Time-Frequency Analysis in Attosecond Spectroscopy

Isinger, Marcus

2018

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Citation for published version (APA): Isinger, M. (2018). Time-Frequency Analysis in Attosecond Spectroscopy. (1st ed.). Division of Atomic Physics, Department of Physics, Faculty of Engineering, LTH, Lund University.

Total number of authors: 1

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LUND UNIVERSITY

PO Box 117 221 00 Lund +46 46-222 00 00 FACULTY OF ENGINEERING | LUND UNIVERSITY |

Time-Frequency Analysis in Time-Frequency Attosecond Spectroscopy ISINGER MARCUS DEPARTMENT OF PHYSICS

MARCUS ISINGER Time-Frequency Analysis in Attosecond Spectroscopy 2019

538929 789177 9 ISSN 0281-2762 Lund UniversityLund - Division of Atomic Physics Faculty Engineering, of LTH ISBN 978-91-7753-893-6 (pdf) ISBN 978-91-7753-892-9 (print) ISBN 978-91-7753-892-9 sis, which involves migration of electronic charges. However, before this can before charges. However, of electronic sis, which involves migration need to be tested and developed on much the available tools be realized, ultrafast some of evolution time the explores then thesis This systems. simpler while to as RABITT, referred gas atoms using the technique in rare processes versatile methods and courses of action for this developing new analytical technique. This thesis deals with ultrafast dynamics of electronic processes in rare gas in rare processes ultrafast dynamics of electronic This thesis deals with take place during a millionth of a billionth we investigate atoms. The processes able are femtosecond (0.000 000 000 000 001 s). We of a second: a so-called light thanks to the possibility of creating processes to take snapshots of these ability (a thousandth of a femtosecond). The bursts of attosecond duration time would give unparalleled insight in real of following charge movements such as photosynthe and biological processes of, chemical into, and control

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رذ 5IF ))( TFUVQ JO -VOE رذ

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زذ (FOFSBUJPO PG 4IPSU -JHIU #VSTUT

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سذ

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ߤߢ 1৚ৡ০ৡ৛ৡৠ৛৬৓০৛ৡৠ

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صذ 1IPUPJPOJ[BUJPO در

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ضذ *OUFSGFSPNFUSZ XJUI 1IPUPFMFDUSPOT

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ߤߣ %ৗ০ৗ৕০৛ৠ৙ ৢ৚ৡ০ৡৗ৞ৗ৕০৤ৡৠ৥

5IF EFWJDF VTFE UP EFUFDU BOE NFBTVSF UIF LJOFUJD FOFSHJFT PG QIP TJODF XF NFBTVSF UIF UPFMFDUSPOT JT PG஽FO DBMMFE B ॾF؝SPNFUFS

طذ BHOFUJD #PUUMF &MFDUSPO 4QFDUSPNFUFS. دذر

TQFDUSVN PG FOFSHJFT PG UIF FMFDUSPOT )FSF BO PWFSWJFX PG UIF UXP TQFDUSPNFUFST VTFE JO ीBQFST ** *** *7 BOE 7* JT HJWFO "T DBO PG஽FO CF UIF DBTF UIFSF JT OP TJOHMF TQFDUSPNFUFS XIJDI TVJUT FWFSZ QPTTJCMF FYQFSJNFOU 4PNF QSFGFSFODFT BSF PG஽FO DPNQFUJOH BHBJOTU FBDI PUIFS BOE PG஽FO POF IBT UP TBDSJஷ஫DF POF BTQFDU JO PSEFS UP FYDFM JO BOPUIFS )PXFWFS UIFZ BMM OFFE UP TVQQPSU BO VMUSBIJHI WBDVVN FOWJSPONFOU 5IF UFDIOJRVFT CFMPX LOPXO BT য়৔ৗ৥ BOE ২য়৛৥ BSF UXP DPNQMFNFOUBSZ UFDIOJRVFT UIF GPS NFS GPDVTJOH PO TJHOBM TUSFOHUI BOE FOFSHZ SFTPMVUJPO XIJMF UIF MBUUFS JODMVEFT BOHVMBS SFTPMWBCJMJUZ XIJMF TVஶGFSJOH JO FOFSHZ SFT PMVUJPO

ߤߣߢ .BHOFUJD #PUUMF &MF؝SPO 4QF؝SPNFUFS

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JHVSF ߤߣ 4DIFNBUJD JMMVTUSBUJPO PG BO ࠰ࠥࠨ࠶ 5IF NBHOFUJD ׾FME' MJOॻ XIJDI SFTVMUT GSPN UIF QFSNBOFOU NBHOFU CMBDL DZMJOEFS BOE UIF TPMFOPJE HSBZ EPUT BSF TIPXO JO SFE "O FMFDUSPO XIJDI ॼ DSFBUFE JO B SFHJPO DMPTF UP UIF NBHOFU XJMM CF GPSDFE UPXBSET UIF FMFDUSPO NVMUJQMJFS JO B XJঁMJOH NPUJPO 5IF WPMUBHF TQJLF ॼ EFUFDUFE CZ BO "OBMPHUP %JHJUBM$POWFSUFS

 JT B 5JNF PS য়৔ৗ৥ 5IF .BHOFUJD #PUUMF &MF؝SPO 4QF؝SPNFUFS PG'MJHIU 5P' TQFDUSPNFUFS NFBOJOH JU NFBTVSFT UIF UJNF JU UBLFT UIF FMFDUSPOT UP USBWFM B LOPXO EJTUBODF 4JODF UIF FMFDUSPOT XJMM IBWF LJOFUJD FOFSHJFT JO UIF SFHJPO PG ߢ߫߫ F7 UIFZ DBO CF ෲಙ USFBUFE DMBTTJDBMMZ BOE UIFJS LJOFUJD FOFSHZ JT TJNQMZ ֍ยพศ ̹ ิಙ

ظر *OUFSGFSPNFUSZ XJUI 1IPUPFMFDUSPOT

XIFSF ֵ JT UIF ஸ஼JHIU UJNF BOE ֔ UIF MFOHUI UIF FMFDUSPOT USBWFM GSPN UIF QPJOU UIFZ BSF DSFBUFE UP UIF QPJOU UIFZ BSF EFUFDUFE "O 4JHOBM GSPN .$1 FMFDUSPOJD TJHOBM JT HFOFSBUFE GSPN B QIPUPEJPEF XIFO UIF MBTFS QVMTF FYJUT UIF MBTFS DIBJO XIJDI DBO CF UIPVHIU PG BT UIF TUBSU  TJHOBM " TFDPOE TJHOBM JT HFOFSBUFE XIFO BO FMFDUSPO IJUT UIF  EFUFDUPS BO FMFDUSPONVMUJQMJFS B .VMUJ$IBOOFM 1MBUF  5IF -FWFM <7> য়৕ৢ HFOFSBUFT B EFUFDUBCMF WPMUBHF GSPN B TJOHMF FMFDUSPO UISPVHI  B DBTDBEJOH DPMMJTJPO QSPDFTT JO UIF BSSBZ PG UIJO UVCFT SFMFBTJOH ߢߦ߫߫ ߢߦߦ߫ ߢߧ߫߫ NJMMJPOT PG TFDPOEBSZ FMFDUSPOT JO UIF QSPDFTT 5IF TFDPOE TJHOBM 4BNQMF NBSLT B TUPQ TJHOBM BOE UIF UJNF EJஶGFSFODF JT UIFO B NFBTVSF PG UIF UJNFPஶஸ஼JHIU PG UIF EFUFDUFE FMFDUSPO 5P' IJTUPHSBN Ϙಜ 5IFSF BSF EJஶGFSFOU NFUIPET PG EJSFDUJOH UIF FMFDUSPOT DSFBUFE   XIFSF GPS FYBNQMF BO BUUPTFDPOE QVMTF JO UIF JOUFSB؝JPO SFHJPO USBJO JPOJ[FT B HBT UBSHFU UP UIF TFOTJUJWF BSFB PG BO য়৕ৢ XIFSF 

UIFZ XJMM CF EFUFDUFE "O য়৔ৗ৥ VTFT B JOIPNPHFOFPVT NBHOFUJD $PVOUT ஷ஫FME UP DPMMFDU BT NVDI BT ߪ߫ PG BMM FMFDUSPOT 5IF য়৔ৗ৥ VTFE   JO UIJT UIFTJT XPSL XBT CBTFE PO UIF EFTJHO GSPN SFGFSFODF <ߥߣ> ߢ߫߫߫ ߢߦ߫߫ ߣ߫߫߫ ߣߦ߫߫ BOE B EFTDSJQUJPO PG UIF UFDIOJRVF JT TFFO JO ஷ஫HVSF ߤߣ " TUSPOH 5P' QFSNBOFOU NBHOFU  5 XJUI B DPOJDBM QPMF EJSFDUFE UPXBSET &OFSHZ IJTUPHSBN UIF JOUFSBDUJPO SFHJPO HFOFSBUFT B EJWFSHFOU NBHOFUJD ஷ஫FME XIJDI Ϙಜ BDUT BT B NBHOFUJD NJSSPS GPS BMM FMFDUSPOT " NBHOFUJD ஷ஫FME XJMM FYFSU OP XPSL PO UIF FMFDUSPOT TJODF UIF GPSDF JT BMXBZT QFSQFOEJD  VMBS UP UIF ஷ஫FME MJOFT *G UIF MJOFT BSF DVSWFE JOXBSET BT UIFZ BSF

DMPTF UP UIF UJQ PG UIF NBHOFU UIFSF XJMM CF B GPSDF DPNQPOFOU $PVOUT  FMFDUSPOT ؤSFஸ஼FDUJOHؤ FTTFOUJBMMZ QPJOUJOH JO UIF PUIFS EJSFDUJPO  XIJDI IBQQFOFE UP CF USBWFMJOH BXBZ GSPN UIF EFUFDUPS 5IF     EJWFSHFOU ஷ஫FME TPPO NFFUT UIF IPNPHFOFPVT ஷ஫FME HFOFSBUFE CZ ,JOFUJD FOFSHZ B TPMFOPJE XIJDI FODBQTVMBUFT B UVCF XJUI FYUFSOBM NBHOFUJD TIJFMEJOH 0WFS UIF MFOHUI PG B GFX DFOUJNFUFST UIF ஷ஫FME MJOFT 'JHVSF ߤߤ 5PQ 5IF WPMUBHF TQJLF CFDPNF QBSBMMFM BOE UIF DPMMFDUFE FMFDUSPOT BSF USBWFMJOH JO IFMJDBM GSPN UIF ࠰ࠦ࠳ ॼ TBNQMFE XJUI BO NPUJPO UPXBSET UIF EFUFDUPS UIFJS JOJUJBM WFMPDJUJFT QSBDUJDBMMZ ࠤࠧࠦ .JEEMF &BDI QFBL BSSJWBM VONPEJஷ஫FE ॼ DPMMFDUFE JO B IJTUPHSBN #PUUPN 5IF UJNFPG׿JHIU IJTUPHSBN Iॺ *U JT FBTZ UP JNBHJOF UXP FMFDUSPOT XJUI UIF TBNF FOFSHZ CFFO USBOTGPSNFE UP BO CFJOH SFMFBTFE JO DPNQMFUF PQQPTJUF EJSFDUJPOT *EFBMMZ UIFTF FRVBMXJEUI CJOOFE LJOFUJD FOFSঀ XPVME CF NFBTVSFE UP IBWF UIF TBNF ஸ஼JHIU UJNF CVU TJODF POF IJTUPHSBN FMFDUSPO OFFET UP UVSO BSPVOE XIJMF UIF PUIFS POF JT BMSFBEZ USBWFMJOH UPXBSET UIF EFUFDUPS UIFZ XJMM SFBDI UIF য়৕ৢ BU TMJHIUMZ EJஶGFSFOU UJNFT NPSF TP BU IJHIFS LJOFUJD FOFSHJFT 5IJT FஶGFDU DBO CF NJOJNJ[FE CZ QVUUJOH B MBSHF OFHBUJWF WPMUBHF PO UIF NBHOFU BOE BO JEFOUJDBM QPTJUJWF WPMUBHF PO UIF FOUSBODF UP UIF ஸ஼JHIU

در BHOFUJD #PUUMF &MFDUSPO 4QFDUSPNFUFS. دذر

UVCF FTTFOUJBMMZ BDDFMFSBUJOH UIF FMFDUSPOT TXJG஽MZ BXBZ GSPN UIF NBHOFU CFGPSF UIFZ BSF EFDFMFSBUFE BT UIFZ SFBDI UIF ஸ஼JHIU UVCF -FU VT BHBJO JNBHJOF UXP FMFDUSPOT DPMMFDUFE GSPN UXP EJஶGFS FOU BUPNT JO B HBT UBSHFU JPOJ[FE CZ B TJOHMF BUUPTFDPOE QVMTF USBJO 5IF MBTFS QVMTF JUTFMG USJHHFST UIF UJNFS PG BO "OBMPHUP%JHJUBM $POWFSUFS ৓৖৕ UP TUBSU DPVOUJOH 5IF GBTUFTU FMFDUSPO OBUVSBMMZ IJUT UIF য়৕ৢ ஷ஫STU DSFBUJOH B TNBMM FMFDUSPOJD QVMTF XIJDI JT NFB TVSFE CZ UIF ৓৖৕ " DPVQMF PG IVOESFE OBOPTFDPOET MBUFS UIF TFDPOE FMFDUSPO NJHIU IJU 5IF FMFDUSPOJD TJHOBM JT TFFO JO UIF UPQ PG ஷ஫HVSF ߤߤ 5IF ৓৖৕ SFDPSET UIF TQMJU UJNFT PG UIF EJஶGFSFOU BS SJWBMT 5IJT QSPDFTT JT UIFO SFQFBUFE BOE DPMMFDUFE JO B IJTUPHSBN XIJDI TIPXT UIF EJTUSJCVUJPO PG FMFDUSPO ஸ஼JHIU UJNFT *O UIF NJEEMF PG ஷ஫HVSF ߤߤ B DPMMFDUJPO PG FMFDUSPO ஸ஼JHIU UJNFT GSPN SPVHIMZ ߢߣ߫ ߫߫߫ MBTFS QVMTFT ߣ NJOVUF BDRVJTJUJPO BU ߢ L)[  "U UIJT QPJOU UIF IBSNPOJD TUSVDUVSF JT DMFBSMZ WJTJCMF %VF UP UIF OPOMJOFBS SFMBUJPO CFUXFFO UJNFPஶஸ஼JHIU BOE LJOFUJD FOFSHZ UIF FWFO TQBDJOH JT OPU QSFTFOU ZFU 6TJOH FRVBUJPO ߤߣ <ߥߤ> XF DBO FBTJMZ USBOTGPSN UIF IJTUPHSBN UP TIPX UIF FRVJWBMFOU LJOFUJD FOFSHJFT ֍ยพศ BT TFFO JO UIF CPUUPN PG ஷ஫HVSF ߤߤ

ಘ ֔ ֮ ֍LJO ࣽ ऑ ֍PஶGTFU ߤߣ ถֵֵ ֧ ֵ JT UIF 5P' BOE PG UIF ஸ஼JHIU UVCF JT  N JO UIJT DBTF ֔ 5IF MFOHUI ถ JT JODMVEFE UP BDDPVOU GPS BOZ FMFDUSPOJD EFMBZ JO UIF USBOTGFSֵ PG UIF TJHOBMT 5IF NBTT BOE DIBSHF PG UIF FMFDUSPO BSF EFOPUFE BOE ֧ SFTQFDUJWFMZ 5IF LJOFUJD FOFSHZ TQFDUSVN DBO CF PஶGTFU ֮ CZ BO BDDFMFSBUJPOEFDFMFSBUJPO WPMUBHF ֍PஶGTFU UP NPWF B TQFDJஷ஫D QBSU PG UIF TQFDUSVN UP UIF TMPX LJOFUJD FOFSHZ SFHJPO CFUXFFO ߫ ߣ F7 "T TFFO JO UIF 5P' IJTUPHSBN JO ஷ஫HVSF ߤߤ B HJWFO IBSNPOJD QFBL JT TBNQMFE NVDI NPSF ஷ஫OFMZ BU MPOH ஸ஼JHIU UJNFT JF MPX LJOFUJD FOFSHJFT UIBO BU GBTU ஸ஼JHIU UJNFT NFBOJOH UIF SFTPMVUJPO JT PQUJNBM BU MPOH ஸ஼JHIU UJNFT 5IF OPOMJOFBS SFMBUJPOTIJQ BMTP NFBOT UIBU FYUSB DBSF OFFET UP CF UBLFO XIFO USBOTGPSNJOH UIF IJTUPHSBN " EJSFDU DPOWFSTJPO PG FBDI 5P' CJO UP FOFSHZ SFTVMUT JO BO OPOVOJGPSN XJEUI PG UIF FOFSHZ CJOT 'PS FRVBMXJEUI FOFSHZ CJOT BO JOUFSQPMBUJPO NFUIPE OFFET UP CF BEPQUFE UP QSFTFSWF UIF UPUBM OVNCFS PG DPVOUT JO UIF USBOTGPSNBUJPO 5IF NFUIPE JT JMMVTUSBUFE JO ஷ஫HVSF ߤߥ "O FOFSHZ BYJT XJUI FRVBM XJEUI FOFSHZ CJOT JT DSFBUFE TQBOOJOH FOFSHJFT CFUXFFO UIPTF DPSSFTQPOEJOH UP UIF NJOJNBM BOE NBYJNBM 5P' PS B TNBMMFS

ذر *OUFSGFSPNFUSZ XJUI 1IPUPFMFDUSPOT

5P' &OFSHZ

*OUFHSBUJPO

֍ยพศ ֵ ֵ ֵ ֬ พ พಖ 'JHVSF ߤߥ *O PSEFS UP QSPEVDF B USVFDPVOU FOFSঀ IJTUPHSBN XJEUI CJOT PG FRVBM XJEUI GSPN UIF 5P' IJTUPHSBN BO JOUFSQPMBUJPO NFUIPE Iॺ CFFO VTFE &BDI DPMPS SFQSFTFOUT UIF USBOTGFSSFE DPVOUT 5IF DPVOUT ֬ CFUXFFO ֵพ BOE ֵพಖ DPSSFTQPOET UP FOFSঀ CJO

UIF 5P'T ֵพ BOE ֵพಖ  'PS FBDI FOFSHZ CJO ֬ JOUFSWBM JG EFTJSFE DPSSFTQPOEJOH UP UIF CFHJOOJOH BOE FOE PG UIF FOFSHZ CJO BSF ֵพ BOE ֵพಖ XJMM NPTU QSPCBCMZ OPU DBMDVMBUFE "T UIF ஷ஫HVSF TIPXT MJOF VQ XJUI UIF CJO JOUFSWBMT JO UIF 5P' IJTUPHSBN 5IF DPVOUT BOE UIF BU ֵพ BOE ֵพಖ BSF JOUFSQPMBUFE GSPN UIF OFBSFTU 5P' CJOT JOUFHSBUFE TJHOBM JT QVU JO FOFSHZ CJO ֬ UJMM UIF FOUJSF FOFSHZ SBOHF JT DPWFSFE 5IF PCWJPVT BEWBOUBHF PG UIF য়৔ৗ৥ JT UIF IJHI DPMMFDUJPO Fஶஷ஫DJFODZ MFBEJOH UP B IJHI RVBMJUZ̵̵TJHOBM BOE UIF MPOH ஸ஼JHIU JF IJHI TJHOBMUPOPJTF UJNFT SFTVMUJOH JO B IJHI SFTPMWBCJMJUZ BU MPX LJOFUJD FOFSHJFT %VF UP UIF NBHOFUJD NJSSPS XF MPTF UIF BCJMJUZ UP EFUFSNJOF UIF FNJT TJPO BOHMFT PG UIF FMFDUSPOT 'PS TPNF FYQFSJNFOUT UIJT JT BO BDDFQUBCMF MPTT *O ीBQFST ** BOE *** XF VTFE BO য়৔ৗ৥ UP UBLF BEWBOUBHF PG JUT FYDFMMFOU FOFSHZ SFTPMVUJPO *O UIF OFYU TFDUJPO XF XJMM EJTDVTT B UFDIOJRVF UP EFUFSNJOF UIF FNJTTJPO BOHMFT PG UIF QIPUPFMFDUSPOT

ߤߣߣ 7FMPDJUZ.BQ *NBHJOH 4QF؝SPNFUFS  VTFT IJHI FMFDUSP PS ২য়৛৥ 7FMPDJUZ.BQ *NBHJOH 4QF؝SPNFUFS " TUBUJD ஷ஫FMET UP BDDFMFSBUF UIF FMFDUSPOT POUP BO JNBHJOH য়৕ৢ " ஸ஼VPSFTDFOU QIPTQIPS TDSFFO QMBDFE CFIJOE UIF য়৕ৢ DPOWFSUT UIF FMFDUSPOT JOUP WJTJCMF QIPUPOT BMMPXJOH UIF JNBHF UP CF DBQUVSFE CZ B DBNFSB BDUT BT B TFFO JO ஷ஫HVSF ߤߦ 5IF 3FQFMMFS BOE &YUSB؝PS QMBUFT WFMPDJUZ MFOT 5IF QPUFOUJBMT PO UIF QMBUFT VTVBMMZ PO UIF PSEFS PG  7 DBO CF DIPTFO TVDI UIBU UIF QPTJUJPO PG BO FMFDUSPO IJUUJOH UIF য়৕ৢ JT EJSFDUMZ QSPQPSUJPOBM UP JUT USBOTWFSTF WFMPDJUZ

رر 7FMPDJUZ.BQ *NBHJOH 4QFDUSPNFUFS ذذر

&YUSBDUPS 'JFMEGSFF ஸ஼JHIU UVCF F ֚ ַ 4QFDUSPNFUFS BYJT

3FQFMMFS

ߣ߫߫߫ 7

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SFHBSEMFTT PG JUT QPTJUJPO JO UIF JOUFSBDUJPO VQPO FNJTTJPO ַ PG UIF SFTVMUJOH JNBHF JT UIFSFGPSF B ֚ SFHJPO <ߥߥ> 5IF SBEJVT NFBTVSF PG UIF USBOWFSTF LJOFUJD FOFSHZ DPNQPOFOU BT FRVBUJPO ߤߤ TIPXT

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زر *OUFSGFSPNFUSZ XJUI 1IPUPFMFDUSPOT

 ࠯ ࠯֦ ิสิฐฤ ࣼ  ࠞ  FRVಘ ࠒ ̰  ऐ ߤߥ  ࠛ ֦ࠬ

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شر *OUFSGFSPNFUSZ XJUI 1IPUPFMFDUSPOT

ઉ੍֩ ֑ฬ *OUFSGFSPNFUFS

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ߣ߫߫ $PVOUT

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߫ ߢߣߤߥߦߧ ߨߩ ,JOFUJD FOFSHZ

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صر 3FDPOTUSVDUJPO PG "UUPTFDPOE #VSTU CZ *OUFSGFSFODF PG 5XPDPMPS 5SBOTJUJPO درر

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ضر *OUFSGFSPNFUSZ XJUI 1IPUPFMFDUSPOT

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طر 5IF *OUFSGFSPNFUFS JO -VOE زر

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ظش 5JNF'SFRVFODZ "OBMZTॼ

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دش POUF$BSMP TJNVMBUJPOT. دزز

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ذش 5JNF'SFRVFODZ "OBMZTॼ

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رش 5IF SFDJQF GPS ৤৓৔৛০০ ذزز

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زش 5JNF'SFRVFODZ "OBMZTॼ

ߥߦ 4১য়য়৓৤৫

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سش

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ضص "ৢৢৗৠ৖৛৪ " %PDVNFOUBUJPO GPS BO ৓৖৕

৥ ৢ৓৤০ PG NZ EPDUPSBM FEVDBUJPO * QSPHSBNNFE BOE UFTUFE B EBUB BDRVJTJUJPO DBSE PG UIF UZQF "OBMPHUP
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طص

%PDVNFOUBUJPO GPS BO ৓৖৕

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دض *QMi2Mib

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k

ذض %PDVNFOUBUJPO GPS BO ৓৖৕

R AMi`Q/m+iBQM

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RX9 _2[mB`2/ /`Bp2`b

;BH2Mi +[B`Bb aQ7ir`2 *. o9XkX+ @ R8fykfkyRR

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رض k *QM};m`iBQM BM G#oA1q

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kXR AMBiBHBx2

AMTmi, _2bQm`+2 MK2 PmiTmi, AMbi`mK2Mi A.

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kXk *QM};m`2 K2KQ`v

AMTmi, AMbi`mK2Mi A.- LmK#2` Q7 a2;K2Mib- LmK#2` Q7 aKTH2b PmiTmi, /mT AMbi`mK2Mi A.

9

زض %PDVNFOUBUJPO GPS BO ৓৖৕

h?Bb oA +QM};m`2b i?2 K2KQ`v Q7 i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A.- BX2X i?2 MmK#2` Q7 bKTH2b M/ i?2 MmK#2` Q7 b2;K2Mib U+M #2 i?Qm;?i Q7 b MmK#2` Q7 i`B;;2`2/ 2p2MibV i?i b?QmH/ #2 biQ`2/X qB`2 i?2 QmiTmi /mT AMbi`mK2Mi A. iQ i?2 BMTmi Q7 i?2 M2ti oAX h?Bb QmiTmi rBHH MQi #2 /Bb+mbb2/ BM i?2 7QHHQrBM; b2+iBQMbX kXj *QM};m`2 ?Q`BxQMiH b2iiBM;b

AMTmi, AMbi`mK2Mi A.- aKTHBM; BMi2`pH UbV PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA +QM};m`2b i?2 ?Q`BxQMiH +QMi`QH T`K2i2`b Q7 i?2 +[B`Bb +`/ rBi? AMbi`m@ K2Mi A.- BX2X i?2 bKTHBM; BMi2`pH ;Bp2M BM b2+QM/bX h?2`2 Bb HbQ M QTiBQMH BMTmi /2Hv iBK2- r?B+? Bb B;MQ`2/ r?2M i?2 +`/ Bb QT2`iBM; BM x2`Q@bmTT`2bbBQM KQ/2 M/ i?2`27Q`2 MQi mb2/ ?2`2X kX9 *QM};m`2 p2`iB+H b2iiBM;b

AMTmi, AMbi`mK2Mi A.- *?MM2H- *QmTHBM;- 6mHH b+H2 UoV- Pzb2i UoV PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA +QM};m`2b i?2 p2`iB+H +QMi`QH T`K2i2`b Q7 i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A. M/ *?MM2H U2Bi?2` R Q` kVX h?2 6mHH b+H2 UoV +QM};m`2b i?2 `2bQHmiBQM Q7 i?2 bKTH2/ bB;MHX aBM+2 BM x2`Q@bmTT`2bbBQM KQ/2 i?2 +`/ bp2b i?2 BMTmi bB;MH b M 3#Bi bB;M2/ BMi2;2` U@Rk3XXRkdV i?2 6mHH b+H2 UoV T`K2i2` /2b+B/2b r?B+? `2H pQHi;2 U8-k-R Q` yX8 oV b?QmH/ +Q``2bTQM/ iQ i?2 KtBKmK BMi2;2` URkdVX a2i b +HQb2 iQ i?2 T2F Q7 i?2 bKTH2/ bB;MH b TQbbB#H2 7Q` KtBKmK `2bQHmiBQMX h?2 Pzb2i UoV T`K2i2` Qzb2ib i?2 `2H pQHi;2 #27Q`2 Bi Bb +QMp2`i2/ iQ M 3#Bi bB;M2/ BMi2;2` U@Rk3XXRkdVX

8

سض kX8 *QM};m`2 2ti2M/2/ i`B;;2` bQm`+2

AMTmi, AMbi`mK2Mi A.- *?MM2H- h`B;;2` +QmTHBM;- h`B;;2` bHQT2- h`B;;2` G2p2H R PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA +QM};m`2b i?2 i`B;;2` bQm`+2 +QMi`QH T`K2i2`b Q7 i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A. 7Q`  bT2+B}2/ i`B;;2` bQm`+2 *?MM2H U2Bi?2` R 7Q` BMi2`MH i`B;;2` Q` @R 7Q` 2ti2`MH i`B;;2` bQm`+2VX h?2 h`B;;2` +QmTHBM; b2ib i?2 +QmTHBM; iQ * Q` .* rBi? M BMTmi BKT2/M+2 Q7 R MΩ Q` 8y ΩX h?2 h`B;;2` bHQT2 /2+B/2b r?2i?2` i?2 +`/ b?QmH/ i`B;;2` QM i?2 `BbBM;fH2/BM; 2/;2 UTQbBiBp2V Q` 7HHBM;fi`BHBM; 2/;2 UM2;iBp2V T`i Q7 i?2 i`B;;2` bB;MHX 6Q`  rBM/Qr i`B;;2` i?2`2 Bb  b2+QM/ i`B;;2` H2p2H r?B+? Bb MQi mb2/ ?2`2X h`B;;2` G2p2H R b2ib i?2 i`B;;2` H2p2H BM KBHHBpQHibX

kXe *QM};m`2 i`B;;2` +Hbb

AMTmi, AMbi`mK2Mi A.- aQm`+2 Sii2`M PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA +QM};m`2b i?2 i`B;;2` +Hbb T`K2i2`b Q7 i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A.X aQK2 BMbi`mK2Mib bmTTQ`i  +QKTH2t 72im`2 b2i Q7 i`B;;2`bX 6Q` i?Bb mb2 +b2- bmTTHv i?2 bi`BM; Ǵyt3yyyyyyyǴ iQ i?2 aQm`+2 Sii2`M BMTmi- r?B+? 2M#H2b i?2 1ti2`MH h`B;;2` RX 6Q` Qi?2` mb2 +b2b- +QMbmHi i?2 KMmH Q` i?2 Ǵ+QMi2ti ?2HTǴ Q7 i?Bb oAX

LQr i?2 +[B`Bb +`/ Bb BMBiBHBx2/ 7Q` MQ`KH mb;2- M/ +QmH/ #2 mb2/ iQ +[mB`2  bB;MH QM +?MM2H RX 6Q` `2/#BHBiv- +`2i2  bm#oA rBi? i?2 oAb #Qp2X q2 MQr M22/ iQ +?M;2 i?2 QT2`iBQMH KQ/2 Q7 i?2 +[mBbBiBQM +`/ 7`QK MQ`KH UKQ/2 yV iQ ambiBM2/ a2[m2MiBH _2+Q`/BM; Q` aa_ UKQ/2 dVX AM i?Bb KQ/2- r2 +M 2M#H2 x2`Q@bmTT`2bbBQM Q7 i?2 BMTmi /iX

e

شض %PDVNFOUBUJPO GPS BO ৓৖৕

kXd *QM};m`2 QT2`iBQM KQ/2

AMTmi, AMbi`mK2Mi A.- JQ/2- 6H;b PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA +QM};m`2b i?2 QT2`iBQMH KQ/2 Q7 i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A.XhQ 2M#H2 i?2 Ǵ_2/JQ/2aa_qǴ- bmTTHv  pHm2 Q7 d iQ i?2 BMTmi JQ/2- HQM; rBi?  pHm2 Ry iQ BMTmi 6H;bX h?2 ~; KQ/B}2` 2M#H2b  b2+QM/ K2KQ`v #mz2` r?B+? Bb M22/2/ 7Q` bBKmHiM2Qmb /i +[mBbBiBQM M/ `2/QmiX kX3 *QM};m`2 2ti2M/2/ p2`;2` b2iiBM;b

AMTmi, AMbi`mK2Mi A.- *?MM2H- S`K2i2` E2v- S`K2i2` oHm2 PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA HHQrb iQ +QM};m`2 //BiBQMH T`K2i2`b Q7 i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A.- r?B+? `2 M22/2/ 7Q` i?2 x2`Q@bmTT`2bbBQM iQ rQ`FX h?2 oA rQ`Fb rBi?  bBM;H2 E2v@ oHm2 TB` i  iBK2- bQ BM Q`/2` iQ b2i KmHiBTH2 pHm2b mb2 i?Bb oA BM  HQQT rBi? irQ ``vb i?i ?QH/ i?2 F2vb M/ pHm2bX h?2 T`K2i2`b r2 rMi iQ b2i `2 L#`aKTH2b- L#`a2;K2Mib- S`2aKTH2b- SQbiaKTH2b M/ AMp2`i.i- 2t+iHv b i?2v `2 r`Bii2M ?2`2X h?2 }`bi irQ rBHH Qp2`r`Bi2 i?2 MmK#2` Q7 bKTH2b M/ MmK#2` Q7 b2;K2Mib +QM};m`2/ BM i?2 K2KQ`v b2iiBM;bX S`2aKTH2b M/ SQbiaKTH2b b2ib i?2 MmK#2` Q7 bKTH2b iQ +QHH2+i #27Q`2 M/ 7i2` i?2 bB;MH i?`2b?QH/ Bb `2+?2/X AMp2`i.i U/27mHi Bb y- MQ BMp2`bBQM TTHB2/V b2ib i?2 +`/ iQ +mi HH /i #Qp2 i?2 i?`2b?QH/ BMbi2/ Q7 #2HQr B7 b2i iQ RX

d

صض kXN *QM};m`2 b2imT ``v

AMTmi, AMbi`mK2Mi A.- *?MM2H- b2imThvT2- M#`a2imTP#D- i?`2b?QH/b PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA HHQrb iQ +QM};m`2 i?2 i?`2b?QH/ T`K2i2`b Q7 i?2 +[B`Bb +`/ rBi? AMbi`m@ K2Mi A. #2HQr r?B+? Bi b?QmH/ TTHv x2`Q@bmTT`2bbBQMX >2`2-  bKHH KQ/B}+iBQM iQ i?2 oA Bb M22/2/ iQ KF2 Bi rQ`F b i?2 T`Q;`KK2`Ƕb KMmH BMi2M/bX 6BM/ i?2 ``v +HH2/ b2imT.i TB+im`2/ #2HQr BM i?2 oAb #HQ+F /B;`KX Ai rBHH MQi HQQF HBF2 i?Bb- BMbi2/ Bi rBHH QMHv ?p2  +Hmbi2` Q7 irQ 2H2K2MibX

JQ/B7v i?2 +Hmbi2` iQ HQQF HBF2 #Qp2 rBi? i?2 MmK#2` `2T`2b2MiiBQMb b b?QrM #2HQrX

*`2i2 M ``v Q7 i?`2b?QH/b +Hmbi2`b b BMTmiX h?2 i?`2b?QH/ Bb b2i BM oQHib- M/ i?2 M2tiaKTH2 i2HHb i?2 +QMi`QHH2` r?2M iQ TTHv i?2 M2ti i?`2b?QH/ BM i?2 i?`2b?QH/ ``vX a2i i?Bb BMTmi iQ L#`aKTH2b B7 vQm QMHv BMi2M/ iQ mb2  bBM;H2 i?`2b?QH/X h?2 _2b2`p2/

3

ضض %PDVNFOUBUJPO GPS BO ৓৖৕

2H2K2Mi +M #2 H27i b y M/ b?QmH/ MQi #2 mb2/X h?2 b2imThvT2 M22/b iQ #2 b2i iQ k b r2HH b i?2 M#`a2imTP#D BMTmiX kXRy *QM};m`2 2ti2M/2/ K2KQ`v b2iiBM;b

AMTmi, AMbi`mK2Mi A.- LmK#2` Q7 a2;K2Mib- LmK#2` Q7 aKTH2b- LmK#2` Q7 "MFb PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA HHQrb iQ +QM};m`2 i?2 2ti2M/2/ K2KQ`v +QMi`QH T`K2i2`b Q7 i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A.- r?B+? Bb `2[mB`2/ 7Q` i?2 aa_ KQ/2 iQ rQ`FX h?2 LmK#2` Q7 a2;K2Mib M/ LmK#2` Q7 aKTH2b `2 i?2 bK2 #27Q`2- `i?2` i?2 LmK#2` Q7 "MFb Bb i?2 BKTQ`iMi pHm2 ?2`2- r?B+? +M #2 b2i iQ k Q` jX

LQr i?2 +`/ Bb +QM};m`2/ iQ rQ`F BM i?2 aa_ KQ/2 rBi? k Q` j K2KQ`v #MFbX uQm b?QmH/ mb2 i?2 /Bz2`2Mi ǴZm2`vǴ oAb iQ KF2 bm`2 i?i i?2 pHm2 +imHHv ?b #22M b2i b vQm BMi2M/2/X

N

طض j +[mBbBiBQM BM G#oA1q

jXR +[mB`2 bB;MH

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jXk _2/ #mz2`2/ bB;MH

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jXkXR _2/ aa_ .i

AMTmi, AMbi`mK2Mi A.- `2/S`- /i``v BM- *?MM2H PmiTmi, /mT AMbi`mK2Mi A.- /i.2b+- /i``v Qmi

h?Bb oA `2/b i?2 `r i?`2b?QH/2/ /i 7`QK i?2 +[B`Bb +`/ rBi? AMbi`mK2Mi A. M/ *?MM2HX h?2 BMTmi /i``v BM Bb  mb2`@HHQ+i2/ /i ``v Q7 3#Bi bB;M2/ BMi2;2`b-

Ry

ظط %PDVNFOUBUJPO GPS BO ৓৖৕

M/ +M #2 2Bi?2` x2`Qb Q` +[mB`2/ pHm2b- i?2v rBHH #2 Qp2`r`Bii2M Mv?QrX h?2 `2/S` BMTmi M22/b +`27mH +QM};m`iBQM 7Q` i?2 `2/Qmi iQ rQ`FX M 2tKTH2 ?Qr iQ +QM};m`2 i?Bb T`K2i2` Bb b?QrM #2HQrX

"v +`2iBM;  +QMbiMi Q7 i?2 BMTmi i2`KBMH Q7 `2/S` r2 ;2i  +Hmbi2` Q7 BMBiBHBx2/ pHm2bX PM T;2 k8 Q7 i?2 T`Q;`KK2`Ƕb KMmH i?2`2 Bb  /2b+`BTiBQM Q7 i?2 T`K2i2`bX h?2 }`bi x2`Q Bb KBbbBM; ?Qr2p2`X h?Bb x2`Q i2HHb i?2 +[B`Bb +`/ i?i i?2 /i b?QmH/ #2 bKTH2/ BM 3#Bi- i?2 QMHv pHB/ /i ivT2 7Q` i?2 aa_ +QM};m`iBQMX h?Bb #`BM;b mb iQ i?2 M2ti pHm2- d- r?B+? i2HHb i?2 +`/ iQ BMi2`T`2i i?2 /i b x2`Q@bmTT`2bb2/ /iX h?2 T`K2i2`b r2 M22/ iQ KMmHHv b2i `2 i?2 bBt T`K2i2`b b?QrM- r?B+? `2 ++2bb2/ #v i?2 ǴlM#mM/H2 #v MK2Ǵ 7mM+iBQMX h?`22 Q7 i?2K `2 H27i b x2`Q- M#`a2;K2Mib M/ L#`aKTH2b b?QmH/ #2 i?2 bK2 b +QM};m`2/ #27Q`2- M/ /i``vaBx2 Bb i?2 bBx2 BM #vi2b Q7 i?2 mb2`@HHQ+i2/ #mz2` i?i i?2 /i Bb i`Mb72``2/ iQX 6Q` bBKTHB+Biv- i?Bb #mz2` +M #2 b2i iQ i?2 rQ`bi +b2 b+2M`BQ- BX2X HH Q7 i?2 bB;MH Bb #Qp2 i?2 i?`2b?QH/ M/ i?2`27Q`2 i`Mb72``2/ iQ i?2 #mz2`, Kt.iaBx2 UBM #vi2bV 4 M#`a2;K2Mib UM#`aKTH2b Y jk Y 3V Y jkX h?2 MmK#2`b +Q``2bTQM/ iQ M Qp2`?2/ r?B+? Bb Hrvb i`Mb72``2/- +QMiBMBM; K2i@/i r?B+? r2 rBHH BMi2`T`2i Hi2` QMX h?2 QmiTmi /i.2b+ +QMiBMb BM7Q`KiBQM #Qmi i?2 x2`Q@bmTT`2bb2/ /i- bm+? b i?2 +imH bBx2 Q7 i?2 /i i`Mb72``2/- i?2 bKTHBM; iBK2 M/ bQ QM- #mi MQi?BM; Q7 ?B;? BKTQ`iM+2X h?2 /i``v Qmi +QMiBMb i?2 /B;Bix2/ i?`2b?QH/2/ /i b 3#Bi bB;M2/

RR

دط BMi2;2`b iQ;2i?2` rBi? i?2 K2i@/i BM  bBM;H2 /i bi`2KX aBM+2 i?Bb K2i@/i Bb MQi +imHHv 7Q`Kii2/ b 3#Bi- #mi ?b #22M BMi2`T`2i2/ b bm+? #v i?2 _2/ aa_ .i oA- Bi iF2b  #Bi Q7 i`B+F2`v iQ `2i`B2p2 i?2 +Q``2+i K2i@/iX JQ`2 QM i?Bb BM b2+iBQM jXjX

jXkXk 6`22 #MF

AMTmi, AMbi`mK2Mi A. PmiTmi, /mT AMbi`mK2Mi A.

h?Bb oA 7`22b i?2 +m``2Mi K2KQ`v #MF- KFBM; Bi pBH#H2 iQ #mz2`  M2r +mBbBiBQMX

jXj S`b2 `r aa_ /i

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Rk

ذط %PDVNFOUBUJPO GPS BO ৓৖৕

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h?2 +imH /B;BiBx2/ /i bi`ib 9y bi2Tb BMiQ i?2 3#Bi ``v- Q` 3 bi2Tb 7i2` i?2 #2;BMMBM; Q7 i?2 ;i2 /2b+`BTiQ`X aBM+2 r2 /QMǶi FMQr i?2 2M/ Q7 i?2 ``v #27Q`2 r2 ?p2 `2/ i?2 ;i2 /2b+`BTiQ`- r2 M22/ iQ T`b2 i?2 /i b2[m2MiBHHvX q2 2ti`+i M ``v rBi?  H2M;i? Q7 ;i2G2M;i? M/ KQp2 i?2 +m``2Mi TQbBiBQM #v b KMv bi2Tb b r2HHX h?2 ;i2SQb Bb mb2/ iQ /2i2`KBM2 i?2 T2F TQbBiBQM Q7 i?2 /i BM `2HiBQM iQ i?2 i`B;;2`X A7 i?2`2 `2 KQ`2 ;i2b r2 HQQT i?`Qm;? HH Q7 i?2K- Qi?2`rBb2 r2 KQp2 iQ i?2 M2ti b2;K2Mi /2b+`BTiQ` M/ /Q Bi HH ;BMX

Rj

رط 9 +[mBbBiBQM S`Q;`K 62im`2b

h?Bb +?Ti2` Bb /2/B+i2/ iQ 2tTHBM bQK2 Q7 i?2 72im`2b Q7 i?2 +[mBbBiBQM T`Q;`K r`Bii2M bT2+B}+HHv 7Q` i?Bb ivT2 Q7 +[mBbBiBQM +`/- rBi?  Tm`TQb2 iQ iF2 /pMi;2 Q7 i?2 72im`2b BKTH2K2Mi2/ BM i?2 2`HB2` +?Ti2`X

9XR :2M2`H ai`m+im`2

h?2 T`Q;`K Bb bi`m+im`2/ b irQ T`HH2HH T`Q+2bb2b UHQQTbV- b b?QrM #2HQrX AM QM2 HQQT- i?2 +`/ Bb i`B;;2`2/ M/ i?2 `r /i UM/ K2i /iV +[mB`2/ Bb //2/iQ [m2m2 Q#D2+iX AM i?2 Qi?2` HQQT- /i Bb +QMiBMmQmbHv rBi?/`rM 7`QK i?2 7`QMi Q7 i?2 [m2m2 M/ T`Q+2bb2/ 7Q` BMi2`T`2iiBQMX

R9

زط %PDVNFOUBUJPO GPS BO ৓৖৕

qBi? i?Bb bi`m+im`2- r2 `2 KFBM; bm`2 MQ i`B;;2`b `2 KBbb2/X 6Q`  i`B;;2` `i2 Q7 R F>x- i?2 iQT HQQT Bb 7bi 2MQm;? iQ `K i?2 i`B;;2` Q7 i?2 +`/ 2+? Bi2`iBQM- #mi 7Q` Km+? 7bi2` i`B;;2` `i2b vQm KB;?i rMi iQ /Q  #mz2`2/ +[mBbBiBQM BMbi2/X h?2 #QiiQK HQQT Bb rBiBM; 7Q` /i b HQM; b i?2 [m2m2 Bb 2KTiv- M/ i?2M rBi?/`rb /i b 7bi b Bi 2t2+mi2bX AM i?Bb bQ +HH2/ Ǵ+QMbmK2`Ǵ HQQT- i?2 `r /i Bb BMi2`T`2i2/ M/ i?2 K2i /i Bb b2T`i2/ 7`QK i?2 bB;MH /iX

9Xk S2F .2i2+iBQM aBM+2 i?2 +[mBbBiBQM +`/ Bb K2Mi iQ +QmMi 2H2+i`QM- r2 M22/ iQ +QMp2`i i?2 bB;MH 7`QK  bBM;H2 2H2+i`QMB+ TmHb2 BMiQ  MmK#2`- i?2 ~B;?i@iBK2X h?2 K2i?Q/ +?Qb2M Bb  7bi T2F /2i2+iBQM K2i?Q/ +HH2/ rp2H2i@#b2/ T2F /2i2+iBQM mbBM; KmHiB@`2bQHmiBQM MHvbBbX

9Xj .i ai`m+im`2 M/ aiQ`;2 h?2 `r- mMKMBTmHi2/ /i r2 +[mB`2 7`QK i?2 +`/- 7i2` T2F /2i2+iBQM- +QMbBbib Q7 i?2 iBK2@Q7@~B;?i U /B;Bi Q7 /Qm#H2 T`2+BbBQMV 7Q` 2+? 2H2+i`QM ?BiX h?Bb /i Bb biQ`2/ BM M ``v /m`BM; `mMiBK2- M/ Bb b2[m2MiBHHv BMi2`T`2i2/ M/ T`2b2Mi2/ BM  ?BbiQ;`K iQ i?2 mb2`X h?2 /i Bb HbQ bp2/ iQ  i2KTQ``v /B`2+iQ`v mbBM; i?2 >.68 }H2 7Q`Ki BM M 2p2Mi #b2/ /i bi`m+im`2- iQ T`2p2Mi ++B/2MiH /i HQbb M/ BM+`2b2 ~2tB#BHBivX h?2 2p2Mi #b2/ bi`m+im`2 Bb /2iBH2/ BM i#H2 9XRX 6Q` 2+? 2p2Mi- r2 biQ`2 i?2 MmK#2` Q7 ?Bib M/ i?2 iBK2@Q7@~B;?i Q7 2+? ?BiX h?2 /i Bb bp2/ b2[m2MiBHHv BM 2[mHHv bBx2/ Ǵ+?mMFbǴ iQ QTiBKBx2 i?2 r`Bi2@iQ@/BbF iBK2X A7 i?2`2 Bb BMbm{+B2Mi /i iQ }HH  +?mMF- i?2 mM}HH2/ bT+2 Bb Qp2`r`Bii2M rBi? Ǵ@RǴ- iQ +H2`Hv BM/B+i2 i?i i?Bb Bb MQi `2H /iX 7i2` M +[mBbBiBQM ?b }MBb?2/- i?2 i2KTQ``v }H2 Bb +HQb2/- M/ Bi KB;?i #2 +QTB2/ iQ  /B`2+iQ`v Q7 i?2 mb2`b +?QB+2X h?Bb 2p2Mi #b2/ /i M22/b iQ #2 `2/ b2[m2MiBHHv b r2HH- bi`iBM; 7`QK i?2 p2`v #2;BMMBM;- iQ 2Mbm`2 i?i 2+? ?Bi +Q``2bTQM/b iQ i?2 +Q``2+i 2p2MiX 6Q`  H`;2 /i b2i- i?Bb +M #2 [mBi2 iBK2 +QMbmKBM;- #mi i?2 /pMi;2 Bb i?2 mb2` +M BMi2`T`2i M/ T`2b2Mi i?2 /i BM  ?m;2 MmK#2` Q7 /Bz2`2Mi rvbX

h#H2 9XR, ai`m+im`2 Q7 biQ`2/ /iX >Bib M` hQ6 (Mb) k Ryy R kyy @R 8y @R @R

R8

سط

"ৢৢৗৠ৖৛৪ # 1IPUPOJRVFT 4QFDJBM *TTVF

ৡ৤ ৓ TQFDJBM JTTVF PG ीIPUPOJRVॻ XF XFSF BTLFE UP XSJUF B QPQVMBS TDJFODF BSUJDMF TVNNBSJ[JOH SFDFOU  SFTVMUT GSPN -VOE PCUBJOFE XJUI UIF ৤৓৔৛০০ UFDI OJRVF 8F GPDVTFE PO QIPUPJPOJ[BUJPO UJNF EFMBZT BOE QSPWJEFE BO PVUMPPL PO UIF ஷ஫FME PG BUUPTFDPOE TDJFODF 5IF BEWFSUJTFNFOUT JO UIF BSUJDMF IBWF CFFO SFNPWFE UIFSFCZ UIF QF DVMJBS XIJUFTQBDFT BOE B NJTTJOH QBHF

صط

1IPUPOJRVॻ 4QFDJBM *TTVF

FOCUS I PHOTONIC DEVICES AND APPLICATIONS

HOW CAN ATTOSECOND PULSE TRAIN INTERFEROMETRY interrogate electron dynamics?

C.L. ARNOLD, M. ISINGER, Light pulses of sub-100 as (1 as=10-18 s) duration, with photon D. BUSTO, D. GUÉNOT, energies in the extreme-ultraviolet (XUV) spectral domain, S. NANDI, S. ZHONG, J.M. DAHLSTRÖM, represent the shortest event in time ever made and controlled M. GISSELBRECHT, by human beings. Their first experimental observation in 2001 A. L’HUILLIER has opened the door to investigating the fundamental dynamics Department of Physics, Lund University, Lund, Sweden of the quantum world on the natural time scale for electrons [email protected] in atoms, molecules and solids and marks the beginning of the scientific field now called attosecond science.

ttosecond light pulses cannot is reached. Depending on the genera- The semi-classical understanding be obtained from a conven- tion conditions, the cut-off can exceed of HHG, generally referred to as the Ational laser, but result from a 100 eV of photon energy, covering se- three-step model, is illustrated in nonlinear interaction, when intense veral tens of harmonics, and the effect Figure 1. First, the atomic binding femtosecond laser pulses are focused was thus named high-order harmonic potential is so strongly distorted into a dilute gas. It was observed in the generation (HHG). It was soon realized near the crests of the driving laser late eighties that this interaction leads that the comb of harmonics could cor- field that the least bound electron to the emission of a comb of odd-or- respond to a train of very short pulses, may tunnel-ionize to the continuum. der harmonics of the driving laser i.e. attosecond pulses, if the harmonics Second, driven by the strong laser [1,2]. Unexpected from the concepts were phase-locked [3]. This view was field, the electron is taken away from of perturbative nonlinear optics, only inspired by a semi-classical model of the parent-ion, picking up kinetic en- the first few orders decrease exponen- the single-atom response in a strong ergy. Finally, when the driving field tially in power, while higher orders driving laser field [4], which was short- changes sign, the electron may return form a plateau of almost equal power, ly after also supported by a fully quan- to its parent-ion and recombine, until a sharp drop, called the cut-off, tum mechanical treatment [5,6]. whereas its excess energy is emitted as an XUV photon. The kinetic ener- gy of the returning electron depends on its trajectory, i.e. the path it takes from the time it was born in the continuum to its return to the pa- rent-ion. Not all possible trajectories return to the parent-ion and contri- bute to HHG. The three-step process repeats itself for every half cycle of the driving field, resulting in an atto- second pulse train (APT). While the spectrum of each individual attose- cond pulse in the train is continuous, the corresponding spectrum of the train results from the spectral inter- ference of all pulses in the train and is composed of odd-order harmo- Figure 1. Illustration of the semi-classical three-step model for high-order nics. This can be understood in ana- harmonic generation. logy to the frequency comb structure

28 Photoniques Special EOS Issue 2 ] www.photoniques.com https://doi.org/10.1051/photon/2018S328

طط PHOTONIC DEVICES AND APPLICATIONS I FOCUS

of the output of an ultrafast oscil- time scale. For that, we will first dis- lator, where the interference of the cuss the RABBIT scheme in more output pulses results in comb lines detail. The principle is illustrated spaced by 1/f, where f is the repetition in Figure 2. APTs synchronized with rate of the oscillator. Single attose- a weak copy of the driving pulse, in cond pulses (SAPs) can be obtained the following referred to as probe by spatially separating the pulses in pulse, are sent into a photoelectron the train [7,8] or by manipulating the spectrometer, where photoelectrons driving pulse in a way that the inte- are generated from a detection gas raction is driven by only one half-cy- (usually noble gases), while the time cle of the field [9]. The conversion delay between the APTs and the probe efficiency for HHG, i.e. the ratio of field is scanned with interferometric the energy of the attosecond pulse precision. Employing photoelectron train or single attosecond pulse to spectroscopy for measuring attose- the energy of the driving laser pulse, cond pulses is somewhat obvious, is about 10-5 at best (usually lower taking into account that the photon for single attosecond pulses and for energy generally overcomes the io- photon energies larger than 50 eV), nization potential of neutral gases. determined both by the single-atom The underlying idea of RABBIT is to response and by phase-matching in measure the phase difference between the generation gas. Still, modern consecutive harmonics, which is the attosecond pulse sources can have information needed to reconstruct average powers in the range of μW the average attosecond pulse in the to mW [10]. train. In optics, a phase difference is After the first observation of often assessed by interference. The HHG, it took almost fifteen more different harmonics of the frequency years until the duration of attose- comb representing an APT do howe- cond pulses in a train as well as that ver not result in a steady and obser- of a single attosecond pulse were vable interference, because they are finally experimentally measured in separated in photon energy, so that 2001 [11,12]. The measurement ap- the generated photoelectrons are also proaches, i.e. RABBIT (Reconstruction well separated in kinetic energy. The of Attosecond Bursts by Interference probe pulse however couples conse- of Two-photon Transitions) for APTs cutive harmonics by introducing side- and the Attosecond Streak Camera bands to the photoelectron spectrum, for SAPs, are based on performing which are located between the harmo- cross-correlations of the APT or SAP nics. The sidebands are due to two-co- with a longer low-frequency pulse, lour two-photon ionization; either a usually a copy of the driving pulse harmonic and a probe photon are ab- for HHG, while the photoelectron sorbed simultaneously or a photon spectrum originating from a detec- from the next harmonic is absorbed tion gas as a result of the two fields and a probe photon is emitted, resul- is recorded. The spectral amplitude ting in two possible quantum paths and phase of the APT or SAP are en- from two consecutive harmonics to coded in the photoelectron spectrum the same sideband, thus leading to and the pulses can be retrieved with interference. The sidebands oscillate different computer algorithms. with the time delay τ between the APT and the probe field as α β ωτ Δϕ Δθ The RABBIT technique S2q = + cos[2 - 2q - 2q], (1) for characterizing α β attosecond pulse trains where and describe the ampli- tude and contrast of the oscillations, Δϕ ϕ ϕ In this article, we will focus on the respectively and 2q = 2q+1 - 2q-1 is RABBIT technique and how it can the phase difference between the be used to learn about fundamental consecutive harmonics of the orders electron dynamics on the attosecond 2q +1 and 2q −1, where q is an integer.

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time scale that was not accessible before. One of the most prominent questions in this respect is “how long does ionization take?”, i.e. “how long does it take for a photoelectron Figure 2. to actually leave the atom after inte- Illustration of racting with an attosecond pulse?” the RABBIT The contrary question, i.e. “how technique. long would it take the parent-atom Panel (a) shows how two-colour or molecule to know that it has (APT + probe) been ionized and become an ion?” ionization is equally intriguing. However, since leads to the the most prominent experimental formation of sidebands tools of the field, i.e. streaking and between the RABBIT, inherently employ photoe- harmonics lectron spectroscopy, the leaving of (blue) in the a photoelectron is more straight- photoelectron spectrum forward to study. It should however plotted in (b). be noted that the ionization time is Panel (c) shows a delicate quantity to define. After a RABBIT ionization, the photoelectron moves trace, i.e. photoelectron in the Coulombic potential of the spectrum vs. ion, which changes with the inverse delay between of the distance to the ion and for- the APTs and mally reaches infinitely far; any de- probe pulses. The white line finition of when the photoelectron indicates the has left the proximity of the ion measured phase would be somewhat arbitrary. What differences helps here, is a more fundamental between harmonics, quantum mechanical view on ioni- encoded in zation, where we consider photoe- the sideband lectron wave packets of Coulombic phases, which waves instead of a classical par- allow for reconstruction ticle-like understanding of photoe- of the average lectrons. An electron wave packet is pulse in the a quantum mechanical construc- APT, as shown tion, describing the electron’s pro- in (d). bability amplitude to be found in a certain position at a certain time. Δϕ The last term, 2q, often referred often is positive, can be compensa- After ionization the photoelectron to as atomic phase, is an intrinsic ted by transmission through thin wave packet moves in the potential contribution from the detection metallic foils that provide anoma- landscape of the ion. Similarly to an gas due to two-colour ionization. lous dispersion in the XUV spectral ultrashort laser pulse propagating If the phase differences between all range [13]. in a dispersive medium, where the consecutive harmonics are known, speed is a function of wavelength, the average attosecond pulse in the Investigating electronic the electron wave packet will pick train can be obtained by coherent- dynamics on the up a group delay, which is defined ly adding the harmonics with their attosecond time scale as the derivative of its phase in res- respective phase offsets. It should be pect to energy. While the Coulomb noted that this is only accurate if the While the early days of attosecond potential formally reaches infinitely Δϕ atomic contribution, i.e. 2q, is small science were mostly dedicated to the far, the group delay of an electron compared to the phase differences characterization of the spectral and wave packet propagating through between the harmonics. Among temporal properties of attosecond it is finite. The acquired group de- many achievements, the RABBIT pulses, the focus has later shifted lay can be interpreted as ionization technique has shown that the intrin- towards actually applying those time. This view was first introduced sic chirp of attosecond pulses, which pulses for studying dynamics on a by Wigner for scattering events [14].

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landscape of the ion in the presence of the probe field, where the contri- bution from the probe can often be determined theoretically [20]. While the contribution from τ θ in the past was considered small, it has now moved into the focus for mea- suring photoionization time delays. However, determining absolute de- lays remains difficult since the ab- solute phase of a RABBIT sideband Figure 3. Measured depends on the delay between the relative ionization time delay between APT and the probe pulse, which the 3s and 3p sub- usually is not known accurately shells in argon in enough. Thus, relative time delay comparison with measurements are performed. For different calculation methods. The figure example in the case of the photoioni- is adapted from zation in the n = 3 shell in argon, two [18] with additional RABBIT traces are recorded simul- calculations taneously for photoelectrons ori- from [19]. ginating from the 3p and from the 3s sub-shells. As the photoelectrons Determining the absolute ioni- [17,18]. The energy range around are generated from identical attose- zation time however is complicated. 40 eV that was investigated is par- cond pulses, any relative shift of the Experiments have therefore mostly ticularly interesting because due to sidebands in the two RABBIT traces focused on measuring the relative strong electron correlation effects, must originate from different group time delay between photoelectron i.e. interactions between the different delays that the respective electron wave packets from different initial electrons of the atom, this energy wave packets experience as a result states, which is an easier question to region is difficult to treat theoreti- of two-colour ionization. Figure 3 answer than the absolute time delay. cally. Thus, the measured difference shows measured relative time delays Prominent early examples of such in time delay can serve as qualitative in comparison to different theore- experiments are the measurement indicator for the suitability of theo- tical models. The different theories of a relative time delay of about 100 retical models. To illustrate how the differ significantly around 40 eV and as between the ionization from va- RABBIT technique can be used to none of them shows perfect agree- lence- and conduction band states in assess time delays, we shall rewrite ment with the measured delays. tungsten [15] as well as the relative equation 1 as It is fascinating to note that the time delay of 21±5 as that was mea- α β ω τ τ τ relative time delays extracted from S2q = + cos[2 ( - 2q - θ)], (2) sured for ionization from the 2p sub- RABBIT traces are usually much shell in neon as compared to the 2s where we express the phase differences smaller than the pulse duration of sub-shell [16]. The latter work, further as finite difference approximations of the attosecond pulses used in the Ѩϕ Δϕ stimulated by the intriguing fact that 2q measurement. The minimum obser- group delays, i.e. τ = — ≈ — 2q Ѩ⍀| ω the magnitude of the observed time ⍀ ω 2 vable delay is limited to how accura- Δθ =2q delay could not be reproduced theo- 2q tely the phase of the sidebands can and τθ ≈ —, where ω is the carrier retically, has triggered a vast number 2ω be determined. This depends on the of experimental and theoretical efforts frequency of the laser pulses. In this signal-to-noise ratio and the stability to understand the origin of ionization view, the sideband oscillations descri- of the interferometer controlling the time delays, and assessing such time bed by equations 1 and 2, respectively delay between the APTs and probe delays became an important direction can be interpreted differently. As io- pulses rather than on the duration in attosecond science throughout the nization happens, the electron wave of the attosecond pulses. It is a very last few years. packet inherits the group delay of the common feature of interferometric While the pioneering experiments harmonics, which explains one contri- measurements, where often the phase mentioned above were performed bution to the phase of the RABBIT of interferometric fringes can be de- with the streaking technique, the sidebands, i.e. the one corresponding termined with much greater accuracy τ τ first attosecond ionization time de- to 2q. The other contribution, θ, re- than the wavelength of the light. One lays investigated with RABBIT were fers to a delay that the electron wave prominent example for this are gravi- measured in the n = 3 shell in argon packet acquires in the potential tational wave detectors.

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A proof-of-principle experiment Further developments performed in xenon showed that the RABBIT technique could be applied Since the first RABBIT measure- for more complicated ionization pro- ments, femtosecond laser tech- cesses than those discussed so far [21]. nology has evolved rapidly. One In one-photon double-ionization, a interesting aspect of that deve- single absorbed XUV photon leads lopment is spectral tunability. to the ejection of two photoelectrons Employing tunability of the carrier which share the excess energy conti- wavelength of the driving pulses for nuously. The two electrons must thus HHG, the high-order harmonics are interact with each other resulting in a no longer fixed at specific photon time delay. Incorporating the ion into energies. If one harmonic is tuned the picture, this is the prototype of through a resonance, the phase of the quantum mechanical three-body that resonance will be carried into problem and therefore extremely in- the sidebands above and below teresting to study. However, recording that harmonic. The respective next a RABBIT trace in this case is much sidebands will however be unaffec- more challenging because the pairs ted and can serve as reference to of correlated photoelectrons must be extract the phase associated with measured in coincidence. This means, the resonance. This technique to be sure that two detected electrons was applied to study the phase in originate from the same ionization two-colour two-photon ionization event, one has to work at a rate of less of helium [22] and more recently than one event per laser shot, which to measure the phase evolution of a makes recording RABBIT traces very Fano resonance in argon [23]. Fano time consuming and puts large de- resonances are a very general phe- mands on the laser’s long-term stabi- nomenon in physics, characterized lity. Comparing to single ionization by an asymmetric line shape that from the 5p-shell, which is recorded originates from the interference simultaneously, the relative ioniza- between a resonant process and a tion time delay for the double-ioniza- background [24]; in atomic systems, tion process could be extracted [21]. between direct photoionization to Here, single ionization was used as a the continuum and excitation to a reference clock, because the absolute quasi-bound state above the ioni- phase of RABBIT sidebands, as dis- zation potential, which will rapidly cussed earlier, is usually unknown. decay (within femtoseconds) to the

Figure 4. Phase variation of sideband 16 plotted against the photon energy of harmonic 17, which is scanned through the Fano resonance. The black circles are the measurement and the red line shows calculations. The figure is adapted from [23].

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Figure 5. Illustration of the spectrally resolved RABBIT sideband analysis applied in [27]. The left graph shows simulated photoelectron spectra, obtained for attosecond pulse trains generated with 800 nm driving pulses, from the 2p sub-shell in neon (red line, ionization potential 21.6 eV), from the 2s sub-shell (yellow line, ionization potential 48 eV) and from ionization with shake-up (blue line, ionization potential 55.8 eV). The photoelectrons due to shake-up ionization lie between the ones from the 2s sub-shell and would thus overlap with 2s sidebands in a RABBIT measurement. The right side of the figure shows the photoelectron kinetic energy region around harmonic 57 and sideband 56 of the 2s sub-shell. The lower plot shows the measured photoelectron spectrum for APTs only (blue line) and APTs+probe (red line), clearly visualizing the spectral overlap of sideband 56 with photoelectrons coming from ionization with shake up by absorption of harmonic 61. The upper plot shows the oscillation amplitude (red line) and extracted phase (black line), obtained from Fourier analysis. Only the low energy part of sideband 56 (which is free from overlap) can be used to retrieve the sideband phase.

continuum, i.e. auto-ionize. In the Conclusion any other states, which would lead experiment, a Fano resonance in ar- to a wrong phase retrieval of the gon is spectrally scanned with har- To conclude our article, we would sideband. In the RABBIT traces re- monic 17 of a 800 nm driving pulse. like to focus on a very recent re- corded for photoelectrons from the The phase of the resonance is im- sult. Enabled by more reliable and 2s and 2p sub-shells in neon in [27], printed on the adjacent sidebands long-term stable lasers as well as the 2s sidebands were overlapping and can be extracted using a side- more efficient and high-resolution with peaks due to 2p ionization with band unaffected by the resonance photoelectron spectrometers, the shake up of another 2p state to the as reference. The experimentally signal-to-noise ratio in RABBIT 3p state, i.e. an ionization event obtained phase is shown in Figure 4. measurements can be increased to where due to electron-electron in- This gives a characterization of the a level that spectral information can teractions the ion is left in an exited electron wave packet in amplitude now often be obtained by directly state. However, the correct phase and phase, which e.g. in the case of analysing the sideband phase en- of the sideband could be obtained helium with a single continuum ergy-resolved instead of averaging by only using the spectral interval channel can be used to analyse it in it over the whole width of the side- where the sideband was free from the time-frequency domain [25,26] band [26]. This approach has helped overlap. Using this technique, rela- similarly to what is done in ultrafast to resolve the long-standing mystery tive ionization time delays between optics for ultra-short optical pulses, of the 2s/2p relative ionization de- the 2s and 2p sub-shells in neon and provides intriguing comple- lay in neon [27]. One condition for were obtained, now in excellent mentary information to the spectral a RABBIT measurement to work agreement with theory [27]. The domain investigations extensively properly is that the sidebands are energy-resolved sideband analysis performed in the past. not overlapping spectrally with is illustrated in Figure 5.

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The probably most exciting as- FURTHER READING pect of the techniques discussed in [1] A. McPherson et al., J. Opt. Soc. Am. B 4, [14] E.P. Wigner, Phys. Rev. 98, 145 (1955) this article is the ability to measure 595 (1987) [15] A.L. Cavalieri et al., Nature 449, amplitude and phase of electron [2] M. Ferray et al., J. Phys. B 21, 31 (1988) 1029 (2007) wave packets and by that have full [3] P. Antoine et al., Phys. Rev. Lett. 77, 1234 (1996) [16] M. Schultze et al., Science 328, 1658 (2010) access to the temporal dynamics on [4] P.B. Corkum, Phys. Rev. Lett. 71, [17] K. Klünder et al., Phys. Rev. Lett. 106, the attosecond time scale. Modern 1994 (1993) 143002 (2011) laser technology in combination [5] K.J. Schafer et al., Phys. Rev. Lett. 70, [18] D. Guénot et al., Phys. Rev. A 85, with high-resolution photoelectron 1599 (1993) 053424 (2012) spectrometers provide high tempo- [6] M. Lewenstein et al., Phys. Rev. A 49, [19] M. Magrakvelidze et al., Phys. Rev. A 91, ral and energy resolution, opening 2117 (1994) 063415 (2015) the door to measurements on more [7] H. Vincenti et al., Phys. Rev. Lett. 108, [20] J.M. Dahlström et al., Chem. Phys. 414, complicated systems like molecules 113904 (2012) 53 (2013) or nano-structures. Furthermore, [8] C.M. Heyl et al., New J. Phys. 16, [21] E.P. Månsson et al., Nature Phys. 10, laser technology currently pushes 1367 (2014) 207 (2014) [9] F. Calegari et al., J. Phys. B: At. Mol. Opt. the development of HHG attose- [22] M. Swoboda et al., Phys. Rev. Lett. 104, Phys. 45, 074002 (2012) cond sources with higher photon 103003 (2010) [10] C.M. Heyl et al., J. Phys. B: At. Mol. Opt. energy in the range of hundreds [23] M. Kotur et al., Nature Comm. 7, 10566 (2016) Phys. 50, 013001 (2017) of electron-volts. After almost two [24] U. Fano, Phys. Rev. 124, 1866 (1961) decades of studying mostly valence [11] P.M. Paul et al., Science 292, 1689 (2001) [25] D. Busto et al., J. Phys. B 51, [12] M. Hentschel et al., Nature 414, shell dynamics, attosecond science 044002 (2018) 509 (2001) is now well prepared to also put its [26] V. Gruson et al., Science 354, 313 (2016) focus on the rich dynamics of the [13] R. López-Martens et al., Phys. Rev. Lett. 94, 033001 (2005) [27] M. Isinger et al., Science 358, 893 (2017) inner atomic shells. Q

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طظد 3FGFSFODॻ

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ظدد 3FGFSFODॻ

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ددد 3FGFSFODॻ

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ذدد 3FGFSFODॻ

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Figure
. technique. developing newanalyticalmethodsandcoursesofactionforthisversatile processes inrare gasatomsusingthetechniquereferred toasRABITT, while simpler systems. This thesis then explores the time evolution of some ultrafast be realized, theavailabletoolsneedtobetestedanddevelopedonmuch sis, whichinvolvesmigrationofelectronic charges.However, before thiscan into, andcontrol of,chemicalandbiologicalprocesses suchasphotosynthe of followingchargemovementsinreal timewouldgiveunparalleledinsight bursts ofattosecondduration(athousandthafemtosecond).Theability to takesnapshotsoftheseprocesses thankstothepossibilityofcreating light of asecond:so-calledfemtosecond(0.000000001s).We are able atoms. Theprocesses weinvestigatetakeplaceduringamillionthofbillionth This thesisdealswithultrafastdynamicsofelectronic processes inrare gas ISBN 978-91-7753-892-9ISBN (print) ISBN 978-91-7753-893-6 (pdf) 978-91-7753-893-6 ISBN Faculty of Engineering, LTH of Engineering, Faculty Division of Atomic Physics Atomic of Division - Lund University ISSN 0281-2762 ISSN

9 789177 538929 MARCUS ISINGER Time-Frequency Analysis in Attosecond Spectroscopy 2019 Time-Frequency Analysis in Attosecond Spectroscopy

MARCUS ISINGER DEPARTMENT OF PHYSICS | FACULTY OF ENGINEERING | LUND UNIVERSITY