Cubic phase distortion of single attosecond pulses being reflected on narrowband Mo/Si filtering mirrors András Lukács

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1 Cubic phase distrtin f single attsecnd pulses being reflected n narrband M/Si filtering mirrrs András Lukács R&D Ultrafast Lasers Ltd, Knkly Thege út 29-33, H-I12I a.lukacs@szipcs.cm Budapest, Hungary Intrductin Zltán Várallyay Technical University f Budapest, Department f Atmic Physics Budafki út 8, H-IIII Budapest, Hungary z.varallyay@feti.hu Róbert Szipcs Research Institute fr Slid State Physics and Optics Knkly Thege út 29-33, H-II2I Budapest, Hungary szipecs@sunserv.kfki.hu Abstract: e sh that cubic phase distrtin caused by narrband M/Si multilayer filtering X-ray mirrrs may cnsiderably increase the time duratin f single attsecnd pulses. OCIS cdes: ( )Femtsecndphenmena;( )X-raymirrrs After reaching the sub-5 fs regime in the field f high per ultrashrt laser pulse generatin [1], an extended effrt has been made in rder t push the tempral reslutin limit in the sub-femtsecnd r attsecnd (as) regime. Perfrming experiments n this timescale is extremely exciting: a many f fundamental physical prcesses, such as ultrafast electrn dynamics, evlve in the sub-femtsecnd regime. The pssibility f generating attsecnd pulses as predicted by Farkas and Tóth [2], and Antine et al [3] by explitatin f high harmnic generatin (HHG). High harmnics are typically generated in rare gases flling the inizatin prcess induced by high intensity lasers pulses and exhibit discrete frequencies that are the dd multiples f the riginal laser frequency. Accrding t thery, selecting a prper range f these harmnics ne can generate a train f attsecnd pulses. Single attsecnd pulses can be btained using a fe cyc1e - abut 5 fs - laser pulses fr generatin f a cntinuum in the sft x-ray spectrum, hich cntinuum must be prperly filtered by narrband Si/M multilayer mirrrs [4]. In rder t btain transfrm limited attsecnd pulses, the intrinsic chirp f the cntinuum [5] shuld be cmpensated as ell: chirped mirrr structures develped fr X-ray avelengths [6] may slve this prblem. An alternative apprach has been recently prpsed by Kim et al. [7] h used a thin Sn (Tin) layer fr spectral filtering and cmpensatin f the psitive line ar chirp f the cntinuum. This latter apprach is limited by the fact that spectral filtering and dispersin cmpensatin can nt be independently adjusted. In this paper e investigate phase prperties f M/Si multilayer filtering mirrrs develpedfr single attsecnd pulse generatin experiments. e sh that cubic phase distrtin riginating frm narr bandidth (LiE '" 3 ev) M/Si multilayer filtering mirrrs results in lnger time duratinand multiple pulsing. Interestingly, this effect reduces fr higher bandidth filtering mirrrs, i.e., fr shrter attsecnd pulses. 806

2 Phase prperties f M/Si multilayer filtering mirrrs Dispersive prperties f thin film spectral filters such as Fabry-Pert thin film interfermeters r reflective ntch filters ere discussed in Ref. [8]. In general, it as fund that arapid change in the spectral reflectivity/transmittance is accmpanied by arapid variatin f the phase shift n reflectin/transmissin seriusly harming femtsecnd pulse peratin. Fr ur studies in the 10 nm - 25 nm avelength regime, hich is typically used fr single attsecnd pulse generatin [4], e used the multilayerm/si filter designs presented in Ref. [9]: 30 bilayers f M and Si ith spacing d f nm ith varying thickness ratis (r). In ur calculatin, r is defined as r = dabs dsp + dabs (1) in hich equatin d Absand dsp stand fr the physical thickness values f absrbing M and the spacer Si layers, respectively. In ur calculatins, refractive index data listed in Ref. [10] ere used ;- 06 >- 0.5 f- 0.4 f Fig.1a Substratel (SiM)3.1Air r =0.17. r-' /',,/ /.j\ ::."'. '. ri \,' '.j \: '.j! -TRANSMITTANCE :\ j REFLECTANCE : \ j: ABSORPTION : '. i : '. '.-' /:. ' ".',,"..'... AVELENGTH (nm) Fig.l Cmputed spectral transmittance, reflectance and absrptin f a multilayer M/Si filtering miitrith r = >- l- s;: i= J LL CI: J Fig. 2a -[=0,33.. r = [ = j Fig. 2b 0.5.',. ;g -05 >-.1.0 <t: uj -1.5 CL -2.0 :::J -2.5 CI: c) " i. I, ::: :: :: :i: 11: i ".,' " :" ".",1,'",'" :"."." :" '". :,, ".,. -[=0,33 ",... [=0.17 [=0,10 AVELENGTH (nm).4.5 AVELENGTH (nm) Fig. 2 Spectral reflectance (Fig. 2a) and grup delay (Fig. 2b) f (M/Si)3 multilayer filters ith different r values f 0.1, 0.17 and 0.33 Onecan bserve that spectral reflectance and absrptin exhibit a parablic shape arund the central avelengthf the filtering mirrr (see Fig. 1). Since transmittance f the multilayer mirrr is nearly zer 807

3 in the nm ave1ength regime ( TrA.) "" O), the reflectivity vs. ave1ength functin R(A) f the M/Si mirrr is determined by the spectral absrptin functin A( A) as flls: R( A) "" 1 - A( A) (2) In Ref. [11], e have pinted ut that there is a strng relatinship beteen reflectin (absrptin, scattering) lsses and dispersive prperties f multilayer die1ectric mirrrs: in general, lssesn reflectin are prprtinal t the grup delay at avelength A, in ther rds, expecting avelength independent pticai cnstants, the spectral absrptin functin A( A) can be apprximated as A(A) ex: 'tea) (3) In case f single attsecndpulse generatin,the time duratinf the pulse is determinedby spectrum I(A) and the spectral phase <pca)f the frequency cmpnents. Expecting a cntinuum f unifnn spectral intensity ver the avelength range f ur interest, spectral intensity f the single attsecnd pulse can be ritten as hile the spectral phase <p(a)is determined I(A) ex: R(A) (4) by the intrinsic line ar chirp <Pcnt (A) f the cntinuum and the (cubic) phase shift <Pfilter (A) intrduced by the M/Si filtering mirrr: the first derivate f <Pfilter(A)by the frequency is a quadratic functin arund the central avelength f the filtering mirrr: 'tfilter (A)ex: 1- R(A) (5) By varying the thickness rati beteen the absrber layer dabs and the spacer layer dsp' hile keepinga fixed bilayer thickness f abut 10 nm, ne can change the high reflectivity bandidth f the multilayer mirrr (see Fig. 2a) and Ref. [8]. The crrespnding (precisely) cmputed grup delay versus avelength functins are displayed in Fig. 2b. As e predicted, the shape f grup delay vs. avelength functins fll that f the crrespnding spectral absrptin functins. Interestingly, the grupdelay variatin 't ver the reflectivity bandidth f the mirrrs des nt depend n the r values, Le.,the cubic phase term reduces fr higher bandidth filtering mirrrs. Cubic phase distrtin f single attsecnd pulses reflected n multilayer M/Si filtering mirrrs Using the spectral reflectivity data R(A) shn in Fig. 2a and the spectral phase data <Pfilter (A)usedfr calculating the grup delay functins shn in Fig. 2b, e can cmpute the tempral shapes f single attsecnd pulses being spectrally filtered by M/Si filtering mirrrs f different r values. The results f calculatins are shn in Fig

4 Translrm limitedpulse SI (SiMO)301 A r= 0.10 FHM=286.5as _u_- Distrtedpulse FHM=437.7as > (jj Z 6000 Z r=0.1 O :::J 50 --' O Q : 1- --' Time (Is) I I SI (SiMO)301A r= '":' ::J.; :;20000 ii <:: Q) Translrm limited pulse FHM=264.7 as u_u Distrted pulse FHM=309.8 as 200 :::J ' 50 cr: ' r= I J SI (SiM)301A r= '":' ::J.; :; ii <:: Q) Time (Is) Translrmlimitedpuls FHM=237.4 as - u - - Distrted pulse FHM=247.9 as ;:; ' O cr: t; ' -200 r= Time(Is) Fig. 3 The change f tempra1 pulse shape f single attsecnd pu1ses being reflected n the filtering mirrr ith r values f 0.1, 0.17, and The cmputed tempra1 intensity (left) and electric field functins (right) are displayed. The mst dramatic change in the pulse shape can be bserved in the case f the filtering mirrr ith r value f 0.1: the pulse duratin is increased frm 286 as t 438 as due t the cubic phase and the pulse shapeis strngly distrted. This effect can be still recgnized in the case f the M/Si multilayer mirrr 809

5 ith r value f 0.17, hen the pulse duratin f the transfrm limited attsecnd pulse is increased frm 264 as t 314 as due t filter dispersin. In case f the highest [' value (and highest bandidth!), the effect f cubic phase can be neglected: this filter supprts nearly transfrm limited pulse duratins bel 250 as. Summary e have shn that cubic phase distrtinriginatingfrm narr bandith (AE '" 3 ev) M/Si multilayerfilteringmirrrsresultsin lngertime duratinand multiplepulsing.interestingly,thiseffect reduces fr higher bandith filtering mirrrs, i.e. fr shrter attsecnd pulses. Acknledgements This research as supprted by the grant OMFB 00240/2004. References M. Nisli, S. DeSilvestri, O. Svelt, R. Szipcs, K. Ferencz, C. Spielmann, S. Sartania, andf. Krausz,"Cmpressin f high-energy laser pulses bel 5 fs" Opt. Lett. 22 (8),522 (1997). G. Farkas and C. Tth,"Prpsal fr attsecnd light pulse generatin using laser-induced multiple-harmnic cnversin prcesses in rare gases" Phys. Lett. A 168 (5-6), 447 (1992). P. Antine, A. LHuillier, and M. Leenstein,"Attsecnd pulse trains using high-rder harmnics" Phys. Rev. Lett. 77 (7), 1234 (1996). M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. Reider, P. Crkum, and F. Krausz,"X-ray pu1sesappraching the attsecnd frntier" Science 291 (5510), 1923 (2001). S. Kazamias and P. Ba1cu,"Intrinsicchirp f attsecnd pulses: Single-atm mdel versus experiment" Phys. Rev. A 69 (6), (2004). R. Szipcs and F. Krausz,"Dispersive dieletcric mirrr" United States Patent 5,734,503 (1998). K. Kim, C. Kim, M. Baik, G. Umesh, and C. Nam,"Single sub-50-attsecnd pulse generatin frm chirp-cmpensated harmnic radiatin using material dispersin" Phys. Rev. A 69 (5), (2004). R. Szipcs, A. Kházi-Kis, P. Apai, E. Finger, A. Euteneuer, and R. Hfmann,"Spectral filtering f femtsecnd laser pulses by interference filters" Appl. Phys. B 70, S63 (2000). Y. Lim, T. estermalbeslh, A. Aschentrup, O. ehmeyer, G. Haindl, U. Kleineberg, and U. Heinzmann,"Fabricatin and characterizatin f EUV multilayer mirrrs ptimized fr small spectral reflectin bandidth" Appl. Phys. A 72 (1), 121 (2001). getdb2.html. R. Szipcs,"Dispersive prperties f dielectric laser mirrrs and their use in femtsecndpulse lasers (PhD thesis)".fslasers.cm (2000). 810