Frequency-resolved optical gating for characterization of VUV pulses using ultrafast plasma mirror switching Ryuji Itakura,∗ Takayuki Kumada, Motoyoshi Nakano and Hiroshi Akagi Quantum Beam Science Center, Kansai Photon Science Institute, Japan Atomic Energy Agency, 8-1-7 Umemidai Kizugawa, Kyoto, 619-0215, Japan ∗ [email protected]
Abstract: We propose and experimentally demonstrate a method for characterizing vacuum ultraviolet (VUV) pulses based on time-resolved reflection spectroscopy of fused silica pumped by an intense laser pulse. Plasma mirror reflection is used as an ultrafast optical switch, which enables us to measure frequency-resolved optical gating (FROG) traces. The VUV temporal waveform can be retrieved from the measured FROG trace using principal component generalized projections algorithm with modification. The temporal profile of the plasma mirror reflectivity is also extracted simultaneously. © 2015 Optical Society of America OCIS codes: (320.7100) Ultrafast optics: Ultrafast measurements; (320.7080) Ultrafast devices; (320.7120) Ultrafast phenomena; (350.5400) Plasmas.
References and links 1. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006). 2. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). 3. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4, 641–647 (2010). 4. M. Yabashi, H. Tanaka, T. Tanaka, H. Tomizawa, T. Togashi, M. Nagasono, T. Ishikawa, J. R. Harries, Y. Hikosaka, A. Hishikawa, K. Nagaya, N. Saito, E. Shigemasa, K. Yamanouchi, and K. Ueda, “Compact XFEL and AMO sciences: SACLA and SCSS,” J. Phys. B: At., Mol. Opt. Phys. 46, 164001 (2013). 5. Y. Mairesse and F. Qu´er´e, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005). 6. H. Mashiko, M. J. Bell, A. R. Beck, M. J. Abel, P. M. Nagel, C. P. Steiner, J. Robinson, D. M. Neumark, and S. R. Leone, “Tunable frequency-controlled isolated attosecond pulses characterized by either 750 nm or 400 nm wavelength streak fields,” Opt. Express 18, 25887–25895 (2010). 7. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004). 8. P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426, 267–271 (2003). 9. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
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10. A. Kosuge, T. Sekikawa, X. Zhou, T. Kanai, S. Adachi, and S. Watanabe, “Frequency-resolved optical gating of isolated attosecond pulses in the extreme ultraviolet,” Phys. Rev. Lett. 97, 263901 (2006). 11. F. Qu´er´e, J. Itatani, G. L. Yudin, and P. B. Corkum, “Attosecond spectral shearing interferometry,” Phys. Rev. Lett. 90, 073902 (2003). 12. E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev. Lett. 94, 033905 (2005). 13. Y. Mairesse, O. Gobert, P. Breger, H. Merdji, P. Meynadier, P. Monchicourt, M. Perdrix, P. Sali`eres, and B. Carr´e, “High harmonic xuv spectral phase interferometry for direct electric-field reconstruction,” Phys. Rev. Lett. 94, 173903 (2005). 14. R. Itakura, “Spectral phase measurement of attosecond pulses using the quantum beat between the P1/2 and P3/2 levels of alkali-metal atoms,” Phys. Rev. A 76, 033810 (2007). 15. J. Chen, R. Itakura, and T. Nakajima, “Characterization of attosecond XUV pulses utilizing a broadband UV∼VUV pumping,” Opt. Express 18, 2020–2035 (2010). 16. J. Chen, R. Itakura, and T. Nakajima, “Reconstruction of attosecond pulses using two-color pumping,” J. Opt. Soc. Am. B 28, 2195–2199 (2011). 17. H. C. Kapteyn, A. Szoke, R. W. Falcone, and M. M. Murnane, “Prepulse energy suppression for high-energy ultrashort pulses using self-induced plasma shuttering,” Opt. Lett. 16, 490–492 (1991). 18. B. Dromey, S. Kar, M. Zepf, and P. Foster, “The plasma mirror–a subpicosecond optical switch for ultrahigh power lasers,” Rev. Sci. Instrum. 75, 645–649 (2004). 19. G. Doumy, F. Qu´er´e, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J. P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E 69, 026402 (2004). 20. C. Thaury, F. Qu´er´e, J.-P. Geindre, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. R´eau, P. D’Oliveira, P. Audebert, R. Marjoribanks, and P. Martin, “Plasma mirrors for ultrahigh-intensity optics,” Nat. Phys. 3, 424–429 (2007). 21. C. Rolland and P. B. Corkum, “Generation of 130-fsec midinfrared pulses,” J. Opt. Soc. Am. B 3, 1625–1629 (1986). 22. K. Michelmann, U. Wagner, T. Feurer, U. Teubner, E. F¨orster, and R. Sauerbrey, “Measurement of the page function of an ultrashort laser pulse,” Opt. Commun. 198, 163–170 (2001). 23. X. Wang, T. Nakajima, H. Zen, T. Kii, and H. Ohgaki, “Damage threshold and focusability of mid-infrared freeelectron laser pulses gated by a plasma mirror with nanosecond switching pulses,” Appl. Phys. Lett. 103, 191105 (2013). 24. C. H. Page, “Instantaneous power spectra,” J. Appl. Phys. 23, 103–106 (1952). 25. D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421–431 (1999). 26. T. Kumada, H. Akagi, R. Itakura, T. Otobe, and A. Yokoyama, “Femtosecond laser ablation dynamics of fused silica extracted from oscillation of time-resolved reflectivity,” J. Appl. Phys. 115, 103504 (2014). 27. J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92, 25–32 (2008). 28. H. H. Li, “Refractive index of alkali halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 5, 329–528 (1976). 29. D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994). 30. M. Lebugle, N. Sanner, N. Varkentina, M. Sentis, and O. Ut´eza, “Dynamics of femtosecond laser absorption of fused silica in the ablation regime,” J. Appl. Phys. 116, 063105 (2014). 31. P. K. Singh, G. Chatterjee, A. Adak, A. D. Lad, P. Brijesh, and G. Ravindra Kumar, “Ultrafast optics of solid density plasma using multicolor probes,” Opt. Express 22, 22320–22327 (2014).
1.
Introduction
Ultrafast coherent light sources in the short wavelength region from vacuum ultraviolet (VUV) to hard X-ray have been intensively developed based on high-order harmonic generation (HHG) [1, 2] and free-electron lasers [3, 4]. In VUV and extreme ultraviolet (EUV), the time resolution has reached the attosecond regime, where we can trace electron dynamics in atoms, molecules, and solids. Such short wavelength light sources enable us to perform photoelectron spectroscopy and photoabsorption spectroscopy by one-photon process for probing transient states with no disturbance by probe itself. Indeed, high-order harmonics in the VUV range is easily generated using a femtosecond (fs) laser pulse with the millijoule-level pulse energy, and
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10915
thus has great potential for various applications. In ultrafast spectroscopy, the characterization of the pump and probe pulses is crucial to extract accurate temporal response of experimental targets. However, characterizing VUV and EUV pulses is not so easy as generating them by simply focusing a laser pulse into nonlinear media of rare gases. Mainly, two types of methods have been experimentally used to date. One is frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG CRAB) with streaking photoelectrons using a carrier-envelop phase (CEP) stabilized laser electric field [1, 2, 5, 6]. The other is non-resonant two-photon ionization with intense VUV/EUV pulses for autocorrelation [7–9] and FROG measurements [10]. In many laboratories using VUV pulses as probe pulses, CEP of laser pulses is not stabilized and the intensity of VUV pulses is not sufficiently strong for non-resonant two-photon processes. As an alternative method, spectral phase interferometry for direct electric-field reconstruction (SPIDER) that requires two VUV pulses with a spectral shift was proposed and expeimentally demonstrated [11–13], but the preparation of a pair of frequency-shifted VUV pulses is a demanding task. Another type of SPIDER using time-resolved photoelectron spectra from coherently superposed states was also theoretically proposed [14–16], but has not been experimentally demonstrated yet. We turn our attention to a plasma mirror formed by an ultrashort laser pulse on a transparent material such as fused silica (FS). Self-induced plasma in an ultrashort laser pulse has been known as a plasma mirror and used for prepulse suppression in an ultraintense laser pulse [17–20]. Plasma formed by an ultrashort laser pulse has also been used as active optical switching devices [21–23]. Such an ultrafast switching device is applicable to characterize an ultrafast laser pulse through measurement of temporally varying spectra of the pulse. Previously, Michelmann et al. performed the time-resolved transmission spectroscopy of FS, on which a pump laser pulse was focused for plasma formation [22]. The plasma makes FS opaque to a probe pulse with λ ∼ 248.5 nm. In their analysis to obtain the amplitude and phase of the electric field of the ultraviolet probe pulse, the transition time from transparent to opaque was assumed to be much shorter than the probe pulse duration, and the Heaviside step function was used for describing the optical switching. As a result, the time-resolved transmission spectrum was simply described by the Page function [24]. In this study, we adopt reflection instead of transmission, because reflection is applicable to the shorter wavelength region in which solid materials are not transparent. The applicable wavelength by the reflection measurement is expected to become shorter than UV. Even in the wavelength region where transmission is applicable, the transmitted probe pulse is influenced by the entire thickness of the plasma consisting of the front and back surfaces and the bulk of the plasma. On the other hand, the reflected one is influenced by only the front surface of the plasma. When the pulse duration becomes comparable to the falling (rising) time of the plasma switching, it is inappropriate that the falling (rising) time of the transmissivity (reflectivity) is treated as the Heaviside step function. In order to solve this problem, we use the principal component generalized projections algorithm (PCGPA) [25] with modification to extract not only the temporal waveform of the probe pulse, but also the temporal response of the plasma switching from the time-resolved reflection spectra. We will demonstrate that a VUV waveform can be retrieved from the spectrogram obtained by time-resolved plasma mirror reflection. Hereafter, we call this method plasma-mirror frequency-resolved optical gating (PM-FROG). 2.
Experimental setup
Experimental setup is shown in Fig. 1. A Ti:Sapphire chirped pulse amplification system provides output laser pulses with λ ∼ 795 nm, 60 fs duration (full width at half maximum) at 10
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10916
Hz repetition rate. Using an aluminum-coated concave mirror with the curvature radius of 2.0 m, the output laser pulses are focused in an Ar gas cell with 2.2 m length to generate high-order harmonics. The pressure of Ar in the cell is optimally set to be around 11 kPa for generation of fifth harmonics (λ ∼ 160 nm) which is characterized in this study. The generated harmonics and the fundamental near-infrared (NIR) laser pulses are collimated by a lithium fluoride (LiF) lens with f = 1.0 m focusing length and 2.3 mm thickness. For simplicity of the vacuum system, the Ar cell is connected to a vacuum chamber with the LiF lens which works as not only a lens but also an entrance window of the vacuum chamber. (a) Concave Mirror f = 1m
Delay Line & Target Chamber
2.2 m
VUV Spectrometer
LiF Lens f=1m
Ar Cell
Imaging Lens, CCD
From TiS CPA
Dielectric Mirror for 800nm LiF lens f=1m
CCD
Dielectric Mirror for 160nm
(b)
Mirror for Alignment VUV
Ar Cell
Concave Al Mirror, r = 0.4m
Gate Valve To VUV Imaging Spectrometer
NIR
Iris Delay stage
Concave Al Mirror, r = 0.3m
Vacuum
Fused Silica Plate on 2D Motorized Stage
50 μm
Mechanical Shutter
Delay Line & Target Chamber Fig. 1. Top view of experimental setup. (a) Overview. (b) Expanded view of the vacuum chamber, in which the delay line and an FS plate on the two-dimensionally motorized stage are installed. A microscope image of craters formed by laser ablation on an FS plate is shown at the bottom-right.
In the vacuum chamber, the NIR and VUV pulses are separated by a dielectric mirror (Layertec, #103841), which reflects VUV (λ ∼ 160 nm) and transmits NIR. After the separation of NIR and VUV, the NIR pulse is reflected twice with dielectric mirrors (CVI, TLM1-800-451025) for attenuation of other frequency components such as third-order harmonics (λ ∼ 265 nm). The NIR and VUV pulses are respectively reflected twice with aluminum-coated flat mirrors, and then recombined collinearly with another dielectric mirror which reflects VUV and transmits NIR. The delay between the NIR and VUV pulses is controlled with a translational stage with a stepping motor (Suruga Seiki, KXC06020-GA). A scan step of the stage is 1 μ m, corresponding to 6.667 fs for a round trip. The combined NIR and VUV pulses are focused on an FS plate using an aluminum-coated concave mirror with the curvature radius of 0.3 m. The incident angle is set to be the Brewster angle of 55◦ for λ ∼ 795 nm. The polarization directions of NIR and VUV are horizontal. The FS plate is moved with the 2D motorized stage so that the fresh surface is exposed to the NIR and VUV pulses every laser shot. The intensity of the NIR pump pulse is adjusted with an iris #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10917
in the middle of the delay line to be just above the ablation threshold of 3.3 J cm−2 [26] for plasma formation on the FS surface. A microscope image of craters formed by laser ablation on an FS plate is shown in the inset of Fig. 1(b). The craters exhibit an ellipse shape because of the incident angle of 55◦ . Its size is 33 μ m × 60 μ m, which is almost half as large as that of the Airy disk of the diffraction limited focal spot. The spot size of the VUV pulse on the FS plate could not be measured in the current setup, but is expected to be smaller than the size of the crater due to the shorter wavelength. Thus, it is considered that the influence of the spatial distribution of the pump laser intensity is not so much. Using an aluminum-coated concave mirror with the curvature radius of 0.4 m, the VUV pulse reflected by the plasma mirror is focused on the entrance slit of a VUV spectrometer (McPherson, 302VM) equipped with an imaging detector (Photonis, APD 2 PS 25/12/10/12 I 60:1 CSI 4.5”FM P43) consisting of a pair of microchannel plates with CsI coating and a phosphor screen. An image on the phosphor screen is recorded by a charge-coupled device (CCD) camera (Allied Vision Technologies, Mako G-125) on a single-shot basis. 3.
Experimental results and data handling
The spectra of the reflection from the FS plate are recorded with changing the delay τ between the NIR pump and VUV probe pulses as shown in Fig. 2(a). The unexcited FS surface reflects VUV with the low reflectivity of ∼ 0.004 at the incident angle of 55◦ . The VUV reflectivity is significantly enhanced by the plasma mirror formation by the NIR pump pulse. In addition, the plasma emission from the FS surface is observed irrespective of the presence of the VUV probe pulse. The plasma emission consists of (i) the broad component due to the recombination and (ii) the sharp lines due to the atomic transitions such as Si I [3s2 3p2 − 3s2 3pnd] at around 166 nm. In Fig. 2(a), the negative delay means that the VUV probe pulse precedes the NIR pump pulse. As τ increases, the VUV probe pulse is delayed with respect to the NIR pump pulse. When the VUV probe pulse precedes the NIR pump pulse, the reflection spectrum in λ = 140 − 180 nm consists of (i) the plasma emission induced by the NIR pump pulse and (ii) the reflection of the VUV probe pulse from the unexcited FS surface. When the VUV probe pulse follows the NIR pump pulse, the reflection of the VUV probe pulse is enhanced by the plasma mirror formed by the NIR pump pulse. The total VUV reflection spectrum Itotal (λ , τ ) is expressed as 0 diff (λ ) + Ireflec (λ , τ ), Itotal (λ , τ ) = Iplasma (λ ) + Ireflec
(1)
0 (λ ) the specwhere Iplasma (λ ) is the spectrum of the plasma emission from the FS surface, Ireflec diff trum of the reflection from the unexcited FS surface, Ireflec (λ , τ ) the difference in the reflection diff (λ , τ ) is obtained by subtractspectrum induced by the plasma mirror at τ . From Eq. (1), Ireflec 0 ing Iplasma (λ ) + Ireflec (λ ) from Itotal (λ , τ ) at each delay τ as shown in Fig. 2(b). In this study, 0 (λ ) is acquired by taking the average of Itotal (λ , τ ) at the five delay points Iplasma (λ ) + Ireflec corresponding to −860 fs ≤ τ ≤ −833.3 fs in Fig. 2(a). Since the VUV pulse is positively chirped due to the transmission through the LiF lens, the higher frequency (shorter wavelength) components in the later part of the pulse start to be reflected at earlier delay τ than the lower frequency (longer wavelength) components in the earlier part of the pulse. It is a characteristic feature of PM-FROG that the frequency-resolved reflectivity rising indicates the group delay of the VUV probe pulse in an intuitive manner. In diff (λ , τ ) is described as exact formulation, the extracted Ireflec diff (λ , τ ) = Ireflec
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2 d ω ∞ EVUV (t − τ ) R(t) − R0 exp (−iω t)dt , d λ −∞
(2)
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10918
Fig. 2. (a) Raw data of the time-resolved reflection spectra Itotal (λ , τ ) of FS. (b) Differdiff (λ , τ ). (c) Spectrum difference ence in the reflection induced by the plasma mirror, Ireflec diff Ireflec (λ , τ = 807 fs) (thin red line) and reflection spectrum of the unexcited FS surface (thick gray line). See text for details.
where ω is the angular frequency of VUV, R0 the reflectivity of the unexcited FS surface, and R(t) the time dependent reflectivity of the FS surface on which the plasma mirror is formed. The complex amplitude of the VUV pulse in time domain is defined as (3) EVUV (t) ≡ IVUV (t) exp{−iφVUV (t)}, where IVUV (t) and φVUV (t) are the temporal intensity and phase of the VUV pulse. diff (λ , τ ) at sufficiently As shown in Fig. 2(c), it is confirmed that the difference spectrum Ireflec large τ is similar to the reflection spectrum from the unexcited FS surface, indicating that the wavelength dependence in the reflection by the plasma mirror is negligibly small in this spectrum range around λ = 160 nm. We define R(t) − R0 as G(t), and describe the PM-FROG trace as follows; IFROG (ω , τ )
dλ diff = Ireflec (λ , τ ) × dω ∞ 2 = EVUV (t − τ )G(t) exp (−iω t)dt . −∞
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(4)
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10919
The signal fields in time and frequency domains are defined as Esig (t, τ ) E˜sig (ω , τ )
≡ EVUV (t − τ )G(t), ≡
∞
−∞
Esig (t, τ ) exp (−iω t)dt,
(5)
respectively, In the next section, we analyze the data of IFROG (ω , τ ) transformed from diff (λ , τ ) in Fig. 2(b). Ireflec 4.
Retrieval of a VUV waveform with modified PCGPA
There are two unknown functions, EVUV (t) and G(t) for reconstruction of a PM-FROG trace as described in Eq. (4). We adopt PCGPA, which is one of basic algorithms for reconstruction of a cross correlation FROG (XFROG) trace with two unknown functions. In usual XFROG, two unknown pulses have non-zero magnitude in confined temporal regions. On the other hand, in PM-FROG, G(t) is not a gate function that have non-zero amplitude in a confined temporal region, but a step function that have a rapid rise followed by a plateau. The temporal region of non-zero amplitude of G(t) = R(t) − R0 is extended to the positive end as illustrated in Fig. 3(a).
Fig. 3. (a) Assumed temporal intensity IVUV (t) (thick red line) and phase φVUV (t) (dotted blue line) of a VUV pulse, and assumed reflectivity difference R(t) − R0 = |G(t)|2 (thin gray line). (b) Delayed temporal intensities IVUV (t − τ ) with τ = 0 fs (thick red line), 427 fs (dotted red line), 846 fs (dashed red line), and −427 fs (dash-dotted red line). When τ = −427 fs, part of a pulse is wrapped around from the negative end to the positive end, resulting in artificial non-zero intensity in the range of t > 600 fs. The reflectivity difference R(t) − R0 (thin gray line) is plotted for reference.
In the numerical process, EVUV (t) and G(t) are represented using discretized time points with a constant spacing of Δt as N N N EVUV − Δt , EVUV (− + 1)Δt , · · · , EVUV ( − 1)Δt , EVUV (ti ) = 2 2 2 #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10920
G(ti ) =
N N N G − Δt , G (− + 1)Δt , · · · , G ( − 1)Δt , 2 2 2
(6)
where N is the number of the discretized time points and set to be an integer power of 2. In PCGPA, the time delayed VUV waveform EVUV (ti − τ j ) is obtained by rotating the elements of EVUV (ti ) in Eq. (6) to the right direction by j, where i and j are integers in the range of [−N/2, (N/2) − 1]. The delayed time is expressed as (ti − τ j ) = (i − j)Δt. In order to confine (i − j) to the range of [−N/2, (N/2) − 1], the element rotation is performed as follows: When (i − j) < −N/2, (i − j) is converted to (i − j + N) and when (i − j) > (N/2) − 1, (i − j) is converted to (i − j − N). The rotation of the EVUV elements causes artificial non-zero amplitude of EVUV due to the connection between the negative end at t = −(N/2)Δt and the positive end at t = {(N/2) − 1}Δt. For example, when the delay is τ < −427 fs in Fig. 3(b), IVUV (t − τ ) in the temporal region earlier than the negative end (t = −853 fs) is transferred to the positive end (t = 846 fs), resulting in artificial non-zero intensity near the positive end as shown by a dash-dotted line in Fig. 3(b). The reflectivity difference R(t) − R0 = |G(t)|2 has non-zero magnitude in the temporal range from a rising moment to the positive end as shown in Fig. 3(a). Therefore, artificial non-zero amplitude of Esig (t, τ ) emerges in the area of (t > 0, τ < 0) in Fig. 4(a). The FROG trace in Fig. 4(b) is obtained through the Fourier transform of Esig (t, τ ) with respect t at each delay τ as described in Eq. (4). In order to separate the true and artifact in the calculated FROG trace, the following two conditions are imposed on IVUV (t) and R(t) − R0 . (i) The VUV pulse is confined in the negative temporal region of t < 0, that is, IVUV (t) = 0 for t ≥ 0. (ii) The plasma mirror is formed around t = 0 fs, that is, R(t) − R0 = 0 in the region of t < 0. The central point ({(N/2) + 1}th point) in the time coordinate is set to be t = 0 fs.
Fig. 4. (a) Simulated reflection intensity in time domain, IVUV (t − τ )(R(t) − R0 )=|Esig (t, τ )|2 . In the simulation, IVUV (t) and R(t) − R0 in Fig. 3(a) are used . (b) Simulated PM-FROG trace obtained through the Fourier transform of Esig (t, τ ). The artificial components emerge in the area of τ < 0.
The above two conditions are imposed on the initial guess of IVUV (t) and R(t) − R0 in the iteration of PCGPA. The measured PM-FROG trace, IFROG (ωi , τ j ), with the pixel size of 256 × 256 is shown in Fig. 5(a). The origin of the delay τ coordinate in the measured FROG trace is also set to be earlier than the rising of the plasma mirror reflection. At the step of imposing the data constraint, the magnitude of E˜sig (ω , τ ) is replaced with the square root of the measured #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10921
FROG intensity IFROG (ω , τ ) only in the area of τ ≥ 0. In the area of τ < 0, the magnitude of E˜sig (ω , τ ) is not replaced by the square root of IFROG (ωi , τ j ) and is left as it is. The FROG error in the k-th iteration is evaluated in the area of τ ≥ 0 as follows:
2
2 N N (k) (k) (7) G = 2 ∑ ∑ IFROG (ωi , τ j ) − μ IFROG (ωi , τ j ) , N i=1 N j= 2 +1
(k)
where μ is a real coefficient that minimizes the FROG error G(k) , IFROG (ωi , τ j ) is the calculated FROG trace, that is, |E˜sig (ωi , τ j )|2 in the k-th iteration. The intensity of IFROG (ωi , τ j ) is normalized so that the maximum IFROG (ωi , τ j ) becomes unity. Through the iteration of PCGPA mentioned above, the FROG trace in τ ≥ 0 is successfully reconstructed with the FROG error of G = 0.0547 as shown in Fig. 5(b). It should be noted that (k) IFROG (ωi , τ j ) in the area of τ < 0 is an artifact. If a more sophisticated FROG algorithm [27] is used, this artifact can be avoided.
Fig. 5. (a) Measured PM-FROG trace, IFROG (ωi , τ j ), with the pixel size of 256 × 256. (b) Retrieved FROG trace with PCGPA modified for plasma mirror reflection. Only the area of τ ≥ 0 is retrieved.
The VUV temporal intensity IVUV (t) and phase φVUV (t) are obtained as shown in Fig. 6(a). It is found that the retrieved VUV waveform is positively chirped due to the transmission through the LiF lens. The spectral intensity and phase of the VUV pulse are obtained by the Fourier transform of the temporal waveform described by IVUV (t) and φVUV (t) as shown in Fig. 6(b). The spectral phase can be expanded in polynomials with respect to the central angular frequency of ω0 = 2π × 1.86 PHz as
ϕ (ω ) = ϕ0 + ϕ1 (ω − ω0 ) +
ϕ2 ϕn (ω − ω0 )2 + · · · + (ω − ω0 )n + · · · . 2 n!
(8)
The constant and linear terms are related to the absolute phase and the time shift, respectively, and are not our concern in this study. By subtracting these two terms, group velocity dispersion (GVD) with higher-order terms is obtained as the spectral phase shown in Fig. 6(b). For comparison, the spectral phase resulting from the propagation in the LiF lens of 2.3 mm thickness is #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10922
Fig. 6. (a) Retrieved temporal intensity IVUV (t) (thick red solid line) and phase φVUV (t) (dotted blue line) of the VUV pulse and retrieved reflectivity difference R(t) − R0 (thin gray line). As τ increases to the maximum delay of 846 fs, IVUV (t − τ ) is shifted to the right direction as plotted by a red dashed line. (b) Retrieved VUV spectrum (thick red line) and spectral phase (dotted blue line). The spectral phase distorted by the propagation in the LiF lens of 2.3 mm thickness is drawn by a thin gray line. See text for details.
also plotted [28]. The retrieved spectral phase is almost explained by the propagation in the LiF lens. The difference is ascribed to the inherent phase resulting from HHG and the propagation in the Ar gas cell, and includes higher order phase terms causing the strong modulation in the temporal intensity profile. It should be emphasized that in the characterization of VUV pulse with the wavelength around 100 nm the optical measurement has higher energy resolution than the photoelectron measurement in two-photon ionization FROG [10] or in SPIDER using coherently excited two levels [14]. The advantage of the high energy resolution makes characterization of significantly chirped pulses as well as narrow band pulses possible. Indeed, the chirped VUV pulse with the pulse duration longer than 200 fs can be characterized as shown in Fig. 6(a). Another advantage of PM-FROG is applicability to the shorter wavelength region of λ < 110 nm where no transmissive material exists. The applicable wavelength is determined by the electron density ne in the plasma formed by an intense laser pulse. The reflectivity enhancement requires that ne exceeds the critical density nc = mε0 ω 2 /e2 , where m and e are the electron mass and charge, ε0 the vacuum dielectric constant. The applicability to shorter wavelength should be confirmed in the near future. The reflection difference of R(t) − R0 is also retrieved by the modified PCGPA as shown in Fig. 6(a). It should be noticed that artificial parts are contained in the retrieved R(t) − R0 . In Fig. 6(a), the red solid line indicates IVUV (t − τ ) at τ = 0 and the red dashed line IVUV (t − τ ) at the maximum delay, τ = {(N/2) − 1}Δt, where N = 256, Δt = 6.667 fs and then τ = 846 fs. As τ increases from 0 to the maximum delay, the VUV pulse of IVUV (t − τ ) moves from the solid line to the dashed line in the right direction, and covers the temporal region from −620 to 670
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10923
fs. Thus, the FROG trace in τ ≥ 0 is determined by G(t) = R(t) − R0 in the temporal region of −620 fs < t < 670 fs. In other words, the retrieved R(t) − R0 is valid within this limited temporal region. Indeed, high plateaus of R(t) − R0 in t ≥ 626 fs and t ≤ −600 fs emerge with the sharp falling and rising, respectively, but are artifacts. It is worth discussing the rising of R(t) − R0 at around t = 0 fs. The retrieved rising time is found to be shorter than 100 fs in spite of the long pulse duration of the VUV probe pulse which is much longer than the rising time response. If the time-resolved reflectivity is recorded without the frequency-resolved measurement, the rising time is convoluted by the temporal profile of the probe pulse through the summation over all the frequency components. The frequency-resolved measurement enables us to extract the accurate temporal profile of the plasma mirror formation whose time scale is shorter than the duration of the probe pulse. The PM-FROG measurement would be useful to not only characterization of VUV pulses, but also investigation of electronic excitation and relaxation dynamics related to plasma formation [29–31] in solid pumped by a strong fs laser pulse. In order to discuss the electronic excitation dynamics, we need to precisely monitor the pump laser pulse in temporal and spatial domains. The shot-to-shot intensity fluctuation is also a factor to be monitored for reducing its influence to the retrieval of EVUV (t) and R(t). We are upgrading our experimental system to meet the requirements for the detailed investigation of electronic excitation of solid in intense laser fields. 5.
Summary
We have demonstrated PM-FROG that enables us to fully characterize the VUV waveform through the measurement of the time-resolved reflection spectrum of the plasma mirror formed on FS by the intense NIR laser pulse. The retrieval algorithm of PCGPA has been modified for the time-dependent reflectivity whose temporal profile is close to a step function. The high energy resolution of the optical measurement in this method has an advantage in characterization of significantly chirped pulses as well as narrow band pulses. The time-dependent reflectivity difference is also retrieved without usage of a fitting function such as Page function. The present method is applicable to not only characterization of VUV pulses, but also investigation of ultrafast electronic dynamics in solid excited by an intense laser pulse. Acknowledgments The authors are grateful to Prof. T. Nakajima (Kyoto University) and Dr. T. Otobe (JAEA) for their valuable discussion, and to Drs. M. Nishikino and N. Hasegawa (JAEA) for their support in the laser operation. This study is partly supported by the Consortium for Photon Science and Technology programed by MEXT of Japan. RI acknowledges JSPS KAKENHI (Grant No. 26288013) and the Joint Usage/Research Program on Zero-Emission Energy Research, Institute of Advanced Energy, Kyoto University (Grant No. ZE26B-27).
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10924
Abstract: We propose and experimentally demonstrate a method for characterizing vacuum ultraviolet (VUV) pulses based on time-resolved reflection spectroscopy of fused silica pumped by an intense laser pulse. Plasma mirror reflection is used as an ultrafast optical switch, which enables us to measure frequency-resolved optical gating (FROG) traces. The VUV temporal waveform can be retrieved from the measured FROG trace using principal component generalized projections algorithm with modification. The temporal profile of the plasma mirror reflectivity is also extracted simultaneously. © 2015 Optical Society of America OCIS codes: (320.7100) Ultrafast optics: Ultrafast measurements; (320.7080) Ultrafast devices; (320.7120) Ultrafast phenomena; (350.5400) Plasmas.
References and links 1. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006). 2. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). 3. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4, 641–647 (2010). 4. M. Yabashi, H. Tanaka, T. Tanaka, H. Tomizawa, T. Togashi, M. Nagasono, T. Ishikawa, J. R. Harries, Y. Hikosaka, A. Hishikawa, K. Nagaya, N. Saito, E. Shigemasa, K. Yamanouchi, and K. Ueda, “Compact XFEL and AMO sciences: SACLA and SCSS,” J. Phys. B: At., Mol. Opt. Phys. 46, 164001 (2013). 5. Y. Mairesse and F. Qu´er´e, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005). 6. H. Mashiko, M. J. Bell, A. R. Beck, M. J. Abel, P. M. Nagel, C. P. Steiner, J. Robinson, D. M. Neumark, and S. R. Leone, “Tunable frequency-controlled isolated attosecond pulses characterized by either 750 nm or 400 nm wavelength streak fields,” Opt. Express 18, 25887–25895 (2010). 7. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004). 8. P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426, 267–271 (2003). 9. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime,” Phys. Rev. Lett. 97, 153904 (2006).
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10914
10. A. Kosuge, T. Sekikawa, X. Zhou, T. Kanai, S. Adachi, and S. Watanabe, “Frequency-resolved optical gating of isolated attosecond pulses in the extreme ultraviolet,” Phys. Rev. Lett. 97, 263901 (2006). 11. F. Qu´er´e, J. Itatani, G. L. Yudin, and P. B. Corkum, “Attosecond spectral shearing interferometry,” Phys. Rev. Lett. 90, 073902 (2003). 12. E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev. Lett. 94, 033905 (2005). 13. Y. Mairesse, O. Gobert, P. Breger, H. Merdji, P. Meynadier, P. Monchicourt, M. Perdrix, P. Sali`eres, and B. Carr´e, “High harmonic xuv spectral phase interferometry for direct electric-field reconstruction,” Phys. Rev. Lett. 94, 173903 (2005). 14. R. Itakura, “Spectral phase measurement of attosecond pulses using the quantum beat between the P1/2 and P3/2 levels of alkali-metal atoms,” Phys. Rev. A 76, 033810 (2007). 15. J. Chen, R. Itakura, and T. Nakajima, “Characterization of attosecond XUV pulses utilizing a broadband UV∼VUV pumping,” Opt. Express 18, 2020–2035 (2010). 16. J. Chen, R. Itakura, and T. Nakajima, “Reconstruction of attosecond pulses using two-color pumping,” J. Opt. Soc. Am. B 28, 2195–2199 (2011). 17. H. C. Kapteyn, A. Szoke, R. W. Falcone, and M. M. Murnane, “Prepulse energy suppression for high-energy ultrashort pulses using self-induced plasma shuttering,” Opt. Lett. 16, 490–492 (1991). 18. B. Dromey, S. Kar, M. Zepf, and P. Foster, “The plasma mirror–a subpicosecond optical switch for ultrahigh power lasers,” Rev. Sci. Instrum. 75, 645–649 (2004). 19. G. Doumy, F. Qu´er´e, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J. P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E 69, 026402 (2004). 20. C. Thaury, F. Qu´er´e, J.-P. Geindre, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. R´eau, P. D’Oliveira, P. Audebert, R. Marjoribanks, and P. Martin, “Plasma mirrors for ultrahigh-intensity optics,” Nat. Phys. 3, 424–429 (2007). 21. C. Rolland and P. B. Corkum, “Generation of 130-fsec midinfrared pulses,” J. Opt. Soc. Am. B 3, 1625–1629 (1986). 22. K. Michelmann, U. Wagner, T. Feurer, U. Teubner, E. F¨orster, and R. Sauerbrey, “Measurement of the page function of an ultrashort laser pulse,” Opt. Commun. 198, 163–170 (2001). 23. X. Wang, T. Nakajima, H. Zen, T. Kii, and H. Ohgaki, “Damage threshold and focusability of mid-infrared freeelectron laser pulses gated by a plasma mirror with nanosecond switching pulses,” Appl. Phys. Lett. 103, 191105 (2013). 24. C. H. Page, “Instantaneous power spectra,” J. Appl. Phys. 23, 103–106 (1952). 25. D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421–431 (1999). 26. T. Kumada, H. Akagi, R. Itakura, T. Otobe, and A. Yokoyama, “Femtosecond laser ablation dynamics of fused silica extracted from oscillation of time-resolved reflectivity,” J. Appl. Phys. 115, 103504 (2014). 27. J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92, 25–32 (2008). 28. H. H. Li, “Refractive index of alkali halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 5, 329–528 (1976). 29. D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser-induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64, 3071–3073 (1994). 30. M. Lebugle, N. Sanner, N. Varkentina, M. Sentis, and O. Ut´eza, “Dynamics of femtosecond laser absorption of fused silica in the ablation regime,” J. Appl. Phys. 116, 063105 (2014). 31. P. K. Singh, G. Chatterjee, A. Adak, A. D. Lad, P. Brijesh, and G. Ravindra Kumar, “Ultrafast optics of solid density plasma using multicolor probes,” Opt. Express 22, 22320–22327 (2014).
1.
Introduction
Ultrafast coherent light sources in the short wavelength region from vacuum ultraviolet (VUV) to hard X-ray have been intensively developed based on high-order harmonic generation (HHG) [1, 2] and free-electron lasers [3, 4]. In VUV and extreme ultraviolet (EUV), the time resolution has reached the attosecond regime, where we can trace electron dynamics in atoms, molecules, and solids. Such short wavelength light sources enable us to perform photoelectron spectroscopy and photoabsorption spectroscopy by one-photon process for probing transient states with no disturbance by probe itself. Indeed, high-order harmonics in the VUV range is easily generated using a femtosecond (fs) laser pulse with the millijoule-level pulse energy, and
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10915
thus has great potential for various applications. In ultrafast spectroscopy, the characterization of the pump and probe pulses is crucial to extract accurate temporal response of experimental targets. However, characterizing VUV and EUV pulses is not so easy as generating them by simply focusing a laser pulse into nonlinear media of rare gases. Mainly, two types of methods have been experimentally used to date. One is frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG CRAB) with streaking photoelectrons using a carrier-envelop phase (CEP) stabilized laser electric field [1, 2, 5, 6]. The other is non-resonant two-photon ionization with intense VUV/EUV pulses for autocorrelation [7–9] and FROG measurements [10]. In many laboratories using VUV pulses as probe pulses, CEP of laser pulses is not stabilized and the intensity of VUV pulses is not sufficiently strong for non-resonant two-photon processes. As an alternative method, spectral phase interferometry for direct electric-field reconstruction (SPIDER) that requires two VUV pulses with a spectral shift was proposed and expeimentally demonstrated [11–13], but the preparation of a pair of frequency-shifted VUV pulses is a demanding task. Another type of SPIDER using time-resolved photoelectron spectra from coherently superposed states was also theoretically proposed [14–16], but has not been experimentally demonstrated yet. We turn our attention to a plasma mirror formed by an ultrashort laser pulse on a transparent material such as fused silica (FS). Self-induced plasma in an ultrashort laser pulse has been known as a plasma mirror and used for prepulse suppression in an ultraintense laser pulse [17–20]. Plasma formed by an ultrashort laser pulse has also been used as active optical switching devices [21–23]. Such an ultrafast switching device is applicable to characterize an ultrafast laser pulse through measurement of temporally varying spectra of the pulse. Previously, Michelmann et al. performed the time-resolved transmission spectroscopy of FS, on which a pump laser pulse was focused for plasma formation [22]. The plasma makes FS opaque to a probe pulse with λ ∼ 248.5 nm. In their analysis to obtain the amplitude and phase of the electric field of the ultraviolet probe pulse, the transition time from transparent to opaque was assumed to be much shorter than the probe pulse duration, and the Heaviside step function was used for describing the optical switching. As a result, the time-resolved transmission spectrum was simply described by the Page function [24]. In this study, we adopt reflection instead of transmission, because reflection is applicable to the shorter wavelength region in which solid materials are not transparent. The applicable wavelength by the reflection measurement is expected to become shorter than UV. Even in the wavelength region where transmission is applicable, the transmitted probe pulse is influenced by the entire thickness of the plasma consisting of the front and back surfaces and the bulk of the plasma. On the other hand, the reflected one is influenced by only the front surface of the plasma. When the pulse duration becomes comparable to the falling (rising) time of the plasma switching, it is inappropriate that the falling (rising) time of the transmissivity (reflectivity) is treated as the Heaviside step function. In order to solve this problem, we use the principal component generalized projections algorithm (PCGPA) [25] with modification to extract not only the temporal waveform of the probe pulse, but also the temporal response of the plasma switching from the time-resolved reflection spectra. We will demonstrate that a VUV waveform can be retrieved from the spectrogram obtained by time-resolved plasma mirror reflection. Hereafter, we call this method plasma-mirror frequency-resolved optical gating (PM-FROG). 2.
Experimental setup
Experimental setup is shown in Fig. 1. A Ti:Sapphire chirped pulse amplification system provides output laser pulses with λ ∼ 795 nm, 60 fs duration (full width at half maximum) at 10
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10916
Hz repetition rate. Using an aluminum-coated concave mirror with the curvature radius of 2.0 m, the output laser pulses are focused in an Ar gas cell with 2.2 m length to generate high-order harmonics. The pressure of Ar in the cell is optimally set to be around 11 kPa for generation of fifth harmonics (λ ∼ 160 nm) which is characterized in this study. The generated harmonics and the fundamental near-infrared (NIR) laser pulses are collimated by a lithium fluoride (LiF) lens with f = 1.0 m focusing length and 2.3 mm thickness. For simplicity of the vacuum system, the Ar cell is connected to a vacuum chamber with the LiF lens which works as not only a lens but also an entrance window of the vacuum chamber. (a) Concave Mirror f = 1m
Delay Line & Target Chamber
2.2 m
VUV Spectrometer
LiF Lens f=1m
Ar Cell
Imaging Lens, CCD
From TiS CPA
Dielectric Mirror for 800nm LiF lens f=1m
CCD
Dielectric Mirror for 160nm
(b)
Mirror for Alignment VUV
Ar Cell
Concave Al Mirror, r = 0.4m
Gate Valve To VUV Imaging Spectrometer
NIR
Iris Delay stage
Concave Al Mirror, r = 0.3m
Vacuum
Fused Silica Plate on 2D Motorized Stage
50 μm
Mechanical Shutter
Delay Line & Target Chamber Fig. 1. Top view of experimental setup. (a) Overview. (b) Expanded view of the vacuum chamber, in which the delay line and an FS plate on the two-dimensionally motorized stage are installed. A microscope image of craters formed by laser ablation on an FS plate is shown at the bottom-right.
In the vacuum chamber, the NIR and VUV pulses are separated by a dielectric mirror (Layertec, #103841), which reflects VUV (λ ∼ 160 nm) and transmits NIR. After the separation of NIR and VUV, the NIR pulse is reflected twice with dielectric mirrors (CVI, TLM1-800-451025) for attenuation of other frequency components such as third-order harmonics (λ ∼ 265 nm). The NIR and VUV pulses are respectively reflected twice with aluminum-coated flat mirrors, and then recombined collinearly with another dielectric mirror which reflects VUV and transmits NIR. The delay between the NIR and VUV pulses is controlled with a translational stage with a stepping motor (Suruga Seiki, KXC06020-GA). A scan step of the stage is 1 μ m, corresponding to 6.667 fs for a round trip. The combined NIR and VUV pulses are focused on an FS plate using an aluminum-coated concave mirror with the curvature radius of 0.3 m. The incident angle is set to be the Brewster angle of 55◦ for λ ∼ 795 nm. The polarization directions of NIR and VUV are horizontal. The FS plate is moved with the 2D motorized stage so that the fresh surface is exposed to the NIR and VUV pulses every laser shot. The intensity of the NIR pump pulse is adjusted with an iris #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10917
in the middle of the delay line to be just above the ablation threshold of 3.3 J cm−2 [26] for plasma formation on the FS surface. A microscope image of craters formed by laser ablation on an FS plate is shown in the inset of Fig. 1(b). The craters exhibit an ellipse shape because of the incident angle of 55◦ . Its size is 33 μ m × 60 μ m, which is almost half as large as that of the Airy disk of the diffraction limited focal spot. The spot size of the VUV pulse on the FS plate could not be measured in the current setup, but is expected to be smaller than the size of the crater due to the shorter wavelength. Thus, it is considered that the influence of the spatial distribution of the pump laser intensity is not so much. Using an aluminum-coated concave mirror with the curvature radius of 0.4 m, the VUV pulse reflected by the plasma mirror is focused on the entrance slit of a VUV spectrometer (McPherson, 302VM) equipped with an imaging detector (Photonis, APD 2 PS 25/12/10/12 I 60:1 CSI 4.5”FM P43) consisting of a pair of microchannel plates with CsI coating and a phosphor screen. An image on the phosphor screen is recorded by a charge-coupled device (CCD) camera (Allied Vision Technologies, Mako G-125) on a single-shot basis. 3.
Experimental results and data handling
The spectra of the reflection from the FS plate are recorded with changing the delay τ between the NIR pump and VUV probe pulses as shown in Fig. 2(a). The unexcited FS surface reflects VUV with the low reflectivity of ∼ 0.004 at the incident angle of 55◦ . The VUV reflectivity is significantly enhanced by the plasma mirror formation by the NIR pump pulse. In addition, the plasma emission from the FS surface is observed irrespective of the presence of the VUV probe pulse. The plasma emission consists of (i) the broad component due to the recombination and (ii) the sharp lines due to the atomic transitions such as Si I [3s2 3p2 − 3s2 3pnd] at around 166 nm. In Fig. 2(a), the negative delay means that the VUV probe pulse precedes the NIR pump pulse. As τ increases, the VUV probe pulse is delayed with respect to the NIR pump pulse. When the VUV probe pulse precedes the NIR pump pulse, the reflection spectrum in λ = 140 − 180 nm consists of (i) the plasma emission induced by the NIR pump pulse and (ii) the reflection of the VUV probe pulse from the unexcited FS surface. When the VUV probe pulse follows the NIR pump pulse, the reflection of the VUV probe pulse is enhanced by the plasma mirror formed by the NIR pump pulse. The total VUV reflection spectrum Itotal (λ , τ ) is expressed as 0 diff (λ ) + Ireflec (λ , τ ), Itotal (λ , τ ) = Iplasma (λ ) + Ireflec
(1)
0 (λ ) the specwhere Iplasma (λ ) is the spectrum of the plasma emission from the FS surface, Ireflec diff trum of the reflection from the unexcited FS surface, Ireflec (λ , τ ) the difference in the reflection diff (λ , τ ) is obtained by subtractspectrum induced by the plasma mirror at τ . From Eq. (1), Ireflec 0 ing Iplasma (λ ) + Ireflec (λ ) from Itotal (λ , τ ) at each delay τ as shown in Fig. 2(b). In this study, 0 (λ ) is acquired by taking the average of Itotal (λ , τ ) at the five delay points Iplasma (λ ) + Ireflec corresponding to −860 fs ≤ τ ≤ −833.3 fs in Fig. 2(a). Since the VUV pulse is positively chirped due to the transmission through the LiF lens, the higher frequency (shorter wavelength) components in the later part of the pulse start to be reflected at earlier delay τ than the lower frequency (longer wavelength) components in the earlier part of the pulse. It is a characteristic feature of PM-FROG that the frequency-resolved reflectivity rising indicates the group delay of the VUV probe pulse in an intuitive manner. In diff (λ , τ ) is described as exact formulation, the extracted Ireflec diff (λ , τ ) = Ireflec
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2 d ω ∞ EVUV (t − τ ) R(t) − R0 exp (−iω t)dt , d λ −∞
(2)
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10918
Fig. 2. (a) Raw data of the time-resolved reflection spectra Itotal (λ , τ ) of FS. (b) Differdiff (λ , τ ). (c) Spectrum difference ence in the reflection induced by the plasma mirror, Ireflec diff Ireflec (λ , τ = 807 fs) (thin red line) and reflection spectrum of the unexcited FS surface (thick gray line). See text for details.
where ω is the angular frequency of VUV, R0 the reflectivity of the unexcited FS surface, and R(t) the time dependent reflectivity of the FS surface on which the plasma mirror is formed. The complex amplitude of the VUV pulse in time domain is defined as (3) EVUV (t) ≡ IVUV (t) exp{−iφVUV (t)}, where IVUV (t) and φVUV (t) are the temporal intensity and phase of the VUV pulse. diff (λ , τ ) at sufficiently As shown in Fig. 2(c), it is confirmed that the difference spectrum Ireflec large τ is similar to the reflection spectrum from the unexcited FS surface, indicating that the wavelength dependence in the reflection by the plasma mirror is negligibly small in this spectrum range around λ = 160 nm. We define R(t) − R0 as G(t), and describe the PM-FROG trace as follows; IFROG (ω , τ )
dλ diff = Ireflec (λ , τ ) × dω ∞ 2 = EVUV (t − τ )G(t) exp (−iω t)dt . −∞
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(4)
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10919
The signal fields in time and frequency domains are defined as Esig (t, τ ) E˜sig (ω , τ )
≡ EVUV (t − τ )G(t), ≡
∞
−∞
Esig (t, τ ) exp (−iω t)dt,
(5)
respectively, In the next section, we analyze the data of IFROG (ω , τ ) transformed from diff (λ , τ ) in Fig. 2(b). Ireflec 4.
Retrieval of a VUV waveform with modified PCGPA
There are two unknown functions, EVUV (t) and G(t) for reconstruction of a PM-FROG trace as described in Eq. (4). We adopt PCGPA, which is one of basic algorithms for reconstruction of a cross correlation FROG (XFROG) trace with two unknown functions. In usual XFROG, two unknown pulses have non-zero magnitude in confined temporal regions. On the other hand, in PM-FROG, G(t) is not a gate function that have non-zero amplitude in a confined temporal region, but a step function that have a rapid rise followed by a plateau. The temporal region of non-zero amplitude of G(t) = R(t) − R0 is extended to the positive end as illustrated in Fig. 3(a).
Fig. 3. (a) Assumed temporal intensity IVUV (t) (thick red line) and phase φVUV (t) (dotted blue line) of a VUV pulse, and assumed reflectivity difference R(t) − R0 = |G(t)|2 (thin gray line). (b) Delayed temporal intensities IVUV (t − τ ) with τ = 0 fs (thick red line), 427 fs (dotted red line), 846 fs (dashed red line), and −427 fs (dash-dotted red line). When τ = −427 fs, part of a pulse is wrapped around from the negative end to the positive end, resulting in artificial non-zero intensity in the range of t > 600 fs. The reflectivity difference R(t) − R0 (thin gray line) is plotted for reference.
In the numerical process, EVUV (t) and G(t) are represented using discretized time points with a constant spacing of Δt as N N N EVUV − Δt , EVUV (− + 1)Δt , · · · , EVUV ( − 1)Δt , EVUV (ti ) = 2 2 2 #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10920
G(ti ) =
N N N G − Δt , G (− + 1)Δt , · · · , G ( − 1)Δt , 2 2 2
(6)
where N is the number of the discretized time points and set to be an integer power of 2. In PCGPA, the time delayed VUV waveform EVUV (ti − τ j ) is obtained by rotating the elements of EVUV (ti ) in Eq. (6) to the right direction by j, where i and j are integers in the range of [−N/2, (N/2) − 1]. The delayed time is expressed as (ti − τ j ) = (i − j)Δt. In order to confine (i − j) to the range of [−N/2, (N/2) − 1], the element rotation is performed as follows: When (i − j) < −N/2, (i − j) is converted to (i − j + N) and when (i − j) > (N/2) − 1, (i − j) is converted to (i − j − N). The rotation of the EVUV elements causes artificial non-zero amplitude of EVUV due to the connection between the negative end at t = −(N/2)Δt and the positive end at t = {(N/2) − 1}Δt. For example, when the delay is τ < −427 fs in Fig. 3(b), IVUV (t − τ ) in the temporal region earlier than the negative end (t = −853 fs) is transferred to the positive end (t = 846 fs), resulting in artificial non-zero intensity near the positive end as shown by a dash-dotted line in Fig. 3(b). The reflectivity difference R(t) − R0 = |G(t)|2 has non-zero magnitude in the temporal range from a rising moment to the positive end as shown in Fig. 3(a). Therefore, artificial non-zero amplitude of Esig (t, τ ) emerges in the area of (t > 0, τ < 0) in Fig. 4(a). The FROG trace in Fig. 4(b) is obtained through the Fourier transform of Esig (t, τ ) with respect t at each delay τ as described in Eq. (4). In order to separate the true and artifact in the calculated FROG trace, the following two conditions are imposed on IVUV (t) and R(t) − R0 . (i) The VUV pulse is confined in the negative temporal region of t < 0, that is, IVUV (t) = 0 for t ≥ 0. (ii) The plasma mirror is formed around t = 0 fs, that is, R(t) − R0 = 0 in the region of t < 0. The central point ({(N/2) + 1}th point) in the time coordinate is set to be t = 0 fs.
Fig. 4. (a) Simulated reflection intensity in time domain, IVUV (t − τ )(R(t) − R0 )=|Esig (t, τ )|2 . In the simulation, IVUV (t) and R(t) − R0 in Fig. 3(a) are used . (b) Simulated PM-FROG trace obtained through the Fourier transform of Esig (t, τ ). The artificial components emerge in the area of τ < 0.
The above two conditions are imposed on the initial guess of IVUV (t) and R(t) − R0 in the iteration of PCGPA. The measured PM-FROG trace, IFROG (ωi , τ j ), with the pixel size of 256 × 256 is shown in Fig. 5(a). The origin of the delay τ coordinate in the measured FROG trace is also set to be earlier than the rising of the plasma mirror reflection. At the step of imposing the data constraint, the magnitude of E˜sig (ω , τ ) is replaced with the square root of the measured #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10921
FROG intensity IFROG (ω , τ ) only in the area of τ ≥ 0. In the area of τ < 0, the magnitude of E˜sig (ω , τ ) is not replaced by the square root of IFROG (ωi , τ j ) and is left as it is. The FROG error in the k-th iteration is evaluated in the area of τ ≥ 0 as follows:
2
2 N N (k) (k) (7) G = 2 ∑ ∑ IFROG (ωi , τ j ) − μ IFROG (ωi , τ j ) , N i=1 N j= 2 +1
(k)
where μ is a real coefficient that minimizes the FROG error G(k) , IFROG (ωi , τ j ) is the calculated FROG trace, that is, |E˜sig (ωi , τ j )|2 in the k-th iteration. The intensity of IFROG (ωi , τ j ) is normalized so that the maximum IFROG (ωi , τ j ) becomes unity. Through the iteration of PCGPA mentioned above, the FROG trace in τ ≥ 0 is successfully reconstructed with the FROG error of G = 0.0547 as shown in Fig. 5(b). It should be noted that (k) IFROG (ωi , τ j ) in the area of τ < 0 is an artifact. If a more sophisticated FROG algorithm [27] is used, this artifact can be avoided.
Fig. 5. (a) Measured PM-FROG trace, IFROG (ωi , τ j ), with the pixel size of 256 × 256. (b) Retrieved FROG trace with PCGPA modified for plasma mirror reflection. Only the area of τ ≥ 0 is retrieved.
The VUV temporal intensity IVUV (t) and phase φVUV (t) are obtained as shown in Fig. 6(a). It is found that the retrieved VUV waveform is positively chirped due to the transmission through the LiF lens. The spectral intensity and phase of the VUV pulse are obtained by the Fourier transform of the temporal waveform described by IVUV (t) and φVUV (t) as shown in Fig. 6(b). The spectral phase can be expanded in polynomials with respect to the central angular frequency of ω0 = 2π × 1.86 PHz as
ϕ (ω ) = ϕ0 + ϕ1 (ω − ω0 ) +
ϕ2 ϕn (ω − ω0 )2 + · · · + (ω − ω0 )n + · · · . 2 n!
(8)
The constant and linear terms are related to the absolute phase and the time shift, respectively, and are not our concern in this study. By subtracting these two terms, group velocity dispersion (GVD) with higher-order terms is obtained as the spectral phase shown in Fig. 6(b). For comparison, the spectral phase resulting from the propagation in the LiF lens of 2.3 mm thickness is #231539 - $15.00 USD (C) 2015 OSA
Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10922
Fig. 6. (a) Retrieved temporal intensity IVUV (t) (thick red solid line) and phase φVUV (t) (dotted blue line) of the VUV pulse and retrieved reflectivity difference R(t) − R0 (thin gray line). As τ increases to the maximum delay of 846 fs, IVUV (t − τ ) is shifted to the right direction as plotted by a red dashed line. (b) Retrieved VUV spectrum (thick red line) and spectral phase (dotted blue line). The spectral phase distorted by the propagation in the LiF lens of 2.3 mm thickness is drawn by a thin gray line. See text for details.
also plotted [28]. The retrieved spectral phase is almost explained by the propagation in the LiF lens. The difference is ascribed to the inherent phase resulting from HHG and the propagation in the Ar gas cell, and includes higher order phase terms causing the strong modulation in the temporal intensity profile. It should be emphasized that in the characterization of VUV pulse with the wavelength around 100 nm the optical measurement has higher energy resolution than the photoelectron measurement in two-photon ionization FROG [10] or in SPIDER using coherently excited two levels [14]. The advantage of the high energy resolution makes characterization of significantly chirped pulses as well as narrow band pulses possible. Indeed, the chirped VUV pulse with the pulse duration longer than 200 fs can be characterized as shown in Fig. 6(a). Another advantage of PM-FROG is applicability to the shorter wavelength region of λ < 110 nm where no transmissive material exists. The applicable wavelength is determined by the electron density ne in the plasma formed by an intense laser pulse. The reflectivity enhancement requires that ne exceeds the critical density nc = mε0 ω 2 /e2 , where m and e are the electron mass and charge, ε0 the vacuum dielectric constant. The applicability to shorter wavelength should be confirmed in the near future. The reflection difference of R(t) − R0 is also retrieved by the modified PCGPA as shown in Fig. 6(a). It should be noticed that artificial parts are contained in the retrieved R(t) − R0 . In Fig. 6(a), the red solid line indicates IVUV (t − τ ) at τ = 0 and the red dashed line IVUV (t − τ ) at the maximum delay, τ = {(N/2) − 1}Δt, where N = 256, Δt = 6.667 fs and then τ = 846 fs. As τ increases from 0 to the maximum delay, the VUV pulse of IVUV (t − τ ) moves from the solid line to the dashed line in the right direction, and covers the temporal region from −620 to 670
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10923
fs. Thus, the FROG trace in τ ≥ 0 is determined by G(t) = R(t) − R0 in the temporal region of −620 fs < t < 670 fs. In other words, the retrieved R(t) − R0 is valid within this limited temporal region. Indeed, high plateaus of R(t) − R0 in t ≥ 626 fs and t ≤ −600 fs emerge with the sharp falling and rising, respectively, but are artifacts. It is worth discussing the rising of R(t) − R0 at around t = 0 fs. The retrieved rising time is found to be shorter than 100 fs in spite of the long pulse duration of the VUV probe pulse which is much longer than the rising time response. If the time-resolved reflectivity is recorded without the frequency-resolved measurement, the rising time is convoluted by the temporal profile of the probe pulse through the summation over all the frequency components. The frequency-resolved measurement enables us to extract the accurate temporal profile of the plasma mirror formation whose time scale is shorter than the duration of the probe pulse. The PM-FROG measurement would be useful to not only characterization of VUV pulses, but also investigation of electronic excitation and relaxation dynamics related to plasma formation [29–31] in solid pumped by a strong fs laser pulse. In order to discuss the electronic excitation dynamics, we need to precisely monitor the pump laser pulse in temporal and spatial domains. The shot-to-shot intensity fluctuation is also a factor to be monitored for reducing its influence to the retrieval of EVUV (t) and R(t). We are upgrading our experimental system to meet the requirements for the detailed investigation of electronic excitation of solid in intense laser fields. 5.
Summary
We have demonstrated PM-FROG that enables us to fully characterize the VUV waveform through the measurement of the time-resolved reflection spectrum of the plasma mirror formed on FS by the intense NIR laser pulse. The retrieval algorithm of PCGPA has been modified for the time-dependent reflectivity whose temporal profile is close to a step function. The high energy resolution of the optical measurement in this method has an advantage in characterization of significantly chirped pulses as well as narrow band pulses. The time-dependent reflectivity difference is also retrieved without usage of a fitting function such as Page function. The present method is applicable to not only characterization of VUV pulses, but also investigation of ultrafast electronic dynamics in solid excited by an intense laser pulse. Acknowledgments The authors are grateful to Prof. T. Nakajima (Kyoto University) and Dr. T. Otobe (JAEA) for their valuable discussion, and to Drs. M. Nishikino and N. Hasegawa (JAEA) for their support in the laser operation. This study is partly supported by the Consortium for Photon Science and Technology programed by MEXT of Japan. RI acknowledges JSPS KAKENHI (Grant No. 26288013) and the Joint Usage/Research Program on Zero-Emission Energy Research, Institute of Advanced Energy, Kyoto University (Grant No. ZE26B-27).
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Received 29 Dec 2014; revised 26 Mar 2015; accepted 9 Apr 2015; published 20 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.010914 | OPTICS EXPRESS 10924
