮFSFOU TQFFET UISPVHI UIF NFEJVN 5IF 'BSBEBZ SPUBUPS JT B LFZ DPNQPOFOU PG BO PQUJDBM JTPMBUPS 5IF BNPVOU PG SPUBUJPO JT HJWFO CZ

θ = νBd, 

XIFSF B JT UIF NBHOFUJD ɯFME d JT UIF MFOHUI PG UIF NBHOFUPPQUJD NBUFSJBM BOE ν JT LOPXO BT UIF 7FSEFU DPOTUBOU XIJDI EFQFOET PO UIF NBUFSJBM BOE WBSJFT PO B TNBMM XBWFMFOHUI 1 SBOHF BT λ2 XIFSF λ JT UIF XBWFMFOHUI <> 5IF ɯSTU QPMBSJ[FS JT BEKVTUFE UP DPSSFMBUF XJUI UIF QPMBSJ[BUJPO PG UIF MBTFS CFBN TFF 'JH   5IF MJHIU USBWFMJOH JO 'BSBEBZ SPUBUPS XJMM CFDPNF QPMBSJ[FE BU 45◦ JO B DMPDL XJTF EJSFDUJPO JG UIF DPOEJUJPOT GPS UIF 7FSEFU DPOTUBOU BSF GVMɯMMFE )PXFWFS PVS MBTFS CFBN EFWJBUFT GSPN JTPMBUPSƫT DFOUSBM XBWFMFOHUI TFF 'JH  BOE SPUBUJPO JT OPU BO JEFBM 45◦ )PXFWFS UIF JTPMBUPS DBO CF UVOFE NBJOUBJOJOH GVMM JTPMBUJPO BOE OFBSPQUJNBM 670 2 USBOTNJTTJPO 5IFSFGPSF SPUBUJPO BU 689 ON JT BU 45◦( 689 ) = 43◦ 5IF CBDL SFɰFDUFE MJHIU NVTU CF SPUBUFE BGUFS UIF QSPQBHBUJPO JO UIF 'BSBEBZ EFWJDF JO UIF CBDLXBSE EJSFDUJPO UP Chapter 4 Optical Setup 27

Fig. 4.3 Transmission and isolation profiles for IOT-5-670-VLP Faraday tandem isolator. The shaded region in this plot indicates the tuning range specified for this isolator. Adopted from [36].

Polarizer 1 Faraday rotator Polarizer 2 B

Input Output

B

block reflected Fig. 4.4 A schematic view of an isolator with input and output polarizer and Faraday rotator. The figure above shows the forward light propagation and the figure below the backward light- propagation. Chapter 4 Optical Setup 28

90◦ GSPN UIF IPSJ[POUBM UP FOTVSF UIF GVMM JTPMBUJPO #FDBVTF PG UIJT UIF TFDPOE QPMBSJ[FS NVTU CF SPUBUFE UP 90◦ 43◦ = 47◦ *O DPOTPOBODF XJUI UIF .BMVTƫT -BX UIF USBOTNJUUBODF − JT BEEJUJPOBMMZ SFEVDFE CZ

I 2 2 1 =1 cos (φ)=1 cos (47◦ 43◦)=0.5%  − I0 − − −

XIJDI JT BDDFQUBCMF DPNQBSFE UP UIF NBYJNVN USBOTNJTTJPO PG 72% *O UIJT XBZ XF DBO FOTVSF UIF GVMM JTPMBUJPO CZ MPTJOH POMZ BEEJUJPOBMMZ 0.5% JO USBOTNJTTJPO

8BWF QMBUFT 0QUJDBM XBWF QMBUFT BSF DPOTUSVDUFE GSPN NBUFSJBMT XIJDI IBWF EJɮFSFOU SFGSBDUJWF JOEJDFT GPS PSEJOBSZ BOE FYUSBPSEJOBSZ QFSQFOEJDVMBS BYFT -FU VT DPOTJEFS UXP PSUIPHPOBM DPNQPOFOUT PG UIF JODJEFOU MJHIU PO UIF QMBUF UIBU FOUFS UIF XBWF QMBUF JO UIF TBNF QIBTF %VF UP EJɮFSFOU TQFFET UIF DPNQPOFOU BMPOH UIF PSEJOBSZ BYJT QSPQBHBUFT GBTUFS UIBO UIF POF BMPOH UIF FYUSBPSEJOBSZ BYJT 8IJMF UIF MJHIU QBTTFT UISPVHI B XBWF QMBUF UIF QIBTF TIJGU δ HSPXT BOE BGUFS B EJTUBODF d JU XJMM CF <>

2πd(ne no) δ = − ,  λ

XIFSF ne BOE no EFTDSJCF UIF EJɮFSFOU SFGSBDUJWF JOEJDFT BMPOH UIF FYUSBPSEJOBSZ BOE PSEJOBSZ BYFT SFTQFDUJWFMZ 'PS UIF IBMGXBWF QMBUF XJUI δ = π UIF MJOFBSMZ QPMBSJ[FE CFBN XJMM SFNBJO MJOFBS CVU SPUBUFE CZ BO BOHMF 2θ XIFSF θ JT UIF BOHMF CFUXFFO UIF QPMBSJ[BUJPO PG JODJEFOU MJHIU BOE UIF GBTU PSEJOBSZ BYJT *O UIJT XBZ POF DBO SPUBUF UIF PSJFOUBUJPO PG MJOFBSMZ QPMBSJ[FE MJHIU

#FBN TQMJUUFS 1PMBSJ[JOH CFBN TQMJUUFST BSF PQUJDBM EFWJDFT UIBU DBO TQMJU B MJHIU CFBN JOUP SFɰFDUFE T BOE USBOTNJUUFE QQPMBSJ[FE CFBNT 5IF DPNNPOMZ VTFE TQMJUUFST BSF DPOTUSVDUFE GSPN UXP QSJTNT BOE IBWF B DVCF TIBQF 'JH   5IF IZQPUFOVTF TVSGBDF PG POF QSJTN JT DPBUFE BOE KPJOFE XJUI BOPUIFS QSJTN XJUI PQUJDBM DFNFOU 5P BWPJE UIF DFNFOU JOɰVFODJOH QPMBSJ[BUJPO UIF MJHIU TIPVME CF USBOTNJUUFE JOUP UIF DPBUFE QSJTN XIJDI JT MBCFMFE XJUI B SFGFSFODF NBSL PO UIF TVSGBDF

'JCFS DPVQMJOH "O PQUJDBM ɯCFS JT B DZMJOESJDBM EJFMFDUSJD XBWFHVJEF DPOTUSVDUFE GSPN B DPSF BOE B DMBEEJOH 'JH   5IF DPSF IBT B SFGSBDUJWF JOEFY ncr IJHIFS UIBO B SFGSBDUJWF PG UIF DMBEEJOH ncl 5IJT EJɮFSFODF SFTVMUT JO UPUBM JOUFSOBM SFɰFDUJPO TP UIBU B CFBN DBO QSPQBHBUF BMPOH UIF ɯCFS BYJT <> "QQMZJOH 4OFMMƫT MBX UIF DSJUJDBM BOHMF θcrit GPS UPUBM JOUFSOBM SFɰFDUJPO DBO CF DBMDVMBUFE GSPN <>

ncl cos θcrit = .  ncr

5IF MJNJUFE FOUFSJOH BOHMF θa JOTJEF PG XIJDI UIF CFBN XJMM QSPQBHBUF XJUIJO UIF DPSF JT EFUFSNJOFE CZ UIF FRVBUJPO sin θa = ncr sin θcrit,  Chapter 4 Optical Setup 29

PBS Coating

ppp pp

sss Cement Reference mark for coated prism

s

s

Fig. 4.5 Polarizing beam splitter cube. The beam enters the cube from left and will be divided into reflected s- and transmitted p-polarized beams.

ncl Cladding

Critical angle ncr Core

Incident angle

Fig. 4.6 Fiber guide from two points of view. Incident angle - θa, Critical angle - θcrit, ncl -a cladding reflective index, ncr - a core reflective index.

BOE DBO CF BMTP FYQSFTTFE JO UFSNT PG UIF OVNFSJDBM BQFSUVSF

2 2 NA = n0 sin θa = n0 n n .  cl − cr % 5IF OVNCFS PG HVJEFE NPEFT DBO CF RVBOUJɯFE CZ B OVNCFS V XIJDI JT HJWFO CZ <> 2πa V = NA,  λ XIFSF a JT B DPSF SBEJVT *G a/λ JT TNBMM FOPVHI TVDI UIBU V JT MFTT UIFO  <> UIF ɯCFS BDUT BT B TJOHMFNPEF HVJEF 5IJT UZQF PG XBWFHVJEF SFRVJSFT UIJO ɯCFST XJUI B DPSF EJBNFUFS MFTT UIFO B GFX XBWFMFOHUIT BOE B DPSF SFGSBDUJWF JOEFY TIPVME CF TMJHIUMZ CFMPX UIF DMBEEJOH SFGSBDUJWF JOEFY <> Chapter 4 Optical Setup 30

Optical fiber f = 6.24 mm

wavemeter

ECDL experiment λ/2 PBS

anamorphic Faraday prism pair Optical fiber isolator λ/2 f = 6.24 mm PBS λ/2

Fig. 4.7 Aschematicoftheopticalsetuponthebreadboard.

4.3 Optical Setup

0ODF BMM FRVJQNFOU GPS UIF TFUVQ JT SFBEZ UP VTF POF DBO QSPDFFE XJUI UIF QMBDJOH BOE BMJHOJOH QSPDFEVSF 5IF TDIFNBUJD PG UIF TFMGEFTJHOFE TFUVQ JT JMMVTUSBUFE JO 'JH  5IJT PQUJDBM TZTUFN PɮFST UIF GPMMPXJOH GFBUVSFT

 5IF FMMJQUJDBM PVUQVU CFBN QBTTFT UISPVHI UIF BOBNPSQIJD QSJTN QBJS BOE XJMM CF SFTIBQFE JOUP B DJSDVMBS POF

 5IF 'BSBEBZ JTPMBUPS JT VTFE UP QSPWJEF UIF JTPMBUJPO GSPN CBDLSFɰFDUJPOT

 5IF ɯSTU QPMBSJ[JOH CFBN TQMJUUFS 1#4 JO DPNCJOBUJPO XJUI B IBMGXBWF QMBUF TQMJUT B TNBMM BNPVOU PG QPXFS UP UIF XBWFNFUFS XIJMF NPTU PG UIF QPXFS JT SFɰFDUFE BOE TFOU UP UIF FYQFSJNFOU

 5IF TFDPOE 1#4 XJUI B IBMGXBWF QMBUF JO GSPOU JT JOUFHSBUFE UP NBUDI UIF CFBN QPMBSJ[BUJPO XJUI UIF TMPX BYJT PG UIF PQUJDBM ɯCFS .PSFPWFS UIF TQPMBSJ[FE QBSU DBO CF VTFE GPS GVUVSF VQHSBEFT UP UIF TFUVQ Chapter 5 Laser Properties 31

Chapter 5

Laser Properties

*O UIJT $IBQUFS XF FYQMPSF UIF PQUJDBM DIBSBDUFSJTUJDT PG PVS MBTFS TZTUFN TVDI BT PVUQVU QPXFS XBWFMFOHUI UVOBCJMJUZ NPEFIPQF GSFF UVOJOH SBOHF BOE MJOFXJEUI 5IFTF QSPQ FSUJFT BSF FBDI QSFTFOUFE JO EJɮFSFOU TFDUJPOT 5IF NPTU SFMFWBOU BSF TVNNBSJ[FE JO UIF DPODMVTJPO

5.1 Output Power

"T EJTDVTTFE JO UIF TFDPOE $IBQUFS PODF UIF DBSSJFS EFOTJUZ JO UIF BDUJWF MBZFS JT IJHI FOPVHI GPS QPQVMBUJPO JOWFSTJPO TUJNVMBUFE FNJTTJPO EPNJOBUFT 5IF PQUJDBM QPXFS FNJU UFE CZ TUJNVMBUFE FNJTTJPO JO UIF MBTFS EJPEF DBWJUZ JT QSPQPSUJPOBM UP UIF OVNCFS PG FMFDUSPOIPMF SFDPNCJOBUJPOT BOE UIF QIPUPO FOFSHZ *O UIJT XBZ UIF PVUQVU QPXFS FNJU UFE GSPN BO &$%- DBO CF XSJUUFO BT

P = η(I I ),  − th

XIFSF Ith JT UISFTIPME JOKFDUJPO DVSSFOU BOE η JT B TMPQF DPFɱDJFOU XIJDI JODMVEFT B QIPUPO FOFSHZ BOE BO FMFDUSPOIPMF SFDPNCJOBUJPO SBUF 5IF WBMVF PG UIF UISFTIPME DVS SFOU EFQFOET PO IPX XFMM JT UIF DBWJUZ BMJHOFE JF IPX NVDI PQUJDBM GFFECBDL UIFSF JT #Z PQUJNJ[JOH UIF PVUQVU DPVQMFS PSJFOUBUJPO BOE MFOT QPTJUJPOT POF DBO NJOJNJ[F UIJT QBSBNFUFS 5IJT QSPDFEVSF MFBET UP BO JODSFBTF JO PVUQVU QPXFS

5ISFTIPME DVSSFOU PQUJNJ[BUJPO 5P QSPDFFE XJUI UIF PQUJNJ[BUJPO QSPDFEVSF EFTDSJCFE JO 3FG <> POF OFFET BEEJUJPOBM FMFDUSJDBM FRVJQNFOU B QIPUPEJPEF B GVODUJPO HFOFSBUPS BOE BO PTDJMMPTDPQF 5IF GVODUJPO HFOFSBUPS HFOFSBUFT B USJBOHMF TJHOBM PG  7 QFBLUP QFBL BNQMJUVEF XJUI B GSFRVFODZ PG  )[ 5IF TJHOBM GSPN UIF QIPUPEJPEF BOE UIF GVODUJPO HFOFSBUPS BSF TJNVMUBOFPVTMZ EJTQMBZFE PO BO PTDJMMPTDPQF 8IJMF BMJHOJOH UIF GPDVTJOH MFOT BOE PVUQVU DPVQMFS POF TIPVME NPOJUPS UIF TJHOBM PO UIF PTDJMMPTDPQF BOE USZ UP EFDSFBTF UIF UISFTIPME DVSSFOU TFF 'JH   #Z SFQFBUJOH UIJT QSPDFEVSF B GFX UJNFT UIF UISFTIPME DVSSFOU DBO CF NJOJNJ[FE 0ODF UIF UISFTIPME DVSSFOU JT PQUJNJ[FE POF DBO QSPDFFE XJUI NFBTVSJOH UIF QPXFS PVUQVU GPS TJOHMFNPEF PQFSBUJPO BU UIF EFTJSFE XBWFMFOHUI PG  ON 'JHVSF  TIPXT UIF MJHUIDVSSFOU -* DIBSBDUFSJTUJDT PG UIF MBTFS BU WBSJPVT UFNQFSBUVSFT #FMPX UIF UISFTIPME DVSSFOU UIFSF BSF OP WJTJCMF DIBOHFT JO UIF PVUQVU QPXFS "GUFS GVSUIFS JO DSFBTJOH UIF DVSSFOU B MJOFBS EFQFOEFODF PG UIF PVUQVU QPXFS XBT PCTFSWFE 'SPN UIF Chapter 5 Laser Properties 32

Fig. 5.1 Threshold current optimization using a function generator to modulate the current. The blue trace is the modulation signal, while the orange trace is the photodiode signal. The point, where the current reaches the threshold value is indicated with an arrow.

HSBQI XF DBO PCUBJO Ith BOE η GPS EJɮFSFOU UFNQFSBUVSFT VTJOH B MJOFBS ɯU 'JHVSF  TIPXT UIF UISFTIPME DVSSFOU WFSTVT UFNQFSBUVSF 5IJT EFQFOEFODF JT EFTDSJCFE JO UIF OFYU TFDUJPO 8F DBO TFF JO 'JH  UIBU UIF UISFTIPME DVSSFOU IBT B NJOJNVN BU  ◦C BOE BU UIF TBNF UJNF η JT NBYJNBM 5IJT NFBOT UIBU UP BDIJFWF NBYJNVN QPXFS PVUQVU BU  ON UIF MBTFS TIPVME SVO BU  ◦C

5.2 Wavelength Selection

5IF QSJODJQMF PG XBWFMFOHUI TFMFDUJPO JO BO &$%- DBO CF FYQMBJOFE XJUI UIF GPMMPXJOH NPEFM 5IF UPUBM HBJO GVODUJPO PG BO &$%- JT HJWFO CZ B DPNCJOBUJPO PG UIF MBTFS EJPEF HBJO QSPɯMF GD UIF USBOTNJTTJPO CBOE QSPɯMF PG UIF JOUFSGFSFODF ɯMUFS Tfilter BOE USBOT NJTTJPO GVODUJPOT PG UIF DBWJUZ GPSNFE CFUXFFO UIF MBTFS EJPEF GBDFU BOE UIF PVUQVU DPVQMFS Tcavity <>

Ttotal = GDTfilterTcavity 

5IF HBJO QSPɯMF GD DBO CF BTTVNFE UP CF B CSPBE (BVTTJBO GVODUJPO IBWJOH B GVMM XJEUI BU IBMG NBYJNVN '8). PG BQQSPYJNBUFMZ  ON <> 5IF USBOTNJTTJPO QSPɯMF PG UIF ɯMUFS BT B GVODUJPO PG XBWFMFOHUI XBT NFBTVSFE VTJOH B QPXFS NFUFS BOE B TFDPOE ɯMUFS TJNJMBS UP UIF POF JO UIF MBTFS TFF 'JH   5IF USBOTNJTTJPO QFBL XBT ɯUUFE CZ B -PSFOU[JBO MJOF TIBQF HJWJOH B '8). PG 0.43 ON "T EJTDVTTFE JO $IBQUFS  UIF DBWJUZ NPEFT DBO CF EFTDSJCFE BT USBOTNJTTJPO NPEFT Chapter 5 Laser Properties 33

40 15°C 30 20°C 25°C 20

15°C 1.5 20°C 25°C 1.0

Power (mW) 10 0.5

0.0 64 66 68 70 72 0 60 80 100 120 140 Current (mA)

Fig. 5.2 Light-current characteristics of the laser at various temperatures.

6 0.54

67 0.53

66 0.52

65 STWpe cWefficient (W/)) ThreshWTd current (m)) 0.51 15.0 17.5 20.0 22.5 25.0 Temperature (°C)

Fig. 5.3 The slope η (blue points) and threshold current Ith (red points) versus temperature. Chapter 5 Laser Properties 34

0. 4Wrentzian Data 0.6

0.4

TransmissiWn 0.2

0.0 6 .5 6 9.0 6 9.5 690.0 WaveTength (nm)

Fig. 5.4 Transmission profile of the band-pass of the filter optimized for transmission at 689 nm. The data is fitted with a Lorentzian function (blue curve) giving a FWHM = 0.43 nm.

PG B DBWJUZ 2 λm = (Lext + n L ),  m D D

XIFSF Lext =6DN JT UIF FYUFSOBM DBWJUZ MFOHUI LD =1NN JT UIF EJPEF DBWJUZ MFOHUI <> nD =4.52 <> JT UIF MBTFS EJPEF SFGSBDUJWF JOEFY BOE m JT UIF NPEF OVNCFS *O PVS DBTF UIF MBTFS UFSN nDLD DBO CF OFHMFDUFE CFDBVTF nDLD/Lext < 4% 5IF NPEF TQBDJOH GPS λm = 689 ON JT HJWFO CZ

2 λm ∆λm = λm λm 1 = =0.004nm  − − 2Lext 5IFSF BSF PUIFS PG QBSBNFUFST UIBU DBO DIBOHF UIF NPEF UIBU IBT UIF MBSHFTU QFBL UIFSF GPSF UIF PQFSBUJOH XBWFMFOHUI *O UIF GPMMPXJOH TFDUJPO XF FYQMPSF TPNF PG UIFN

'JMUFS 'JSTU POF DBO UJMU UIF JOUFSGFSFODF ɯMUFS XIJDI MFBET UP B TIJGU PG UIF CBOEQBTT QPTJUJPO 5IF EFSJWBUJPO PG &R  HJWFT

2 dλ λ0 = 2 sin(2α),  dα −2λneff

'PS λ0 = 699 ON neff  BOE λ = 689 ON XF HFU Chapter 5 Laser Properties 35

24

22

20

Temperature (°C) 18

680 685 690 695 Wavelength (nm)

Fig. 5.5 Filter wavelength tuning range investigated for different operating temperatures.

dλ nm =0.096 .  dα deg ! " .PSFPWFS UIF UFNQFSBUVSF JOɰVFODF PO UIF XBWFMFOHUI UVOJOH SBOHF WJB ɯMUFS UJMUJOH XBT BMTP JOWFTUJHBUFE BU WBSJPVT PQFSBUJOH UFNQFSBUVSFT TFF 'JH   8F EFTDSJCF UIJT EFQFOEFODF XF NPWF PO UIF OFYU 4FDUJPO

5FNQFSBUVSF 5IF UFNQFSBUVSF EFQFOEFODF PG UIF XBWFMFOHUI PDDVST CFDBVTF PG TFW FSBM FɮFDUT <> *O UIF GPMMPXJOH XF EJTDVTT UIF NPTU JNQPSUBOU PG UIFN 5IF PQUJDBM QBUI MFOHUI WBSJFT CFDBVTF CPUI UIF MBTFS EJPEF DBWJUZ MFOHUI UIFSNBM FYQBOTJPO BOE UIF DIBOHF PG UIF SFGSBDUJPO JOEFY PG UIF TFNJDPOEVDUPS MBTFS EJPEF NBUFSJBM 5IF DPSSFMBUJPO CFUXFFO UIF SFGSBDUJWF JOEFY BOE FOFSHZ HBQ DBO CF EFTDSJCFE CZ EJɮFSFOU FNQJSJDBM SF MBUJPOT 4PNF PG UIFN BSF QSFTFOUFE BOE BOBMZ[FE JO 3FG <> 5P VOEFSTUBOE IPX UIF MBTFS EJPEF PQFSBUJOH UFNQFSBUVSF JOɰVFODFT UIF MBTFS EJPEF HBJO DVSWF XF DPOTJEFS B MJOFBS NPEFM EFTDSJCJOH UIF EFQFOEFODF PG UIF XJEUI PG UIF CBOE HBQ PO UIF UFNQFSBUVSF

Eg = E0(1 AT ),  − 4 1 XIFSF E0 =1.52 eV JT UIF XJEUI PG CBOE HBQ BU T   , BOE A = 10− (K− ) JT B UIFSNBM DPFɱDJFOU PG UIF TFNJDPOEVDUPS (B"T NBUFSJBM <> 8F TFF UIBU JODSFBTJOH UIF UFNQFSBUVSF DBVTFT DPOUSBDUJPO PG UIF FOFSHZ CBOE HBQ BOE UIVT UIF XBWFMFOHUI DIBOHFT Chapter 5 Laser Properties 36

689.5

689.49

689.48

689.47 Wavelength (nm)

689.46 20.0 20.5 21.0 Temperature (°C)

Fig. 5.6 Change of wavelength with temperature. Blue lines are linear fits to the data.

BDDPSEJOH UP dλ d hc hc dEg E0 = = = Aλ  dT dT E −E2 dT E ! "gap ! g " g g 5IF OFYU TJHOJɯDBOU FɮFDU JT UIF UIFSNBM FYQBOTJPO PG UIF NFUBM IPVTJOH %VF UP DBWJUZ MFOHUI WBSJBUJPOT UIF XBWFMFOHUI DIBOHFT BT

dλ 2 dL λ dL = = = k λ,  dT m dT L dT Al ! "th 6 1 XIFSF k =2 10− (K− ) JT UIF UIFSNBM FYQBOTJPO DPFɱDJFOU PG BMVNJOVN <> %VF Al × UP CPUI GBDUPST UIF DIBOHF JO XBWFMFOHUI JT UIFSFGPSF HJWFO CZ

dλ E0 nm = k + A λ =0.075 ,  dT Al E K ! g " 5IF HSBQI JO 'JH  TIPXT UIF NFBTVSFE XBWFMFOHUI WFSTVT UFNQFSBUVSF GPS B DVSSFOU PG I = 140 N" #Z UIFSNBM UVOJOH POF DBO UZQJDBMMZ BDIJFWF B NPEFIPQGSFF UVOJOH SBOHF PO UIF PSEFS PG ∆λ =0.005 ON 'SPN 'JH  B TMPQF PG dλ =(0.037 0.005) nm DBO CF dT ± K PCUBJOFE XIBU EJɮFST GSPN PVS UIFPSFUJDBM NPEFM 5IF DPFɱDJFOU A JT QSPCBCMZ MPXFS GPS PVS TFNJDPOEVDUPS NBUFSJBM Chapter 5 Laser Properties 37

5.3 Mode-Hop-Free Tuning Range

5IFSF BSF B MPU PG GBDUPST UIBU EFUFSNJOF UIF TJOHMF NPEF MBTFS GSFRVFODZ FNJUUFE CZ BO &$%- UIF HBJO QSPɯMF PG UIF MBTFS EJPEF UIF JOUFSOBM SFTPOBUPS MBTFS EJPEF DBWJUZ UIF FYUFSOBM SFTPOBUPS PQUJDBM TZTUFN DPOTJTUJOH UIF SBSF GBDFU PG MBTFS EJPEF BOE PVUQVU DPVQMFS BOE BO JOUFSGFSFODF ɯMUFS *G UIF MBTFS EJPEF PQFSBUJPO DVSSFOU PS UFNQFSBUVSF DIBOHF UIF HBJO QSPɯMFT TIJGU BTZODISPOPVTMZ BOE XJUI EJɮFSFOU SBUFT " TJNQMF XBZ UP DIFDL XIFUIFS UIF MBTFS JT PQFSBUJOH JO B TJOHMF NPEF JT UP BOBMZ[F UIF NPEF PO UIF XBWFNFUFS 0O UIF PUIFS IBOE CZ TDBOOJOH UIF QJF[P BDUVBUPS UIF MFOHUI PG UIF FYUFSOBM DBWJUZ DIBOHFT *O PSEFS UP OPU DBVTF NPEF IPQT UIF SFGSBDUJWF JOEFY PG UIF TFNJDPOEVDUPS NBUFSJBM TIPVME BMTP CF TJNVMUBOFPVTMZ TDBOOFE UP DPNQFOTBUF UIF PQUJDBM MFOHUI DIBOHF PG UIF DBWJUZ EVF UP UIF QJF[P BDUVBUPS 5IJT JT UZQJDBMMZ EPOF CZ NPEVMBUJOH UIF DVSSFOU XJUI UIF TBNF TJHOBM XF VTF UP NPEVMBUF UIF QJF[P BMCFJU NVMUJQMJFE CZ B HBJO GBDUPS UZQJDBMMZ NVDI MFTT UIFO POF  5IJT GFBUVSF JT DBMMFE CJBTJOH PS GFFE GPSXBSE BOE DBO CF VTFE UP JNQSPWF UIF UIF NPEFIPQGSFF UVOJOH SBOHF PG BO &$%- 'PS UIF QSPDFEVSF PG PQUJNJ[JOH UIF NPEFIPQGSFF UVOJOH SBOHF POF OFFET B GBTU QIPUPEJPEF BO PTDJMMPTDPQF BOE B IJHI WPMUBHF BNQMJɯFS 8F VTF UIF 4$  DPOUSPMMFS GSPN 5PQUJDB XIJDI XF EFTDSJCFE JO $IBQUFS  5IF BEKVTUNFOU QSPDFEVSF DBO CF GPVOE JO UIF 3FG <> 'PS PVS IPNFNBEF MBTFS XF BDIJFWFE B NPEFIPQF GSFF UVOJOH SBOHF BQQSPYJNBUFMZ PG  ()[

5.4 Linewidth

5IF MJHIU FNJUUFE CZ B MBTFS JEFBMMZ IBT B -PSFOU[JBO TIBQF )PXFWFS NFDIBOJDBM WJ CSBUJPOT PG UIF DBWJUZ UFNQFSBUVSF ɰVDUVBUJPOT QJF[P WPMUBHF ESJWF OPJTF BOE DVSSFOU DPOUSPMMFS OPJTF JOɰVFODFT UIF MJOF QSPɯMF NBLJOH JU NPSF CSPBE <> 5IF GVMM XJEUI BU IBMG NBYJNVN '8). PG UIF TQFDUSBM MJOFTIBQF JT DBMMFE UIF MJOFXJEUI 5IJT QBSBNFUFS JT POF PG UIF GVOEBNFOUBM TQFDUSBM QSPQFSUJFT PG UIF MBTFS 5IF QVSQPTF PG UIJT 4FDUJPO JT UP FYQMBJO IPX XBT UIF MJOFXJEUI PG UIF IPNFCVJME MBTFS EFUFSNJOFE BOE DPNQBSFE XJUI UIF MJOFXJEUI PG DPNNFSDJBM MBTFST GSPN .PHMBCT BOE 5PQUJDB 5IF FYQSFTTJPO GPS UIF RVBOUVNMJNJUFE MBTFS MJOFXJEUI XBT QSFTFOUFE JO 3FG <> BOE JT LOPXO BT UIF 4DIBXMPX5PXOFT VOJU

hν 2 ∆νFWHM = (∆ν) ,  πPout

XIFSF Pout JT UIF PVUQVU QPXFS ν JT UIF GSFRVFODZ BOE ∆ν JT UIF MBTFS DBWJUZ MJOFXJEUI 5ZQJDBMMZ UIF MJOFXJEUI QSFEJDUFE CZ &R  JT BCPVU B UXP PSEFST PG NBHOJUVEF TNBMMFS UIFO PCTFSWFE GPS TFNJDPOEVDUPS MBTFST 5IJT PCTFSWBUJPO XBT KVTUJɯFE CZ B GFX QIFOPN FOB FYQMBJOFE JO 3FG <> 5P EFUFSNJOF UIF FYQFSJNFOUBM WBMVF PG UIF MJOFXJEUI BOE UP DPNQBSF JU XJUI DPNNFSDJBM MBTFST B TFSJFT PG PQUJDBM IFUFSPEZOF CFBU OPUFT IBWF CFFO UBLFO VTJOH B TQFDUSVN BOBMZ[FS BOE B GBTU QIPUPEJPEF " VTFE TFUVQ JT JMMVTUSBUFE JO UIF 'JH  5P NFBTVSF UIF MJOFXJEUI JU JT OFDFTTBSZ UP PWFSMBQ UIF CFBNT PO B QIPUPEJPEF BOE NBUDI UIF QPMBSJ[BUJPO PG UIFN "TTVNJOH UIBU UIF FMFDUSJD ɯFMET PG CPUI CFBNT E1 Optical fiber f = 6.24 mm

wavemeter

ECDL experiment λ/2 PBS

anamorphic Faraday prism pair Optical fiber isolator λ/2 f = 6.24 mm PBS

Chapter 5 Laser Properties 38

f = 6.24 mm Laser 2 Laser 1

f = 6.24 mm Photodiode

λ/2 λ/2

NPBS f = 40 mm

PBS

Fig. 5.7 Aschematicsetupofabeatsignalmeasurement.

E2 BSF TJOVTPJEBM XJUI GSFRVFODJFT ω1 BOE ω2 UIF JOUFOTJUZ PG UIF TJHOBM PO UIF QIPUPEJ PEF JT QSPQPSUJPOBM UP UIF JOUFOTJUJFT PG UIF JODJEFOU MJHIU GSPN UIF UXP MBTFS CFBNT BOE JT HJWFO CZ

I (E cos(ω t)+E cos(ω t))2 = E2 cos2(ω t)+E2 cos2(ω t)+2E E cos(ω t) cos(ω t) ∼ 1 1 2 2 1 1 2 2 1 2 1 2 VTJOH B TJNQMF USJHPOPNFUSJDBM JEFOUJUZ BOE JHOPSJOH UIF DPOTUBOU QBSU XF DBO EFSJWF

I 2E1E2 cos(ω1t) cos(ω2t)=E1E2(cos((ω1 ω2)t)+cos((ω1 + ω2)t)  ∼ − 5IF UXP MBTFS GSFRVFODJFT NVTU CF DMPTF UP FBDI PUIFS TP UIBU UIF CFBU TJHOBM JT XJUIJO UIF CBOEXJEUI PG GBTU QIPUPEJPEF "T XF EJTDVTTFE JO UIF QSFWJPVT 4FDUJPO UIF XBWF MFOHUI DBO CF DPBSTFMZ UVOFE CZ WBSZJOH UIF BOHMF PG UIF JOUFSGFSFODF ɯMUFS PS DIBOHJOH UIF UFNQFSBUVSF 'JOF BEKVTUNFOU DBO CF BDIJFWFE CZ UVOJOH UIF MFOHUI PG UIF DBWJUZ XJUI UIF QJF[P FMFNFOU <> %VF UP UIF IJHIFS GSFRVFODZ UIF TFDPOE UFSN JO &R  DBO OPU CF EFUFDUFE FWFO XJUI B GBTU QIPUPEJPEF 5IF NFBTVSFNFOUT PG UIF CFBU OPUF TJHOBMT PG UXP MBTFS DPOɯHVSBUJPOT BSF TIPXO JO 'JH  BOE 'JH  4JODF UIF 5PQUJDB MBTFS JT TUBCJMJ[FE UP B IJHIɯOFTTF DBWJUZ JUT MJOFXJEUI JT TJHOJɯDBOUMZ TNBMMFS UIBO GPS Chapter 5 Laser Properties 39

UIF IPNFCVJME MBTFS 5IJT NFBOT UIBU UIF MJOFXJEUI PG UIF ɯSTU CFBU HJWFT VT EJSFDUMZ UIF MJOFXJEUI PG PVS MBTFS

∆νhome made = (271 30)kHz. − ± 5IF .PHMBCT MBTFS XBT OPU TUBCJMJ[FE BOE UIF CFBU OPUF GSFRVFODZ NPWFE BSPVOE NPSF TUSPOHMZ UIBO XJUI 5PQUJDB 5P BWPJE CSPBEFOJOH PG UIF MJOF EVF UP UIJT FɮFDU TFWFSBM TJOHMF NFBTVSFNFOUT PG  NT IBWF CFFO UBLFO %VF UP UIF UFDIOJDBM GSFRVFODZ OPJTF BSPVOE UIF QFBL UIF CFBU TJHOBM JT XFMM ɯUUFE XJUI B (BVTTJBO GVODUJPO 5IBU JT B DPOWPMVUJPO PG UIF XJEUIT PG UIF UXP MBTFST JO RVFTUJPO BOE JT HJWFO CZ UIF GPMMPXJOH FYQSFTTJPO <>

2 2 2 ∆νbeat =∆νhome made +∆νMoglabs.  − 6TJOH UIJT FYQSFTTJPO XF ɯOE UIF MJOFXJEUI PG UIF .PHMBCT MBTFS UP CF

∆ν = (806 70)kHz. Moglabs ± 5IJT NFBOT UIBU UIF MJOFXJEUI QSPQFSUJFT PG PVS MBTFS JT DPNQBSBCMF UP UIF DPNNFSDJBM POF Chapter 5 Laser Properties 40

/aussian -100 Data

-110

-120

-130 8owMr (dBm/0z) -140

-150

5.0 7.5 90.0 92.5 95.0 97.5 100.0 102.5 .rMquMnca (50z)

Fig. 5.8 A beat note signal of home-made laser and Toptica: RBW = 30 kHz,sweeptime1s, FWHM = 271 kHz. Chapter 5 Laser Properties 41

-110 /aussian Data

-120

-130

-140 PowMr (dBm/0z)

-150

10 15 20 25 30 35 40 45 50 FrMquMnca (50z)

Fig. 5.9 A beat note signal of home-made laser and Moglabs: RBW = 300 kHz,sweeptime1ms, FWHM = 850 kHz. Chapter 6 Conclusion 42

Chapter 6

Conclusion

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References

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<> #BJMMBSE 9 " (BVHVFU 4 #J[F 1 -FNPOEF 1 -BVSFOU BOE " $ BOE 1 3PTFOCVTDI *OUFSGFSFODFȸMUFSTUBCJMJ[FE FYUFSOBMDBWJUZ EJPEF MBTFST 0QUJDT $PNNVOJDBUJPOT     ɶʁɻ KPQUDPN <> #PSO . BOE & 8PMG 1SJODJQMFT PG 0QUJDT &MTFWJFS -UE  ɻʅɴʀ  <> 1FESPUUJ ' - *OUSPEVDUJPO UP 0QUJD  ɻʅɴʀ  <> -´GEBIM . ( 7 . + )FOSJRVFT BOE % ,JTFMNBO " UJMUFE JOUFSGFSFODF ȸMUFS JO B DPOWFSHJOH CFBN "TUSPOPNZ  "TUSPQIZTJDT  "   ɶʁɻ  <> %PCSPXPMTLJ + " )BOECPPL PG PQUJDT .D(SBX)JMM  ɻʅɴʀ 9 <> +BOTB / ƭ" GSFRVFODZTUBCMF EJPEF MBTFS TZTUFN GPS TQFDUSPTDPQZ BOE USBQQJOH PG 4S BUPNTƮ .BTUFSƫT 5IFTJT -VEXJHT.BYJNJMJBOT6OJWFSTJU¢U .ºODIFO ." UIFTJT  ʇʄɾ IUUQVMUSBDPMETSQVCMJDBUJPOTUIFTJT@OFKD@KBOTBQEG <> 4DIFS[ 1 BOE 4 .POL 1SBDUJDBM FMFDUSPOJDT GPS JOWFOUPST SE FEJUJPO .D(SBX)JMM ɻʅɴʀ  <> 5IFSNJTUPS 5IPSMBCT )BOT#´DLMFS4USBF   %BDIBV ʇʄɾ IUUQTXXXUIPSMBCTDPNESBXJOHTGCGCDFE#%# '''$'5),4QFD4IFFUQEG <> #VSOT ( 8 BOE . ( 4DSPHFS 5IF DBMJCSBUJPO PG UIFSNPDPVQMF BOE UIFSNPDPVQMF NBUFSJBMT /*45 4QFDJBM 1VCMJDBUJPO    ʇʄɾ IUUQTOWMQVCTOJTUHPWOJTUQVCT-FHBDZ41OJTUTQFDJBMQVCMJDBUJPOQEG <> 1BUJO / 1PXFS &MFDUSPOJDT "QQMJFE UP *OEVTUSJBM 4ZTUFNT BOE 5SBOTQPSUT &MTFWJFS  ɻʅɴʀ  <> #IBUUBDIBSZB 1 3 'PSOBSJ BOE ) ,BNJNVSB $PNQSFIFOTJWF 4FNJDPOEVDUPS 4DJFODF BOE 5FDIOPMPHZ &MTFWJFS 4DJFODF  ɻʅɴʀ  <> ƭ5IF 'VOEBNFOUBMT PG 5IFSNPFMFDUSJDTƮ " CBDIFMPSƫT MBCPSBUPSZ QSBDUJDBM -.6 ʇʄɾ IUUQTXXXOBOPQIZTJLVOJ NVFODIFOEFOBOPQIPUPOJDT@BTTFUTQEGG,@5IFSNPFMFDUSJDTQEG <> .PFIMF , ƭ1JF[PFMFDUSJDBMMZ 5VOBCMF 0QUJDBM $BWJUJFT GPS UIF (SBWJUBUJPOBM 8BWF %FUFDUPS -*4"Ʈ 1I% UIFTJT .BUIFNBUIJTDI/BUVSXJTTFOTDIBGUMJDIFO 'BLVMU¢U * )VNCPMEU6OJWFSTJU¢U [V #FSMJO  <> ,BU[JS 4 BOE # + ; 5IF %JTDPWFSZ PG UIF 1JF[PFMFDUSJD &ȷFDU "SDIJWF GPS )JTUPSZ PG &YBDU 4DJFODFT     ɶʁɻ T <> (PNF[ & 4 1JF[PFMFDUSJD $FSBNJDT 4DJZP  ɻʅɴʀ  <> 48  ) 4POPTXJTT 4POOFOTUSBTTF   3BNTFO ʇʄɾ IUUQTXXXTPOPTXJTTDIGJMFBENJONFEJB$MFBOJOH6OJUT%BUB4IFFUTEF %BUFOCMBUU@48@@)QEG References 45

<> 4DIPMM . 8 $BJSODSPTT BOE * ,JWMJDIBO *OUFSGFSFODF 'JMUFS 4UBCJMJ[FE &YUFSOBM$BWJUZ %JPEF -BTFST 0QUJDT $PNNVOJDBUJPOT     ɶʁɻ KPQUDPN <> 5SJQBUIZ 4 , 3FGSBDUJWF JOEJDFT PG TFNJDPOEVDUPST GSPN FOFSHZ HBQT 0QUJDBM .BUFSJBMT     ɶʁɻ KPQUNBU <> &:138&405 &BHMFZBSE 3VEPXFS $IBVTTFF   #FSMJO ʇʄɾ IUUQTXXXFBHMFZBSEDPNGJMFBENJOEPXOMPBETEBUB@TIFFUT&:138& 405QEG <> $" 4DI¢GUFS ,JSDIIPɮ ,JFMFS 4US   )BNCVSH ʇʄɾ IUUQTXXXTVLIBNCVSHDPNEPXOMPBE$@NPVOUJOHQEG <> 14#/4' 5IPSMBCT )BOT#´DLMFS4USBF   %BDIBV ʇʄɾ IUUQTXXXUIPSMBCTEFESBXJOHTEDGFC"#$#' %'14#"VUP$"%1%'QEG <> *057-1 'BSBEBZ UBOEFN JTPMBUPS 5IPSMBCT )BOT#´DLMFS4USBF   %BDIBV ʇʄɾ IUUQTXXXUIPSMBCTDPNESBXJOHTGCGCDFE #%#'''$'*057-1.BOVBMQEG <> #BSUM + 3 'JSB BOE 7 +BDLP ƭ5IFSNPFMFDUSJD UVOJOH PG UIF MBTFS EJPEF SBEJBUJPO GSFRVFODZƮ UI $[FDI4MPWBL1PMJTI 0QUJDBM $POGFSFODF PO 8BWF BOE 2VBOUVN "TQFDUT PG $POUFNQPSBSZ 0QUJDT 7PM 41*&   Q  ɶʁɻ  <> %JPEF -BTFS 4VQQMZ &MFDUSPOJDT .BOVBM 5PQUJDB -PDIIBNFS 4DIMBH   (S¢GFMɯOH ʇʄɾ IUUQTXXXUPQUJDBDPNQSPEVDUTUVOBCMFEJPEFMBTFSTMBTFS ESJWJOHFMFDUSPOJDTTZTEDBOBMPHDPOUSPM <> 8JTFNBO ) . 5IF VMUJNBUF RVBOUVN MJNJU UP UIF MJOFXJEUI PG MBTFST BS9JWRVBOUQI   <> 4WFMUP 0 1SJODJQMFT PG -BTFST  ɻʅɴʀ  References 46

Acknowledgements

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