András Lukács, Zoltán Várallyay and Róbert Szipocs- Cubic phase distortion of single attosecond...

8/3/2019 Andrs Lukcs, Zoltn Vrallyay and Rbert Szipocs- Cubic phase distortion of single attosecond pulses being reflect

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Advanced Solid-State Photonics

Cubic phase distortion of single attosecond pulses being reflected on narrowbandMo/Si filtering mirrors

Andrs LukcsR&D Ultrafast Lasers Ltd, Konkoly Thege t 29-33, H-I12I Budapest, [email protected]

Zoltn VrallyayTechnical University of Budapest, Department of Atomic Physics

Budafoki t 8, H-IIII Budapest, [email protected] Szipocs

Research Institute for Solid State Physics and OpticsKonkoly Thege t 29-33, H-II2I Budapest, [email protected]

Abstract: We show that cubic phase distortion caused by narrowband Mo/Si multilayerfiltering X-ray mirrors may considerably increase the time duration of single attosecondpulses.OCIS codes: (320.2250)Femtosecondphenomena;(340.7470)X-raymirrors

IntroductionAfter reaching the sub-5 fs regime in the field of high power ultrashort laser pulse generation [1],anextended effort has been made in order to push the temporal resolution limit in the sub-femtosecond orattosecond (as) regime. Performing experiments on this timescale is extremely exciting: a many offundamental physical processes, such as ultrafast electron dynamics, evolve in the sub-femtosecondregime. The possibility of generating attosecond pulses was predicted by Farkas and Tth [2], andAntoine et al [3] by exploitation of high harmonic generation (HHG). High harmonics are typicallygenerated in rare gases following the ionization process induced by high intensity lasers pulses andexhibit discrete frequencies that are the odd multiples of the original laser frequency. Accordingtotheory, selecting a proper range of these harmonics one can generate a train of attosecond pulses.

Single attosecond pulses can be obtained using a few cyc1e - about 5 fs - laser pulses forgeneration of a continuum in the soft x-ray spectrum, which continuum must be properly filteredbynarrowband Si/Mo multilayer mirrors [4]. In order to obtain transform limited attosecond pulses, theintrinsic chirp of the continuum [5] should be compensated as well: chirped mirror structures developedfor X-ray wavelengths [6] may solve this problem. An alternative approach has been recently proposedby Kim et al. [7] who used a thin Sn (Tin) layer for spectral filtering and compensation of the positivelinear chirp of the continuum. This latter approach is limited by the fact that spectral filtering anddispersion compensation can not be independently adjusted.

In this paper we investigate phase properties of Mo/Si multilayer filtering mirrors developedforsingle attosecond pulse generation experiments. We show that cubic phase distortion originating fromnarrow bandwidth (LiE '" 3 eV) Mo/Si multilayer filtering mirrors results in longer time durationandmultiple pulsing. Interestingly, this effect reduces for higher bandwidth filtering mirrors, i.e., forshorterattosecond pulses.

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ase properties of Mo/Si multilayer filtering mirrorsispersive properties of thin film spectral filters such as Fabry-Perot thin film interferometers orflective notch filters were discussed in Ref. [8]. In general, it was found that arapid change in theectral reflectivity/transmittance is accompanied by arapid variation of the phase shift onflection/transmission seriously harming femtosecond pulse operation. For our studies in the 10nm - 25wavelength regime, which is typically used for single attosecond pulse generation [4], we used theltilayerMo/Si filter designs presented in Ref. [9]: 30 bilayers of Mo and Siwith spacing d of 9.1-9.5mwith varying thickness ratios (r). In our calculation, r is defined as

r = dAbsdsp + dAbs

(1)

which equation dAbsnd dspstand for the physical thickness values of absorbing Mo and the spacer Siyers, respectively. In our calculations, refractive index data listed in Ref. [10] were used.

0.9 Substratel (SiMo)3.1Air r =0.17 ~.r-'~/',,/

/.j\ :: ."'. '. ri\,' '.j\: '.j~ ! -TRANSMITTANCE:\ j REFLECTANCE: \ j: ABSORPTION: '. i :'. /:'.-' .

0.80.7

;- 06~>- 0.5fo-~ 0.4wfo-~ 0.30.2 Fig.1a

'. .. ...', ,"..'.. . . .. .. "0.10.0 15 16 17 18 19 20

WAVELENGTH (nm)

Fig.l Computed spectral transmittance, reflectance and absorption of a multilayer Mo/Si filtering miITorwith r =0.170.8..J Fig. 2a

1.510 j Fig. 2b

0.6

-[=0,33.. r = 0.17- -- - [ = 0.100.50.0

.' , .

11:

"i . I, :::~ :::::i: i".,' "" :"" .",1 ,'",'" :"." .":" :,'" ., "., .

;g -05>- .1.0-l-s;:i= 0.4()w...JLLWCI:0.2

0.0 -3.5-4.0

-[=0,33",... [=0.17

[=0,10

15 16 17 18 19 20 .4.5 15 16 17 18 19 20WAVELENGTH (nm) WAVELENGTH (nm)ig. 2 Spectral reflectance (Fig. 2a) and group delay (Fig. 2b) of (Mo/Si)3o multilayer filters with different r values of 0.1,0.17 and 0.33ecan observe that spectral reflectance and absorption exhibit a parabolic shape around the centralvelengthof the filtering mirror (see Fig. 1). Since transmittance of the multilayer mirror is nearly zero

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in the 17-18 nm wave1ength regime ( TrA.) "" O), the reflectivity vs. wave1ength function R(A) of theMo/Si mirror is determined by the spectral absorption function A( A) as follows:

R( A) "" 1 - A( A) (2)In Ref. [11], we have pointed out that there is a strong relationship between reflection (absorption,scattering) losses and dispersive properties of multilayer die1ectric mirrors: in general, lossesonreflection are proportional to the group delay at wavelength A, in other words, expecting wavelengthindependent opticaI constants, the spectral absorption functionA( A)can be approximated as

A(A) ex: 'teA) (3)In caseof singleattosecondpulse generation,the time durationof the pulse is determinedby spectrumI(A) and the spectral phase


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16000 - Translorm limitedpulseFWHM=286.5as_u_- DistortedpulseFWHM=437.7as

SI (SiMO)301 A r= 0.101400012000

~ 10000>-1- 8000(jjZ~ 6000Z40002000

o .-2.0 0.0Time (Is)

0.5 1.0 1.51.0 -0.51.5

40000SI (SiMO)301A r= 0.1735000. - Translorm limited pulseFWHM=264.7 asu_u Distorted pulseFWHM=309.8 as30000

:' 25000::J.;20000


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with r value of 0.17, when the pulse duration of the transform limited attosecond pulse is increasedfrom 264 as to 314 as due to filter dispersion. In case of the highest [' value (and highest bandwidth!),the effect of cubic phase can be neglected: this filter supports nearly transform limited pulse durationsbelow 250 as.SummaryWe have shown that cubic phase distortionoriginatingfrom narrowbandwith (AE '" 3 eV) Mo/Simultilayerfilteringmirrorsresultsin longertimedurationandmultiplepulsing.Interestingly,thiseffectreduces for higher bandwith filtering mirrors, i.e. for shorter attosecond pulses.AcknowledgementsThis research was supported by the grantOMFB 00240/2004.References

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M. Nisoli, S. DeSilvestri, O. Svelto, R. Szipocs, K. Ferencz, C. Spielmann, S. Sartania, andF.Krausz,"Compression of high-energy laser pulses below 5 fs" Opt. Lett. 22 (8),522 (1997).G. Farkas and C. Toth,"Proposal for attosecond light pulse generation using laser-inducedmultiple-harmonic conversion processes in rare gases" Phys. Lett. A 168 (5-6), 447 (1992).P. Antoine, A. LHuillier, and M. Lewenstein,"Attosecond pulse trains using high-orderharmonics" Phys. Rev. Lett. 77 (7), 1234(1996).M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. Reider, P. Corkum,and F. Krausz,"X-ray pu1sesapproaching the attosecond frontier" Science 291 (5510), 1923(2001).S. Kazamias and P. Ba1cou,"Intrinsicchirp of attosecond pulses: Single-atom model versusexperiment" Phys. Rev. A 69 (6), 063416 (2004).R. Szipocs and F. Krausz,"Dispersive dieletcric mirror" United States Patent 5,734,503 (1998).K. Kim, C. Kim, M. Baik, G. Umesh, and C. Nam,"Single sub-50-attosecond pulse generationfrom chirp-compensated harmonic radiation using material dispersion" Phys. Rev. A 69 (5),051805 (2004).R. Szipocs, A. Kohzi-Kis, P. Apai, E. Finger, A. Euteneuer, and R. Hofmann,"Spectral filteringof femtosecond laser pulses by interference filters" Appl. Phys. B 70, S63 (2000).Y. Lim, T. Westermalbesloh, A. Aschentrup, O.Wehmeyer, G. Haindl, U. Kleineberg,andU.Heinzmann,"Fabrication and characterization of EUV multilayer mirrors optimized for smallspectral reflection bandwidth" Appl. Phys. A 72 (1), 121 (2001).http://www.cxro.lbl.gov/opticaCconstants/ getdb2.html.R. Szipocs,"Dispersive properties of dielectric laser mirrors and their use in femtosecondpulselasers (PhD thesis)" www.fslasers.com (2000).

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