1

Kenichi Ishikawa (石川顕一)http://ishiken.free.fr/english/lecture.htmlishiken@atto.t.u-tokyo.ac.jp

Advanced Plasma and Laser Scienceプラズマ・レーザー特論E

attosecond laser pulseアト秒レーザーパルス

2

アト秒パルス列

単独アト秒パルスと

attosecond pulse train (APT)

isolated attosecond pulse (IAP)

石川顕一

高次高調波は、基本波レーザーの半周期ごとにアト秒のバーストとして発生する（アト秒パルス列）

3

the emission of a pulse of a high-order harmonic field everyhalf-cycle period. In this model, the trajectory of theelectron, moving along the direction of the electric fieldof the fundamental laser, determines the phase of theemitted harmonic field. Therefore, our finding of the!-flipped phase in the attosecond pulse train verifies thatharmonic pulses are certainly from electrons detachedfrom opposite sides at every half-cycle period of the fun-damental laser field.

Note that the clear observation of phase locking in theactual experiment is due to the small number of interfer-ence fringes emerging from near single-cycle pulses in theAPT. We estimated the duration of the pulse by comparingthe calculated results of the interferometric autocorrelationof the harmonic fields with group-delay dispersion (GDD)and its Fourier transform to the measured results. Details ofthis calculation will be reported elsewhere. We plot thecalculated autocorrelation trace and its magnitude squareof Fourier amplitude as solid blue curves in Figs. 2(a) and2(b), respectively. Setting the GDD to 1:3! 10"32 #s2$,which is the measured numeric value with the separateexperiment [11], there is fairly good agreement betweenthe experimental observation and the calculated result ofboth autocorrelation and Fourier transform. The increasedGDD to 2:0! 10"32 #s2$ reduced the height of the enve-lope with the remaining interference fringe in the autocor-relation so that the intensity at 2"f in the Fourier transformis almost equal to that at 11"f. Therefore, 1:3! 10"32 #s2$is the reasonable GDD in practice, although we might takeinto account the intrinsic response of N2 to two-photonabsorption, as was mentioned in Refs. [27,28] for rare-gasatoms, in order to determine GDD in more detail.

The envelope and optical field of the attosecond pulsetrain, evaluated from the measured intensity ratio of theharmonic fields from the 9th to 19th orders and the esti-mated GDD, are shown in Fig. 3. The duration of the pulseenvelope is 320 attoseconds in full width at half maximum,which corresponds to only an %1:3-cycle period of theprincipal carrier frequency of the 11th harmonic field.Thus, we can clearly see the relative phase of interferencefringes to pulse envelopes.

In conclusion, we have shown clear evidence of thelocked phase in an attosecond pulse train by interferomet-ric autocorrelation. The detection of fringes that emergedfrom the interference of a pulse sequence in the XUV rangeenables us to determine the phase difference betweenpulses, so that we would obtain the instantaneous shapeof the optical field in the attosecond pulse train by combin-ing this result with those obtained by other techniques formeasuring the chirp [9,11,29] and by using a driving laserfield whose absolute phase is stabilized [1,2]. Thus, anoptical synthesizer of XUV light comes into the realm ofreality.

We thank Dr. E. J. Takahashi at RIKEN for his support ingenerating intense harmonic fields. This study was finan-cially supported by MEXT through a Grant-in-Aid forScientific Research on Priority Areas, for YoungScientists (A) and for Young Scientists (B).

*Electronic address: nabekawa@riken.jp[1] A. Baltuska et al., Nature (London) 421, 611 (2003).[2] R. Kienberger et al., Nature (London) 427, 817 (2004).[3] J. Reichelt et al., Opt. Commun. 172, 59 (1999).[4] H. R. Telle et al., Appl. Phys. B 69, 327 (1999).[5] D. H. Jones et al., Science 288, 635 (2000).[6] C. Gohle et al., Nature (London) 436, 234 (2005).[7] R. J. Jones et al., Phys. Rev. Lett. 94, 193201 (2005).[8] P. Antoine et al., Phys. Rev. Lett. 77, 1234 (1996).[9] P. M. Paul et al., Science 292, 1689 (2001).

[10] P. Tzallas et al., Nature (London) 426, 267 (2003).[11] Y. Nabekawa et al., Phys. Rev. Lett. 96, 083901 (2006).[12] T. Sekikawa et al., Nature (London) 432, 605 (2004).[13] K. Varju et al., Phys. Rev. Lett. 95, 243901 (2005).[14] E. J. Takahashi et al., Opt. Lett. 27, 1920 (2002).[15] E. Takahashi et al., Phys. Rev. A 68, 023808 (2003).[16] Y. Nabekawa et al., Phys. Rev. Lett. 94, 043001 (2005).[17] H. Hasegawa et al., Laser Phys. 15, 812 (2005).[18] E. J. Takahashi et al., Opt. Lett. 29, 507 (2004).[19] E. J. Takahashi et al., IEEE J. Sel. Top. Quantum Electron.

10, 1315 (2004).[20] K. Hoshina et al., J. Phys. B 39, 813 (2006).[21] T. E. Glover et al., Phys. Rev. Lett. 76, 2468 (1996).[22] E. W. Thulstrup and A. Andersen, J. Phys. B 8, 965 (1975).[23] R. W. Wetmore and R. K. Boyd, J. Phys. Chem. 90, 5540

(1986).[24] In fact, the fringes corresponding to the carrier frequencies

of the harmonic fields in the IAC trace should originatefrom the term ~S&'(&!2&N'1(; 0(~S&'() &!2&N'1(; #(, where themode-resolved correlation amplitude ~S&'(&!2&N'1(; #( wasdefined as Eq. (2) in Ref. [11]. The factor ei&2n'1(!f# in~S&'(&!2&N'1(; #( necessarily yields the odd parity of thefringes to the translation of the delay with &q' 1=2(Tf.

[25] P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).[26] M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994).[27] T. Nakajima and S. Watanabe, Phys. Rev. A 70, 043412

(2004).[28] L. A. A. Nikolopoulos et al., Phys. Rev. Lett. 94, 113905

(2005).[29] T. Sekikawa et al., Phys. Rev. Lett. 88, 193902 (2002).

-3 -2 -1 0 1 2 3

time [fs]

FIG. 3 (color online). Estimated intensity profile of the atto-second pulse train (dark-green curve with hatched area) and theoptical field (dark-blue curve).

PRL 97, 153904 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending13 OCTOBER 2006

153904-4

Nabekawa et al., Phys. Rev. Lett. 97, 153904 (2006)

１回だけバーストが発生するようにすれば、単独パルスになる。

世界初Paul et al., Science 292, 1689 (2001)

Only one burst Isolated attosecond pulse (IAP)

Optical cycle(2.7 fs)

High-order harmonics are generated as attosecond bursts repeated each half cycle of the fundamental laser (attosecond pulse train)

石川顕一

単独アト秒パルス

Light emission takes place only once.

光の放出は１回だけ Attosecond (10-18 sec) pulseアト秒パルス

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Hentschel et al. Nature 414, 509 (2001)

4

世界初

Baltuska et al. Nature 421, 611 (2003)

Zhao et al. (2012)

by a 300 mm focal length lens. The diameter of the centerspot of the focused Bessel streaking beam was 55 μm.The delay between the XUV and NIR pulses was con-trolled by a piezo-electric transducer (PZT). A 532 nm la-ser beam co-propagating through both arms was used tostabilize the Mach-Zehnder interferometer [12].The continuous XUV spectra generated with DOGmea-

sured by the MBES without streaking are shown in Fig. 2.By tuning the Ne pressure in the gas cell from 0.03 to0.33 bar, the cutoff photon energy was reduced from160 to 120 eV, which corresponds to Ip ! 2.6Up toIp ! 1.8Up. The calculated single-atom cutoff is 190 eV.The spectrum with pressure below 0.03 bar was not mea-sured due to the low count rate. The observed cutoff re-duction with increasing generation gas pressure isqualitatively consistent with previous experiments withXUV pulse trains [8,9]. Finally, the pressure of 0.2 bar inthe generation cell was chosen for the streaking experi-ment, where the entire spectrum, from 55 to 130 eV, wasconfined within the low-energy part of the Zr transmis-sion window where the filter GDD is negative.The attosecond pulses were retrieved from the streak-

ing trace shown in Fig. 3(a) using both the PROOF(phase retrieval by omega oscillation filtering) [13] andFROG-CRAB (frequency-resolved optical gating for com-plete reconstruction of attosecond bursts) [14,15] techni-ques. Whereas the FROG-CRAB technique requires thebandwidth of the photoelectron spectrum to be smallcompared to its central energy, PROOF is applicableto much broader spectra [13]. Here, we apply the princi-pal component generalized projections algorithm toPROOF [16], which is more robust than the methoddeveloped in [13]. In the limit of low streaking intensi-ties, Up < ωL, the streaking spectrogram is given byS"v; τ# ≈ I0"v# ! IωL

"v; τ# ! I2ωL"v; τ#, where IωL

and I2ωL

oscillate with the streaking laser frequency,ωL, and twicethe frequency, respectively [13], τ is the delay betweenthe XUV and laser pulses, and v is the photoelectronspeed. Since the spectrum and phase information ofthe attosecond pulses are completely encoded in IωL

,the amplitude and phase of the XUV pulse are guessed

in PROOF to match the modulation depth and phaseangle of IωL

.The streaking trace was obtained at a low streaking

intensity, 2.5 × 1011 W ∕cm2, to satisfy the requirementsof PROOF. Two methods are used to confirm the correct-ness of the phase retrieval. The first is to compare thephotoelectron spectrum obtained experimentally to theretrieved ones. This criterion was used in the past [17],and is a necessary condition of an accurate retrieval. An-other criterion is the agreement between the filtered IωL

trace from the measured spectrogram and the retrievedone. It is a much stricter requirement than the first one,because the modulation depth and phase angle of IωL

aredetermined by both the spectrum and phase, whereas thefirst method compares a quantity that is dominated byI0"v#, the unstreaked component of the spectrogram.Our retrieval meets both criteria very well, as shownin Figs. 3(c) and 3(b), respectively. Both the FROG-CRABand PROOF retrievals yield nearly identical temporalprofiles with a pulse duration of 67$ 2 as, as shownin Fig. 3(d), close to the transform-limited value of 62 as.The error bar was obtained following the treatment in [1],by taking each delay slice in the final guessed spectro-gram as a separate measurement of the pulse duration.The experiment was repeated at a higher streaking inten-sity (5 × 1011 W ∕cm2) and yielded the same result. Withthe intrinsic and Zr phase, we calculated a pulse durationof 68 as with the experimental spectrum, in agreementwith our retrieved result. At generation gas pressures sig-nificantly lower than 0.2 bar, the count rate was not suf-ficient for obtaining streaking traces with satisfactorysignal to noise ratio. Streaking was also performed athigher pressures, which yielded longer pulses due tothe reduced spectral bandwidth. For instance, at 0.36 bar,the retrieved pulse duration was 88 as.

Both PROOF and FROG-CRAB assume that onlyphotoelectrons emitted in a small angle in the streaking

Fig. 2. (Color online) XUV continuum generated by DOG inNe gas at six pressures. The length of the gas cell is 1 mm.The peak intensity at the center of the polarization gate is1 × 1015 W ∕cm2.

Fig. 3. (Color online) Characterization of a 67 as XUV pulse.(a) Streaked photoelectron spectrogram obtained experimen-tally. (b) Filtered IωL

trace (left) from the spectrogram in(a) and the retrieved IωL

trace (right). (c) Photoelectron spec-trum obtained experimentally (thick solid) and retrieved spec-tra and spectral phases from PROOF (solid) and FROG-CRAB(dashed). (d) Retrieved temporal profiles and phases fromPROOF (solid) and FROG-CRAB (dashed).

3892 OPTICS LETTERS / Vol. 37, No. 18 / September 15, 2012

Isolated attosecond pulse generation by a few-cycle laser pulse

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XUV pulse duration, (ii) improved signal-to-noise(S/N) ratio due to the increased XUV photonflux, and (iii) stronger streaking before the onsetof the NIR field–induced ionization in attosecondstreaking (2) or enhanced S/N ratio due to areduced number of tunneling steps in attosecondtunneling spectroscopy (14).

Figure 1 summarizes results of the modelingof the single-cycle interaction of ionizing NIRradiation with an ensemble of neon atoms (17). InFig. 1A, the left panels plot possible NIR elec-tric waveforms,ELðtÞ ¼ E0aLðtÞe−iðwL tþϕÞ þ cc(where cc stands for complex conjugate) derivedfrom our streaking measurements (as presentedin the next sections) for different settings of thecarrier-envelope (CE) phase, ϕ. Here, E0 is thepeak electric-field strength, aL(t) is the normal-ized complex amplitude envelope, and wL is thecarrier frequency. The probability of ionizationoutside the central cycle is more than two ordersof magnitude lower than that at the field maxi-mum and hence is negligible.

The spectra ofXUVemissions originating fromthe individual recollisions (18) are predicted todiffer by tens of electron volts in cut-off energy andby up to orders of magnitude in intensity as a con-sequence of the single-cycle nature of the drivingfield. The strong variation of emission energies andintensities within a single wave cycle creates idealconditions for isolated sub-100-as pulse genera-tion. Indeed, filtering radiation with the bandpassdepicted by the dashed-and-dotted line is predictedto isolate XUVradiation withmore than 90% of itsenergy delivered in a single attosecond pulse for arange of CE phases as broad as 30° ≤ϕ ≤ 90° (Fig.1B). In contrast, with few-cycle-driven harmonicgeneration resulting in isolated subfemtosecondpulses over only a relatively narrow range of theCE phase near ϕ ≈ 0° (3), single-cycle excitationappears to permit robust isolated attosecond pulsesfor a variety of driver waveforms, ranging fromnear-cosine– to sine-shaped ones, owing to theorder-of-magnitude variation of the ionizationprobability within a single wave cycle.

We used phase-controlled sub-1.5-cycle laserpulses carried at a wavelength of lL = 2pc/wL =720 nm (19) to generate XUV harmonics in aneon gas jet up to photon energies of ~110 eV(fig. S1). The emerging XUV pulse—followinga spectral filtering through a bandpass (dashed-and-dotted line in Fig. 1A) introduced by metalfoils and a Mo/Si multilayer mirror (fig. S2)—subsequently propagates, along with its NIR driv-er wave, through a second jet of neon atoms inwhich the XUV pulse ionizes the atoms in thepresence of the NIR field. The freed electronswith initial momenta directed along the electric-field vector of the linearly polarized NIR field arecollected and analyzed with time-of-flight spec-trometry (17).

The variation of the measured photoelectronspectra versus CE phase shows good agreementwith the predictions of our simulations (Fig. 2,A and B). Figure 2, C to E, shows plots ofelectron spectra corresponding to the CE phase

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Fig. 3. Sub-100-as XUV pulse retrieval. (A) Measured ATR spectrogram compiled from 126 energyspectra of photoelectrons launched by an XUV pulse with a bandwidth of ~28 eV (FWHM) and recordedat delay settings increased in steps of 80 as. Here, a positive delay corresponds to the XUV pulsearriving before the NIR pulse. The high flux of the XUV source allows this spectrogram to be recordedwithin ~30 min. (B) ATR spectrogram reconstructed after ~103 iterations of the FROG algorithm (17).(C) Retrieved temporal intensity profile and spectral phase of the XUV pulse. The intrinsic chirp of theXUV emission (Fig. 4B) is almost fully compensated by a 300-nm-thick Zr foil introduced into the XUVbeam between the attosecond source and the ATR measurement. Arrows indicate the temporal FWHM ofthe XUV pulse. (D) XUV spectra evaluated from the measurement of the XUV-generated photoelectronspectrum in the absence of the NIR streaking field (blue dashed line) and from the ATR retrieval (bluesolid line). The black dotted line indicates the retrieved spectral phase.

www.sciencemag.org SCIENCE VOL 320 20 JUNE 2008 1615

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1614 (2008)

8

Baltuska et al. Nature 421, 611 (2003)

� 5 fs

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K. L. Ishikawa

IONIZATION SHUTTER

9

HHG is suppressed when neutral atoms are depleted

tional two-photon ionization10. When a nonlinear optical process isobserved, it becomes possible to characterize the pulses bythe intensity autocorrelation, which is the standard diagnostictechnique in the visible region14. In the autocorrelation measure-ment, the intensity of nonlinear optical signal is recorded as afunction of the delay time between two replicas of a laser pulse. Theautocorrelation measurement is therefore the simplest type ofpump-probe experiments immediately extendable to femtosecondand attosecond nonlinear optical spectroscopy. In comparison withsynchrotron radiation (SR), which also covers the XUV and softX-ray regions, high harmonic pulses have temporal coherence andshort pulse duration—that is, high peak intensity. Thus, highharmonics are expected to open the new field of XUV nonlinearoptics.Previous work motivated us to generate and characterize high

harmonic pulses experimentally in the expectation of generatingintense attosecond pulses (Fig. 1). We focus on the ninth harmonicgenerated by the sub-10-fs blue laser pulse (photon energy 3.1 eV)in a multi-cycle regime, in contrast with previously reportedattosecond pulse generation in a few-cycle regime from the coher-ently superimposed broadband continuum in the cut-off region4,5.From nonadiabatic viewpoints, in which the slowly varying envel-ope approximation is not valid, Christov et al. simulated the 51sthigh harmonic generation of a 25-fs Ti:sapphire laser15. The 51stpulse lasts for about three optical cycles with ionization of theinteracting gas medium. A driving laser with a shorter pulseduration and shorter wavelength is expected to generate a shorterpulse. Together with the nonadiabatic effect, the dipole moment oflower order induced by the blue laser is larger than that induced by aTi:sapphire laser7. An enhancement of the pulse energy is thereforeexpected. From the adiabatic viewpoints16, a ninth-harmonic pulseof a 3.1-eV laser pulse was simulated by using a zero-range potentialmodel17. The ninth-harmonic pulse driven by an 8-fs pulse evolvessteeply with the highly nonlinear response of the dipole moment inthe rising edge of a driving pulse. When the optical electric fieldbecomes high enough to ionize the interacting atoms18, highharmonic generation is shut off because of the small dipole momentof the ions. In this case, a driving laser with a shorter pulse durationis also preferred.With the foregoing as a basis, modifications could be made by

taking account of the spatial intensity distribution in the drivinglaser beam and the propagation of harmonics. For example,harmonic pulses would be generated at different times at differentpositions, but the phase-matching effect would not preserve thedifference19. However, two-dimensional or three-dimensionalsimulations of high harmonic generation indicate that the harmo-nic pulses still retain the features of the single atom in the cut-off

region8,15. The autocorrelationmeasurement will make it possible toinvestigate these effects experimentally.

Blue laser pulses lasting 8.3 fs and 12 fs were generated by thefrequency conversion of a Ti:sapphire laser (photon energy 1.55 eV)as driving laser pulses20,21. Figure 2 shows the experimental setup forthe autocorrelation measurement. Two optically delayed replicas ofa blue laser pulse were focused into an argon gas jet to generate theninth high harmonic. The gas jet operating at 1 kHz was placed4mm after the focus and there was no spatial overlap between twobeams at high harmonic generation, where the peak intensity was3.9 £ 1014W cm22. The fundamental and lower-order harmonicswere eliminated by an aluminium filter. The ninth-harmonic pulseswere focused into helium gas by an Sc/Si multilayer spherical mirrorwith a focal length of 5 cm. The total pulse energy on the target was2 nJ. The ejected photoelectrons were collected and energy-resolvedby a magnetic bottle photoelectron spectrometer, ensuring a highcollection efficiency of 50%. Figure 2b is the photoelectron spec-trum of two-photon ATI. The observed highest photoelectronsejected by a one-photon process were from the 11th harmonicabsorption of Ar atoms and the peak by two-photon ATI was wellseparated from the other peaks, ensuring the assignment and thetwo-photon process. An autocorrelation trace was recorded bymeasuring the electron number at each optical delay.

The autocorrelation traces obtained by using 8.3-fs and 12-fs laserpulses are shown in Fig. 3a and Fig. 3b, respectively. Two electricfields superimpose coherently at a delay time of 0 fs, leading to theenhancement of two-photon ATI. The ratio of the peak to the

Figure 1 High harmonic pulse generation in the adiabatic picture. The red line is the ninthharmonic pulse of the 8-fs driving pulse with a peak intensity of 5.5 £ 1014W cm22

(dashed line). The blue line is the density of the neutral Ar atoms radiating high harmonics

calculated by using a tunnelling ionization theory18. The generation of high harmonics

ceases with the ionization of neutral atoms.

Figure 2 Two-photon above-threshold-ionization (ATI) autocorrelator. a, Experimentalsetup for the autocorrelation measurement of the ninth harmonic (9q) of the blue laser. To

improve the spectral resolution of the photoelectron spectrometer, an electrostatic field

was applied to the time-of-flight (TOF) tube and the photoelectrons were decelerated

inside the tube. b, The photoelectron spectrum. c, Diagram of the two-photon ATI

process. The area in red in b indicates the photoelectrons ejected from He atoms by the

process shown in c.

letters to nature

NATURE |VOL 432 | 2 DECEMBER 2004 | www.nature.com/nature606 © 2004 Nature Publishing Group

density of neutral Ar atoms fundamental field envelope (400 nm)

9th harmonic (of 400 nm) = 27.9 eV

backgroundwas almost 3:1, in good agreement with the ideal case ofthe autocorrelation measurement, indicating that the peak is notthe coherent spike. To estimate the pulse durations of the ninthharmonics, the autocorrelation traces were fitted to gaussianfunctions; the results are shown by the red lines in Figs 3a and 3b.The corresponding full widths at half maximum of the autocorrela-tion traces were 1.3 ^ 0.1 and 1.8 ^ 0.1 fs, resulting in pulsedurations of 950 ^ 90 as and 1.3 ^ 0.1 fs, respectively.

In the 950-as pulse, however, bumps appeared around the mainpeak and the gaussian function does not seem to be appropriate todescribe the pulse shape. To check the validity of the experimentalresults, the spectra of the ninth harmonic (Fig. 3c) were Fourier-transformed with an assumption of a flat phase in the frequencydomain, and the autocorrelation functions were then calculated.The results are shown by the blue lines in Fig 3a, b. Both theautocorrelation trace of the 1.3-fs pulse and that of 8.3-fs pulse arereproduced well. The bumps are therefore attributable to thespectrum shape. Consequently, no other pulses were observedwithin the scanned time range of 20 fs, showing the isolated single

pulses. This is an advantage of the autocorrelation measurementover electron streaking, in which the measurable time range islimited by one-half of the optical cycle22. In future this method willbe extended to frequency-resolved optical gating (FROG)23 byimproving the spectral resolution to characterize the harmonicpulses completely.The spectra of the ninth harmonic reflect the spectra of the

Ti:sapphire and blue lasers. To increase the spectrumwidth, the gainaround 800 nmwas reduced by inserting an etalon in a regenerativeamplifier of the Ti:sapphire laser system, resulting in a spectrumwith two peaks24. This type of spectrum gives a relatively short pulseduration, although side bumps appear. Two peaks in the harmonicspectra are made prominent by the nonlinear process.For further pulse shortening to the attosecond timescale with the

use of a multi-cycle driving laser, one experimental approach is togenerate higher-order harmonics; the lower-order harmonics riseearlier than the higher-order harmonics, resulting in a longer pulseduration. Higher-order harmonics would therefore be adequate forattosecond pulse generation, and a driving laser with shorter pulseduration is also required. However, it would be difficult to shortenthe temporal duration below the half cycle of the driving laser(650 as). The feature of this scheme is a peak intensity high enoughto induce nonlinear phenomena.Finally, we estimate the photoelectron numbers created by the

two-photon ATI. The photoelectron yield Y from the interactionvolume V ( ¼ 3.1 £ 1029 cm3) with an atomic density n( ¼ 1011 cm23) is given by Y ¼ j (2)F2t n V, where j (2) is thecross-section of two-photon ATI, F is the photon flux, and t isthe pulse duration. In the present experimental conditions, F and twere 7.8 £ 1030 photons s21 cm22 and 1 fs, respectively, and j (2)

was set to 10252 cm2 from ref. 10. Consequently, Y is estimated to be1.6 £ 1023 electrons per pulse. The observed yield was 1.0 £ 1023

electrons per pulse, taking account of the collection and quantumefficiencies, which is consistent with the estimation. A

MethodsDriving laserBlue laser pulses were generated by broadband frequency doubling of the Ti:sapphire laserpulses to obtain shorter pulses than originally generated21. To broaden the bandwidth ofthe laser pulse, broadband frequency conversion was realized by spatial dispersion of eachspectrum component of the Ti:sapphire laser pulse so that it was phase-matched20. Thepulse energies of the blue laser pulses were 1.3mJ at a repetition rate of 1 kHz. The pulsedurations were controlled by changing the spectral bandwidth of the Ti:sapphire lasersystem. The optical system for spectrum dispersion was modified to employ a telescopeconfiguration for a large beam diameter of 2 cm. If this was not done, spatial pulse-fronttilt and phase mismatch were so large that high harmonics were not generated. Spatialcoherence of the driving laser is also important for generating two identical harmonicpulses. The pulses were characterized by self-diffraction frequency-resolved optical gatingand were found to be Fourier-transform limited.

Autocorrelation measurementIn the present experiment, two harmonic pulses were generated from two beamsproduced by spatially dividing a blue laser beam into two. This is different fromconventional autocorrelation measurements in the visible range, in which a beamsplitter is used. However, the original driving laser beam had high spatialcoherence, ensured by interfering the inverted image with the original one, so thetwo harmonic pulses naturally retained coherence. There still remained thepossibility of generating different pulses because of inequality in beam division.However, because the energy difference was less than a few per cent, the harmonicpulses generated were almost identical.

Anothermethod of producing two identical harmonic pulses has been shown6, involvingthe division of a harmonic beam spatially into two by a split XUV mirror after harmonicgeneration. However, in this case too the two pulses are not always identical. Because of theintensity distributionwithin a driving laser beam, harmonic pulses are generated at differenttimes. So, unequal spatial division of the harmonic beam leads to the production of twodifferent harmonic pulses even when a split XUV mirror is used.

Received 4 June; accepted 11 October 2004; doi:10.1038/nature03108.

1. McPherson, A. et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare

gases. J. Opt. Soc. Am. B 4, 595–601 (1987).

2. Corkum, P. B. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71,

1994–1997 (1993).

3. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science

292, 1689–1692 (2001).

Figure 3 Autocorrelation traces and the spectra of the ninth harmonic of the blue laser.a, b, Autocorrelation traces of the ninth harmonic pulses generated by using 8.3-fs (a)and 12-fs (b) blue lasers. The error bars show the standard deviation of each data point.

The full widths at half maximum of the autocorrelation traces obtained by the least-

squared fit to the gaussian functions were 1.3 ^ 0.1 and 1.8 ^ 0.1 fs, resulting in pulse

durations of 950 ^ 90 as and 1.3 ^ 0.1 fs, respectively. The lines in red show the fitting

results. The lines in blue are the calculated autocorrelation traces from the spectra (c) ofthe ninth harmonic. c, The spectra of the ninth harmonic pulses generated by using 12-fsand 8.3-fs pulses are shown by the blue and red lines, respectively.

letters to nature

NATURE |VOL 432 | 2 DECEMBER 2004 | www.nature.com/nature 607© 2004 Nature Publishing Group

950 as from 8.3 fs

1.3 fs from 12 fs

Ar

Isolated sub-fs pulse generation from a ~10 fs pulseSekikawa et al., Nature 432, 605 (2004)

K. L. Ishikawa

POLARIZATION GATING (PG)

10

NATURE PHOTONICS | VOL 4 | DECEMBER 2010 | www.nature.com/naturephotonics 827

plasma cannot be eliminated, even by using very short driving laser pulses. As higher harmonics are generated at higher levels of ioniza-tion, the phase-matching cut-off is always less than the single-atom cut-off given by equation (1), and is <150 eV even for helium driven by Ti:Sapphire lasers35. For harmonics generated at ionization lev-els of >ηcr, the finite phase mismatch due to uncompensated plasma

dispersion reduces the coherent build-up length to the microme-tre range, which reduces the yield by several orders of magnitude. Overcoming this phase-matching limit to generate bright harmon-ics in the soft- and hard-X-ray regions (required for many appli-cations in spectroscopy and imaging) has therefore been a grand challenge in extreme nonlinear optics.

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L = 2.0 µm L = 1.3 µm

Figure 6 | Attosecond pulse generation. a, Isolated attosecond pulse generation driven by a few-cycle laser field. The cut-off photon energy varies significantly on a cycle-by-cycle basis, so that simple spectral filtering can isolate HHG emission from a single electron recollision at the peak of the laser field95. This approach has yielded isolated extreme-ultraviolet (EUV) pulses as short as 80 as (ref. 96). b, Isolated 130 as EUV pulse generation using polarization gating97,98. HHG emission is suppressed except during the most intense central cycle of the field, where the laser polarization is linear. c, If a second laser field of a different colour is added to this polarization gating method, even shorter EUV pulses can be generated99. d, Isolated attosecond pulse generation using gated phase-matching confined to a narrow temporal window near the critical ionization level. This approach results in isolated 210 as EUV pulses at photon energies around 50 eV, using multicycle driving lasers33. e, Isolated attosecond pulses through gated infrared phase-matching in the soft-X-ray region of the spectrum. Bandwidths sufficient to support 10 ± 1 as pulses are observed at around 400 eV. Figure reproduced with permission from: a (right), ref. 96, © 2008 AAAS; b (right), ref. 97, © 2006 AAAS; c (left), ref. 100, © 2010 NPG; c (right), ref. 99, © 2010 APS.

REVIEW ARTICLE | FOCUS NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256 FOCUS | REVIEW ARTICLENATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256HHG is suppressed when circular polarization is used

Sansone et al., Science 314, 443 (2006)

counter-rotating circularly polarized pulses with a delay

K. L. Ishikawa

DOUBLE OPTICAL GATING (DOG)

11

Polarization gating + two-color gating

of the cell, the energies of the fundamental and secondharmonic pulses were 150 and 30 !J, respectively. Theestimated effective intensities inside the gate were 2:8!1014 W=cm2 and 7! 1013 W=cm2, respectively. The gen-erated harmonics were measured with a gratingspectrometer.

The laser field can be expressed as the combination oftwo perpendicularly polarized fields ~E"t# $ Edrive"t#i%Egate"t#j. The driving field is

Edrive"t# $ E0&"e'2 ln2&"t%Td=2#2="2!(

% e'2 ln2&"t'Td=2#2="2!(# cos"!0t% ’CE#

% ae'2 ln2"t2="22!# cos"2!0t% 2’CE %#!;2!#(

(1)

and the gating field is

Egate"t#$E0"e'2ln2&"t%Td=2'T0=4#2="2!(

'e'2ln2&"t'Td=2'T0=4#2="2!(#sin"!0t%’CE#; (2)

where E0 is the amplitude of the circularly polarizedfundamental laser field with carrier frequency !0 (periodT0), pulse duration "!, and CE phase ’CE. Td is the timedelay between the two circular pulses. The delay, T0=4,between the gating and the driving fields is introduced bythe quarter-wave plate. #!;2! is the relative phase betweenthe fundamental and second harmonic pulses. The durationof the SH pulse is "2!. Finally, a represents the strength ofthe second harmonic field relative to the fundamental field.

Figure 2(a) shows harmonic spectra of argon for one-color (linearly polarized fundamental field only, Td $ 0,a $ 0), two-color (a second harmonic field added to afundamental field polarized in the same direction, Td $0), conventional PG (a $ 0), and DOG fields. Notice that

FIG. 2 (color). Comparison of harmonic spectra and pulses.(a) The harmonic spectrum images obtained by various gatingmethods. The lineout plots in (b) compare the spectral profileand intensity obtained from DOG (blue line) with those from PGfor delays of 12 fs (red line) and 15 fs (green line). The resultsfrom numerical simulations are shown in (c). (d) Shows theFourier transform for the DOG and (e) shows the Fourier trans-forms for the PG and two-color spectra. These were doneassuming flat phase.

FIG. 1 (color). The driving filed components for PG corre-spond to (a) without and (b) with the second harmonic field,respectively. The driving field is shown as the red line. The twovertical lines represent the gate width. Here, the filled curves arethe attosecond pulses emitted when the driving fields alone areapplied. The background color shows the strength of the PG. Infigure (c) the ionization probability of an argon atom in the fieldof PG pulses is compared with that in the field of DOG. Thelongest pulses that can be used are those at which the probabilityreaches one.

PRL 100, 103906 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending14 MARCH 2008

103906-2

�

� + 2�with second-harmonic field

Mashiko et al., PRL 2008, 103906 (2008)

IAP generation from a ~10 fs pulse

by a 300 mm focal length lens. The diameter of the centerspot of the focused Bessel streaking beam was 55 μm.The delay between the XUV and NIR pulses was con-trolled by a piezo-electric transducer (PZT). A 532 nm la-ser beam co-propagating through both arms was used tostabilize the Mach-Zehnder interferometer [12].The continuous XUV spectra generated with DOGmea-

sured by the MBES without streaking are shown in Fig. 2.By tuning the Ne pressure in the gas cell from 0.03 to0.33 bar, the cutoff photon energy was reduced from160 to 120 eV, which corresponds to Ip ! 2.6Up toIp ! 1.8Up. The calculated single-atom cutoff is 190 eV.The spectrum with pressure below 0.03 bar was not mea-sured due to the low count rate. The observed cutoff re-duction with increasing generation gas pressure isqualitatively consistent with previous experiments withXUV pulse trains [8,9]. Finally, the pressure of 0.2 bar inthe generation cell was chosen for the streaking experi-ment, where the entire spectrum, from 55 to 130 eV, wasconfined within the low-energy part of the Zr transmis-sion window where the filter GDD is negative.The attosecond pulses were retrieved from the streak-

ing trace shown in Fig. 3(a) using both the PROOF(phase retrieval by omega oscillation filtering) [13] andFROG-CRAB (frequency-resolved optical gating for com-plete reconstruction of attosecond bursts) [14,15] techni-ques. Whereas the FROG-CRAB technique requires thebandwidth of the photoelectron spectrum to be smallcompared to its central energy, PROOF is applicableto much broader spectra [13]. Here, we apply the princi-pal component generalized projections algorithm toPROOF [16], which is more robust than the methoddeveloped in [13]. In the limit of low streaking intensi-ties, Up < ωL, the streaking spectrogram is given byS"v; τ# ≈ I0"v# ! IωL

"v; τ# ! I2ωL"v; τ#, where IωL

and I2ωL

oscillate with the streaking laser frequency,ωL, and twicethe frequency, respectively [13], τ is the delay betweenthe XUV and laser pulses, and v is the photoelectronspeed. Since the spectrum and phase information ofthe attosecond pulses are completely encoded in IωL

,the amplitude and phase of the XUV pulse are guessed

in PROOF to match the modulation depth and phaseangle of IωL

.The streaking trace was obtained at a low streaking

intensity, 2.5 × 1011 W ∕cm2, to satisfy the requirementsof PROOF. Two methods are used to confirm the correct-ness of the phase retrieval. The first is to compare thephotoelectron spectrum obtained experimentally to theretrieved ones. This criterion was used in the past [17],and is a necessary condition of an accurate retrieval. An-other criterion is the agreement between the filtered IωL

trace from the measured spectrogram and the retrievedone. It is a much stricter requirement than the first one,because the modulation depth and phase angle of IωL

aredetermined by both the spectrum and phase, whereas thefirst method compares a quantity that is dominated byI0"v#, the unstreaked component of the spectrogram.Our retrieval meets both criteria very well, as shownin Figs. 3(c) and 3(b), respectively. Both the FROG-CRABand PROOF retrievals yield nearly identical temporalprofiles with a pulse duration of 67$ 2 as, as shownin Fig. 3(d), close to the transform-limited value of 62 as.The error bar was obtained following the treatment in [1],by taking each delay slice in the final guessed spectro-gram as a separate measurement of the pulse duration.The experiment was repeated at a higher streaking inten-sity (5 × 1011 W ∕cm2) and yielded the same result. Withthe intrinsic and Zr phase, we calculated a pulse durationof 68 as with the experimental spectrum, in agreementwith our retrieved result. At generation gas pressures sig-nificantly lower than 0.2 bar, the count rate was not suf-ficient for obtaining streaking traces with satisfactorysignal to noise ratio. Streaking was also performed athigher pressures, which yielded longer pulses due tothe reduced spectral bandwidth. For instance, at 0.36 bar,the retrieved pulse duration was 88 as.

Both PROOF and FROG-CRAB assume that onlyphotoelectrons emitted in a small angle in the streaking

Fig. 2. (Color online) XUV continuum generated by DOG inNe gas at six pressures. The length of the gas cell is 1 mm.The peak intensity at the center of the polarization gate is1 × 1015 W ∕cm2.

Fig. 3. (Color online) Characterization of a 67 as XUV pulse.(a) Streaked photoelectron spectrogram obtained experimen-tally. (b) Filtered IωL

trace (left) from the spectrogram in(a) and the retrieved IωL

trace (right). (c) Photoelectron spec-trum obtained experimentally (thick solid) and retrieved spec-tra and spectral phases from PROOF (solid) and FROG-CRAB(dashed). (d) Retrieved temporal profiles and phases fromPROOF (solid) and FROG-CRAB (dashed).

3892 OPTICS LETTERS / Vol. 37, No. 18 / September 15, 2012

Ne

Zhao et al., Opt. Lett. 37, 3891 (2012)

K. L. Ishikawa

GENERALIZED DOUBLE OPTICAL GATING (GDOG)

12

Elliptical instead of circular polarization

Gilbertson et al., PRL 105, 093902 (2010)

IAP generation from a > 20 fs pulse without need of carrier-envelope stabilization

Gilbertson et al., PRA 81, 043810 (2010)

NATURE PHOTONICS | VOL 4 | DECEMBER 2010 | www.nature.com/naturephotonics 827

plasma cannot be eliminated, even by using very short driving laser pulses. As higher harmonics are generated at higher levels of ioniza-tion, the phase-matching cut-off is always less than the single-atom cut-off given by equation (1), and is <150 eV even for helium driven by Ti:Sapphire lasers35. For harmonics generated at ionization lev-els of >ηcr, the finite phase mismatch due to uncompensated plasma

dispersion reduces the coherent build-up length to the microme-tre range, which reduces the yield by several orders of magnitude. Overcoming this phase-matching limit to generate bright harmon-ics in the soft- and hard-X-ray regions (required for many appli-cations in spectroscopy and imaging) has therefore been a grand challenge in extreme nonlinear optics.

a

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Figure 6 | Attosecond pulse generation. a, Isolated attosecond pulse generation driven by a few-cycle laser field. The cut-off photon energy varies significantly on a cycle-by-cycle basis, so that simple spectral filtering can isolate HHG emission from a single electron recollision at the peak of the laser field95. This approach has yielded isolated extreme-ultraviolet (EUV) pulses as short as 80 as (ref. 96). b, Isolated 130 as EUV pulse generation using polarization gating97,98. HHG emission is suppressed except during the most intense central cycle of the field, where the laser polarization is linear. c, If a second laser field of a different colour is added to this polarization gating method, even shorter EUV pulses can be generated99. d, Isolated attosecond pulse generation using gated phase-matching confined to a narrow temporal window near the critical ionization level. This approach results in isolated 210 as EUV pulses at photon energies around 50 eV, using multicycle driving lasers33. e, Isolated attosecond pulses through gated infrared phase-matching in the soft-X-ray region of the spectrum. Bandwidths sufficient to support 10 ± 1 as pulses are observed at around 400 eV. Figure reproduced with permission from: a (right), ref. 96, © 2008 AAAS; b (right), ref. 97, © 2006 AAAS; c (left), ref. 100, © 2010 NPG; c (right), ref. 99, © 2010 APS.

REVIEW ARTICLE | FOCUS NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256 FOCUS | REVIEW ARTICLENATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256

K. L. Ishikawa

INFRARED TWO-COLOR SYNTHESIS

13

800 nm + 1300 nm two-color driving field

Infrared Two-ColorMulticycle Laser Field Synthesis for Generating an Intense Attosecond Pulse

Eiji J. Takahashi,1,* Pengfei Lan,1 Oliver D. Mucke,2 Yasuo Nabekawa,1 and Katsumi Midorikawa1

1Extreme Photonics Research Group, RIKEN Advanced Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan2Photonics Institute, Vienna University of Technology, Gusshausstrasse 27-387, A-1040 Vienna, Austria

(Received 24 December 2009; published 7 June 2010)

We propose and demonstrate the generation of a continuum high-order harmonic spectrum by mixing

multicycle two-color (TC) laser fields with the aim of obtaining an intense isolated attosecond pulse. By

optimizing the wavelength of a supplementary infrared pulse in a TC field, a continuum harmonic

spectrum was created around the cutoff region without carrier-envelope phase stabilization. The obtained

harmonic spectra clearly show the possibility of generating isolated attosecond pulses from a multicycle

TC laser field, which is generated by an 800 nm, 30 fs pulse mixed with a 1300 nm, 40 fs pulse. Our

proposed method enables us not only to relax the requirements for the pump pulse duration but also to

reduce ionization of the harmonic medium. This concept opens the door to create an intense isolated

attosecond pulse using a conventional femtosecond laser system.

DOI: 10.1103/PhysRevLett.104.233901 PACS numbers: 42.65.Ky, 32.80.Rm, 42.65.Re

To achieve a breakthrough in attosecond science [1] fornonlinear optics and other applications, one of the mostimportant issues is the development of high-power atto-second pulse sources. The progress of high-order harmonicgeneration (HHG) techniques has resulted in the creationof isolated attosecond pulses (IAPs) [2–6] and attosecondpulse trains (APTs) [7,8]. High-power APTs have beensuccessfully generated as a result of research on harmonicenergy scaling using a loosely focusing geometry [9].Meanwhile, various methods have been proposed for cre-ating an IAP, such as the use of a few-cycle infrared (IR)pulse as a driving laser [2–4], polarization gating [6],double optical gating (DOG) [10], and so forth [5,11–14]. Although the shortest pulse duration of IAPs attainedis 80 as [15], the output energy is still not sufficient toinduce nonlinear phenomena because the pump pulse en-ergy is typically limited to a few mJ owing to the require-ments of sophisticated laser technology such as a few-cyclepulse duration and carrier-envelope phase (CEP; !CE)stabilization. The scalability of pump laser energy is ofparamount importance for the development of intense IAPsources. It is, however, still difficult to apply high-powerconventional femtosecond laser technology to increase thepower of IAPs.

In this Letter, we present the generation of a continuumhigh-order harmonic spectrum by mixing multicycle two-color (TC) laser fields with the aim of easily obtaining anintense IAP. We utilize a TC IR driver source to greatlyreduce the requirements for the pump laser system used forgenerating an IAP. A similar theoretical proposal has beenreported by other groups [16,17]; essentially, they assumedthat a CEP-stabilized pulse is used for the driving field. Asmentioned above, the requirement of CEP stabilization isone of the factors hindering the generation of an intenseIAP by a TW-class high-power laser system. To meet thisrequirement for laser technology, we optimize and demon-strate, for the first time, the creation of an IAP with non-

CEP-stabilized multicycle laser pulses. By adjusting thewavelength of the supplementary IR pulse, we suppress themultiple pulse burst and successfully generate an IAP.The synthesized TC electric field (Emix) is expressed

as EmixðtÞ ¼ E0 exp½%2 ln2ð t"0Þ2& cosð!0tþ!CEÞ þ

E1 exp½%2 ln2ðtþ!t"1

Þ2& cosðK!0tþ!CE þ!1Þ, where K

and !t are the frequency ratio and the delay time betweenthe main field (!0) and the supplementary IR field (!1 ¼K!0, K < 1), the subscripts 0 and 1 denote the two laserfield components, E0;1 is the electric field amplitude, and"0;1 and !1 denote the pulse duration and constant phaseoffset, respectively. When the TC field is generated by an800 nm, 30 fs pulse and a 1300 nm, 40 fs pulse, the fieldamplitude (E2

mix) of the near neighbors on both sides of thecentral peak is markedly suppressed [see Fig. 1(a)]. Here,the intensity ratio (# ¼ E2

1=E20) and the phases (!CE, !1)

are fixed at 0.15 and 0 rad, respectively. The intensity ratiobetween the central peak and the highest side peak is 0.8,which is almost the same as that of a 5 fs pulse at 800 nm(red line). Note that the second most intense peak appears

1.0

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arb.

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FIG. 1 (color). (a) Field amplitude (E2mix) of an 800 nm, 5 fs

pulse (red line) and a TC field (green line). The TC field isgenerated by an 800 nm, 30 fs pulse mixed with a 1300 nm, 40 fspulse. The intensity ratio (#) and the phases (!CE, !1) are fixedat 0.15 and 0 rad, respectively. (b) ADK ionization probability ofan argon atom calculated for the DOG (blue line), OC (red line),and TC (green line) methods as a function of the pulse durationof the main field.

PRL 104, 233901 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending11 JUNE 2010

0031-9007=10=104(23)=233901(4) 233901-1 ! 2010 The American Physical Society

800 nm 800 nm + 1300 nm

Takahashi et al., PRL 104, 233901 (2010)

As we successfully obtained the AC trace of the TC-HH in themid-plateau, we furthermore explored the temporal characteriza-tion for the HH cutoff. In this experiment, we switched thefocusing mirror from the SiC mirror to the Sc/Si multilayermirror. The signal is scanned every 148 as from ! 8.5 to 8.5 fswith 1" 103 laser shot accumulation at each delay point. Theresultant signal points versus delay are shown in the top panel inFig. 3. Three distinct signal points around 0 delay seem to be acorrelation peak and there are no noticeable side peaks in thisfigure, although our simulation result (see Discussion section)exhibits side peaks at ±6.7 fs with B0.2 relative AC amplitudecompared with the maximum peak at 0 delay. To confirm that thesignal around 0 delay is certainly the correlation signal and thatthere are no significant side peaks at ±6.7 fs, we performed ahigh-resolution AC measurement in the delay scanning rangesaround 0 fs and ±6.7 fs, as shown in the bottom panels in Fig. 3.We accumulated 1" 103 laser shots at each delay point and set thescanning delay step Dt to be 28 as. We can demonstrate a clearpeak at 0 delay as an AC in the middle-bottom panel in Fig. 3. TheAC duration was evaluated to be tAC¼ (700±90) as by fitting theexperimental trace to a Gaussian function; hence, the pulseduration is estimated to be tHHB500 as. We also find that thereare no noticeable side peaks in the measured AC traces in the left-bottom and right-bottom panels in Fig. 3. This is owing to the factthat the background noise amplitude (see Methods section) iscomparable to the amplitude of the side peaks expected from oursimulation. The noise magnitude against the peak AC amplitude isestimated to be B0.24; thus, we cannot clearly find side peakswith amplitudes o0.24. In other words, we can safely concludethat the side-peak ratio should be o0.24. As discussed below, wecan find both pre- and post-pulse in the calculated temporal pro-file at any CEP and relative phase. By assuming that the HH pulseconsists of three (pre-, main and post-) pulses and the upper limitof the side peaks in the AC trace should be 0.24, we can estimatethe possible largest peak height ratio of the pre- and post-pulses tobe B0.14. Further detailed analysis of the pre-/post-pulse issue ispresented in the next section with the help of our numerical modelof the TC-HH and statistical analysis of the relative phase.

From the measured pulse energy and pulse duration, the peakpower of the IAP nonlinearly interacting with the target medium

is evaluated to be 2.6 GW with weak satellite pulses (seeDiscussion section). This ultrahigh power from our tabletoplight source even surpasses that from a compact XUV FEL16,17.The peak brightness is also estimated to be B2" 1030 photonsper s! 1 mm! 2 mrad! 2, assuming a 60-mm beam diameter atthe exit of the gas cell.

DiscussionFinally, we examine attosecond pulse generation in our TC-HHscheme by numerical simulations. In these simulations, thesingle-atom response is calculated within the strong-fieldapproximation. The propagation of the TC laser pulse and thehigh harmonics are computed separately in cylindrical coordi-nates14,18. All the parameters, such as laser intensity, target gaspressure and medium length, are determined by the experimentalconditions. Here we assume that the CEP fCE fluctuatesrandomly during the AC measurement, whereas the statisticalfluctuations of the relative phase f0 are characterized by themeasured histogram of the relative phase in the TC inter-ferometer. To evaluate the relative phase variation with time inthe TC interferometer, we injected a continuous-wave (CW) laserbeam with a wavelength of 547 nm into the TC interferometer inthis measurement. We recorded spatial interference fringes on thesuperposed beam profile of the CW laser with a charge-coupleddevice camera (exposure time: B10 ms with 10 Hz repetition rate,which is synchronized with the pump laser) during B35 min,which is equivalent to the data acquisition time of one AC trace inour measurements. The phase of the spatial fringes at eachrecorded profile was converted to the relative delay and relativephase corresponding to the 1,300-nm field. The measured timeevolution of the relative phase, f0, is shown in Fig. 4a. We canthen evaluate the s.d. of f0 fluctuations, s, to be 0.23p from thismeasurement, whereas the offset of f0 is arbitrary. We adjust theoffset in Fig. 4a such that the average of f0 is equal to 0. Toimprove the S/N ratio of the AC trace, we overlapped ten ACtraces in Figs 2 and 3. The s-value with a typical normaldistribution of the ten AC traces’ f0 fluctuations was almost thesame during the experiment, even though the phase profile as afunction of time was different.

–1.0 0.0 1.0

–70

–60

–50

–40

–7.98 –5.32 –2.66 0.00 2.66 5.32 7.98

–70

–60

–50

–40

–7.0 –6.0 7.06.0

(×1

0–3 a

.u.)

(×1

0–3 a

.u.)

!t (fs)

Figure 3 | Measured AC traces of an IAP obtained from the side peak of Nþ ion signals. The time resolutions of the top and bottom panels correspondto 148 and 28 as, respectively. The error bars show the s.d. of each data point. The grey solid profiles are AC traces obtained using the simulated HH fields.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3691

4 NATURE COMMUNICATIONS | 4:2691 | DOI: 10.1038/ncomms3691 | www.nature.com/naturecommunications

& 2013 Macmillan Publishers Limited. All rights reserved.

autocorrelation traceXe 500 as

29 eV

Takahashi et al., Nat. Commun. 4, 2691 (2013)

High-energy (1.3 micro J), high-power (2.6 GW) IAPmore than 100 times more energetic than previously reported

K. L. Ishikawa

FROM FEMTOSECOND TO ATTOSECOND

14

8@;LP(-%.�$���)#*&F�!"&F

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<2 /�.0%,'+"I �������������������������� 61CAI �����������������

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Single cycle at 800 nm

increase in intensity

K. L. Ishikawa

Quest for higher photon energy (shorter wavelength)

15

Ec = Ip + 3.17Upcutoff

Up(eV) =e2E2

0

4m�2= 9.3� 10�14I(W/cm2)�2(µm)

Longer fundamental wavelength is advantageous

Optical parametric chirped-pulse amplification (OPCPA)

K. L. Ishikawa

WATER-WINDOW HHG

16

spectral range between the K-absorption edges of C (284 eV) and O (543 eV)

absorbed by biological samples but not by water

attractive for high-contrast biological imaging

Figure 2 shows the measured Ne HH spectra driven by a1:55 !m laser pulse at a focusing intensity of 3:5!1014 W=cm2, at which the ionization rate was estimatedto be approximately 0.35% from the Ammosov-Delone-Krainov ionization theory [27]. The pump energy was setat 2.2 mJ. Note that the vertical axis of HH intensity isplotted with a linear scale. The measured harmonic spec-trum gradually increases up to 250 eV, which is in strongcontrast to the previously reported HH spectra in the waterwindow region [1,2,11–14,28]. To evaluate the intensitydistribution of the lower harmonics, we changed the spec-trometer’s grating from 2400 to 1200 grooves=mm. TheHH intensity (dotted blue profile in Fig. 2) with the1200 grooves=mm grating exhibits a broad plateau up to150 eV. In contrast, the HH intensity rapidly increasesabove 150 eV, which agrees with the spectrum obtainedfrom the grating with 2400 grooves=mm, then it starts todecrease at 170 eV because of the low diffraction effi-ciency of the 1200 grooves=mm grating above 170 eV.The HH yield is optimized by adjusting the focusing pointand by varying the backing pressure of the gas jet. The HHyield gradually increases as the gas pressure increases,which shows a quadratic dependence of the harmonic yieldas a function of gas backing pressure. The HH intensityabove the carbonK edge (284 eV) is found to be maximumat a backing pressure of approximately 20 atm with aGaussian-like spatial profile. By using the configurationparameter of supersonic gas get [29], the effective gaspressure at the interaction region is estimated to be ap-proximately 580 Torr. At the 250 eV photon energy, Gouyphase and gas dispersion are evaluated to be 360 cm"1

from the spot size of pump pulse and 615 cm"1 frombacking pressure, respectively. Also, plasma dispersion is

calculated to be 980 cm"1 at the 0.35% ionization. Tocompensate the total phase mismatch, the pump pulse isfocused after the gas jet, at which the Gouy phase has aminus sign. The coherence length and absorption lengthare estimated to be approximately 0.6 and 0.085 cm at the250 eV HH, respectively. Therefore, our condition almostsatisfies the optimized phase-matching condition. Thesolid red curve in Fig. 2 shows the evolution of ð1=f2Þ2as a function of HH photon energy. As expected, the HHintensity increases with increasing ð1=f2Þ2 up to 250 eV.Above 250 eV, the HH intensity decreases because thecutoff energy of 270 eV set by the interaction laser inten-sity prevents further extension of the plateau region. Thus,the HH intensity reaches a maximum at 250 eV. Themeasured HH spectrum is in sharp contrast to the conven-tional plateau of HH and clearly shows that the ALC isachieved by phase matching. The generation of the waterwindow wavelength HH from the neutral Ne medium hasbeen clearly demonstrated. The inset of Fig. 2 shows themeasured far-field spatial profile of the water window x ray(290–310 eV). We directly obtained the spatial profile ofthe water window HH beam using a two-dimensionaldetector. The beam divergence was measured and had a7 mrad full width at half maximumwith a Gaussian profile.This good beam quality also indicates that the phasematching is substantially satisfied along the propagationaxis of the pump pulse. Moreover, this 2D image ensuresthat our coherent water window source will be useful foracquiring 2D diffraction images.We further explored the generation of HH under a

neutral-medium condition by changing the nonlinear me-dium from Ne to He with the aim of obtaining a higherphoton energy. Figure 3 shows the measured He HH spec-tra driven by a 1:55 !m pulse with a focusing intensity of5:5! 1014 W=cm2, which is obtained with a2400 grooves=mm grating. The pump energy, beam di-

1.0

0.8

0.6

0.4

0.2

0.0

1.55

µm

He

HH

G [a

rb. u

nits

]

550500450400350300250200

Photon energy [eV]

0.8

0.6

0.4

0.2

0.0

Transm

ission of Mylar filter

Spa

ce

Photon energy

Carbon K edge

FIG. 3 (color). Measured harmonic spectra from neutral He.These spectra (left axis) are obtained with a 2400 grooves=mmgrating. The red line and the blue line, respectively, correspondto the spectra with and without a 1-!m-thick Mylar filter(C10H8O4). Both HH spectra are normalized to the peak inten-sity. The inset depicts a 2D HH spectrum image with a1-!m-thick Mylar filter on a microchannel plate. This imageis obtained by the accumulation of 1000 shots.

1.0

0.8

0.6

0.4

0.2

0.0

1.55

µm

Ne

HH

G [a

rb. u

nits

]

400350300250200150100

Photon energy [eV]

0.8

0.6

0.4

0.2

0.0

(1/f2 ) 2

Int.

Space

FIG. 2 (color). Measured harmonic spectra from neutral Neand evolution of the square of the reciprocal of imaginarycomponent f2. The solid blue line and the dashed blue line(left axis) correspond to the Ne spectrum obtained with a2400 grooves=mm grating and a 1200 grooves=mm grating,respectively. Both HH spectra are normalized to the peak inten-sity. The inset shows the far-field spatial profile of the waterwindow x ray (280–310 eV) obtained from neutral Ne gas. Sincea toroidal mirror is not set in front of the spectrometer, we candirectly observe the spatial profile of the HH beam (see inset ofFig. 3).

PRL 101, 253901 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending

19 DECEMBER 2008

253901-3

He�0 = 1.55µm

I = 5.5⇥ 1014 W/cm2

Takahashi et al., PRL 101, 253901 (2008)

K. L. Ishikawa

keV HHG

17

Even up to 1.6 keV, > 5000 ordersalmost x-ray!

a  new  type  of  laser-‐‑‒based  radiation  sourcePopmintchev et al., Science 336, 1287 (2012)

�0 = 3.9µm

K. L. Ishikawa

ATTOSECOND SCIENCE

18

real-time observation and time-domain control of atomic-scale electron dynamics

atomic unit of time = 24 attosecondsElectron

Nucleus mω2r =1

4πϵ0

e2

r2

Orbital period of the Bohr electron

T =2⇡

!= 2⇡

r4⇡✏0mr3

e2= 152 as = 2⇡ a.u.