Abstract

We demonstrate spatially resolved supercontinuum spectral phase interferometry with an isolated attosecond pulse (IAP). The measured spatial-spectral interferogram over the broadband region indicates a high degree of IAP coherence in both spatial and spectral domains. In addition, the spectral-delay interferogram shows periodic temporal oscillations over the full IAP continuous spectrum, which indicates high temporal coherence. The supercontinuum spectral phase interferometry with broadband IAP will contribute to exploring spatiotemporal dispersive electronic dynamics through phase-based spectroscopy in the future.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

A. Wituschek, L. Bruder, E. Allaria, U. Bangert, M. Binz, R. Borghes, C. Callegari, G. Cerullo, P. Cinquegrana, L. Giannessi, M. Danailov, A. Demidovich, M. D. Fraia, M. Drabbels, R. Feifel, T. Laarmann, R. Michiels, N. S. Mirian, M. Mudrich, I. Nikolov, F. H. O’Shea, G. Penco, P. Piseri, O. Plekan, K. C. Prince, A. Przystawik, P. R. Ribič, G. Sansone, P. Sigalotti, S. Spampinati, C. Spezzani, R. J. Squibb, S. Stranges, D. Uhl, and F. Stienkemeier, “Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses,” Nat. Commun. 11(1), 883 (2020).
[Crossref]

2019 (3)

D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13(1), 54–59 (2019).
[Crossref]

H. Dacasa, H. Coudert-Alteirac, C. Guo, E. Kueny, F. Campi, J. Lahl, J. Peschel, H. Wikmark, B. Major, E. Malm, D. Alj, K. Varjú, C. L. Arnold, G. Dovillaire, P. Johnsson, A. L’Huillier, S. Maclot, P. Rudawski, and P. Zeitoun, “Single-shot extreme-ultraviolet wavefront measurements of high-order harmonics,” Opt. Express 27(3), 2656–2670 (2019).
[Crossref]

H. Wikmark, C. Guo, J. Vogelsang, P. W. Smorenburg, H. Coudert-Alteirac, J. Lahl, J. Peschel, P. Rudawski, H. Dacasa, S. Carlström, S. Maclot, M. B. Gaarde, P. Johnsson, C. L. Arnold, and A. L’Huillier, “Spatiotemporal coupling of attosecond pulses,” Proc. Natl. Acad. Sci. U. S. A. 116(11), 4779–4787 (2019).
[Crossref]

2018 (1)

2017 (2)

S. Fuchs, M. Wünsche, J. Nathanael, J. J. Abel, C. Rödel, J. Biedermann, J. Reinhard, U. Hübner, and G. G. Paulus, “Optical coherence tomography with nanoscale axial resolution using a laser-driven high-harmonic source,” Optica 4(8), 903–906 (2017).
[Crossref]

M. Ossiander, F. Siegrist, V. Shirvanyan, R. Pazourek, A. Sommer, T. Latka, A. Guggenmos, S. Nagele, J. Feist, J. Burgdörfer, R. Kienberger, and M. Schultze, “Attosecond correlation dynamics,” Nat. Phys. 13(3), 280–285 (2017).
[Crossref]

2016 (3)

H. Mashiko, K. Oguri, T. Yamaguchi, A. Suda, and H. Gotoh, “Petahertz optical drive with wide-bandgap semiconductor,” Nat. Phys. 12(8), 741–745 (2016).
[Crossref]

H.-S. Kim, P. Baksh, M. Odstrcil, M. Miszczak, J. G. Frey, L. Juschkin, and W. S. Brocklesby, “Lloyd’s mirror interference lithography with EUV radiation from a high-harmonic source,” Appl. Phys. Express 9(7), 076701 (2016).
[Crossref]

S. Hädrich, J. Rothhardt, M. Krebs, S. Demmler, A. Klenke, A. Tünnermann, and J. Limpert, “Single-pass high harmonic generation at high repetition rate and photon flux,” J. Phys. B: At., Mol. Opt. Phys. 49(17), 172002 (2016).
[Crossref]

2015 (1)

2014 (3)

M. M. Mang, C. Bourassin-Bouchet, and I. A. Walmsley, “Simultaneous spatial characterization of two independent sources of high harmonic radiation,” Opt. Lett. 39(21), 6142–6145 (2014).
[Crossref]

M.-C. Chen, C. Mancuso, C. Hernández-García, F. Dollar, B. Galloway, D. Popmintchev, P.-C. Huang, B. Walker, L. Plaja, A. A. Jaroń-Becker, A. Becker, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Generation of bright isolated attosecond soft X-ray pulses driven by multi-cycle mid-infrared lasers,” Proc. Natl. Acad. Sci. U. S. A. 111(23), E2361–E2367 (2014).
[Crossref]

H. Mashiko, T. Yamaguchi, K. Oguri, A. Suda, and H. Gotoh, “Characterizing inner-shell with spectral phase interferometry for direct electric-field reconstruction,” Nat. Commun. 5(1), 5599 (2014).
[Crossref]

2013 (1)

J. B. Bertrand, H. J. Wörner, P. Salières, D. M. Villeneuve, and P. B. Corkum, “Linked attosecond phase interferometry for molecular frame measurements,” Nat. Phys. 9(3), 174–178 (2013).
[Crossref]

2012 (2)

2011 (1)

S. Roling, B. Siemer, M. Wöstmann, H. Zacharias, R. Mitzner, A. Singer, K. Tiedtke, and I. A. Vartanyants, “Temporal and spatial coherence properties of free-electron-laser pulses in the extreme ultraviolet regime,” Phys. Rev. Spec. Top.--Accel. Beams 14(8), 080701 (2011).
[Crossref]

2009 (2)

Y. Nabekawa, T. Shimizu, Y. Furukawa, E. J. Takahashi, and K. Midorikawa, “Interferometry of attosecond pulse trains in the extreme ultraviolet wavelength region,” Phys. Rev. Lett. 102(21), 213904 (2009).
[Crossref]

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

2008 (2)

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett. 100(10), 103906 (2008).
[Crossref]

C. Valentin, J. Gautier, J.-P. Goddet, C. Hauri, T. Marchenko, E. Papalazarou, G. Rey, S. Sebban, O. Scrick, P. Zeitoun, G. Dovillaire, X. Levecq, S. Bucourt, and M. Fajardo, “High-order harmonic wave fronts generated with controlled astigmatic infrared laser,” J. Opt. Soc. Am. B 25(7), B161–B166 (2008).
[Crossref]

2007 (3)

Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express 15(18), 11341–11357 (2007).
[Crossref]

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[Crossref]

T. Kanai, E. J. Takahashi, Y. Nabekawa, and K. Midorikawa, “Destructive interference during high harmonic generation in mixed gases,” Phys. Rev. Lett. 98(15), 153904 (2007).
[Crossref]

2006 (1)

C. Corsi, A. Pirri, E. Sali, A. Tortora, and M. Bellini, “Direct interferometric measurement of the atomic dipole phase in high-order harmonic generation,” Phys. Rev. Lett. 97(2), 023901 (2006).
[Crossref]

2005 (1)

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(3), 033905 (2005).
[Crossref]

2003 (2)

P. Tzallas, D. Charalambidis, N. A. Papadogiannis, K. Witte, and G. D. Tsakiris, “Direct observation of attosecond light bunching,” Nature 426(6964), 267–271 (2003).
[Crossref]

H. Mashiko, A. Suda, and K. Midorikawa, “All-reflective interferometric autocorrelator for the measurement of ultra-short optical pulses,” Appl. Phys. B 76(5), 525–530 (2003).
[Crossref]

2001 (1)

K. Tamasaku, Y. Tanaka, M. Yabashi, H. Yamazaki, N. Kawamura, M. Suzuki, and T. Ishikawa, “SPring-8 RIKEN beamline III for coherent X-ray optics,” Nucl. Instrum. Methods Phys. Res., Sect. A 467-468, 686–689 (2001).
[Crossref]

1999 (1)

P. Salières, L. L. Déroff, T. Auguste, P. Monot, P. d’Oliveira, D. Campo, J.-F. Hergott, H. Merdji, and B. Carré, “Frequency-domain interferometry in the XUV with high-order harmonics,” Phys. Rev. Lett. 83(26), 5483–5486 (1999).
[Crossref]

1994 (1)

1992 (1)

Abel, J. J.

Alj, D.

Allaria, E.

A. Wituschek, L. Bruder, E. Allaria, U. Bangert, M. Binz, R. Borghes, C. Callegari, G. Cerullo, P. Cinquegrana, L. Giannessi, M. Danailov, A. Demidovich, M. D. Fraia, M. Drabbels, R. Feifel, T. Laarmann, R. Michiels, N. S. Mirian, M. Mudrich, I. Nikolov, F. H. O’Shea, G. Penco, P. Piseri, O. Plekan, K. C. Prince, A. Przystawik, P. R. Ribič, G. Sansone, P. Sigalotti, S. Spampinati, C. Spezzani, R. J. Squibb, S. Stranges, D. Uhl, and F. Stienkemeier, “Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses,” Nat. Commun. 11(1), 883 (2020).
[Crossref]

Antonetti, A.

Arnold, C. L.

H. Wikmark, C. Guo, J. Vogelsang, P. W. Smorenburg, H. Coudert-Alteirac, J. Lahl, J. Peschel, P. Rudawski, H. Dacasa, S. Carlström, S. Maclot, M. B. Gaarde, P. Johnsson, C. L. Arnold, and A. L’Huillier, “Spatiotemporal coupling of attosecond pulses,” Proc. Natl. Acad. Sci. U. S. A. 116(11), 4779–4787 (2019).
[Crossref]

H. Dacasa, H. Coudert-Alteirac, C. Guo, E. Kueny, F. Campi, J. Lahl, J. Peschel, H. Wikmark, B. Major, E. Malm, D. Alj, K. Varjú, C. L. Arnold, G. Dovillaire, P. Johnsson, A. L’Huillier, S. Maclot, P. Rudawski, and P. Zeitoun, “Single-shot extreme-ultraviolet wavefront measurements of high-order harmonics,” Opt. Express 27(3), 2656–2670 (2019).
[Crossref]

Audebert, P.

Auguste, T.

P. Salières, L. L. Déroff, T. Auguste, P. Monot, P. d’Oliveira, D. Campo, J.-F. Hergott, H. Merdji, and B. Carré, “Frequency-domain interferometry in the XUV with high-order harmonics,” Phys. Rev. Lett. 83(26), 5483–5486 (1999).
[Crossref]

Azoury, D.

D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13(1), 54–59 (2019).
[Crossref]

Baksh, P.

H.-S. Kim, P. Baksh, M. Odstrcil, M. Miszczak, J. G. Frey, L. Juschkin, and W. S. Brocklesby, “Lloyd’s mirror interference lithography with EUV radiation from a high-harmonic source,” Appl. Phys. Express 9(7), 076701 (2016).
[Crossref]

Bangert, U.

A. Wituschek, L. Bruder, E. Allaria, U. Bangert, M. Binz, R. Borghes, C. Callegari, G. Cerullo, P. Cinquegrana, L. Giannessi, M. Danailov, A. Demidovich, M. D. Fraia, M. Drabbels, R. Feifel, T. Laarmann, R. Michiels, N. S. Mirian, M. Mudrich, I. Nikolov, F. H. O’Shea, G. Penco, P. Piseri, O. Plekan, K. C. Prince, A. Przystawik, P. R. Ribič, G. Sansone, P. Sigalotti, S. Spampinati, C. Spezzani, R. J. Squibb, S. Stranges, D. Uhl, and F. Stienkemeier, “Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses,” Nat. Commun. 11(1), 883 (2020).
[Crossref]

Becker, A.

M.-C. Chen, C. Mancuso, C. Hernández-García, F. Dollar, B. Galloway, D. Popmintchev, P.-C. Huang, B. Walker, L. Plaja, A. A. Jaroń-Becker, A. Becker, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Generation of bright isolated attosecond soft X-ray pulses driven by multi-cycle mid-infrared lasers,” Proc. Natl. Acad. Sci. U. S. A. 111(23), E2361–E2367 (2014).
[Crossref]

Bellini, M.

C. Corsi, A. Pirri, E. Sali, A. Tortora, and M. Bellini, “Direct interferometric measurement of the atomic dipole phase in high-order harmonic generation,” Phys. Rev. Lett. 97(2), 023901 (2006).
[Crossref]

Bertrand, J. B.

J. B. Bertrand, H. J. Wörner, P. Salières, D. M. Villeneuve, and P. B. Corkum, “Linked attosecond phase interferometry for molecular frame measurements,” Nat. Phys. 9(3), 174–178 (2013).
[Crossref]

Biedermann, J.

Binz, M.

A. Wituschek, L. Bruder, E. Allaria, U. Bangert, M. Binz, R. Borghes, C. Callegari, G. Cerullo, P. Cinquegrana, L. Giannessi, M. Danailov, A. Demidovich, M. D. Fraia, M. Drabbels, R. Feifel, T. Laarmann, R. Michiels, N. S. Mirian, M. Mudrich, I. Nikolov, F. H. O’Shea, G. Penco, P. Piseri, O. Plekan, K. C. Prince, A. Przystawik, P. R. Ribič, G. Sansone, P. Sigalotti, S. Spampinati, C. Spezzani, R. J. Squibb, S. Stranges, D. Uhl, and F. Stienkemeier, “Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses,” Nat. Commun. 11(1), 883 (2020).
[Crossref]

Borghes, R.

A. Wituschek, L. Bruder, E. Allaria, U. Bangert, M. Binz, R. Borghes, C. Callegari, G. Cerullo, P. Cinquegrana, L. Giannessi, M. Danailov, A. Demidovich, M. D. Fraia, M. Drabbels, R. Feifel, T. Laarmann, R. Michiels, N. S. Mirian, M. Mudrich, I. Nikolov, F. H. O’Shea, G. Penco, P. Piseri, O. Plekan, K. C. Prince, A. Przystawik, P. R. Ribič, G. Sansone, P. Sigalotti, S. Spampinati, C. Spezzani, R. J. Squibb, S. Stranges, D. Uhl, and F. Stienkemeier, “Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses,” Nat. Commun. 11(1), 883 (2020).
[Crossref]

Bourassin-Bouchet, C.

Brocklesby, W. S.

H.-S. Kim, P. Baksh, M. Odstrcil, M. Miszczak, J. G. Frey, L. Juschkin, and W. S. Brocklesby, “Lloyd’s mirror interference lithography with EUV radiation from a high-harmonic source,” Appl. Phys. Express 9(7), 076701 (2016).
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Figures (7)

Fig. 1.
Fig. 1. Schematic view of the spatially resolved phase interferometry setup with IAP. BSM: beam splitting mirror, which has a delay stage function and is equipped with a piezo-electric transducer with 1-nm distance resolution. Mo/Si: Mo/Si multilayer-coated spherical mirrors with curvature radiuses of 500 and 400 mm (10% reflectivity at 25–70 eV). Grating: XUV diffraction grating with 600 lines/mm. XCCD: X-ray CCD camera with 13.5-µm pixel resolution.
Fig. 2.
Fig. 2. Spatial-spectral interferograms with spatially split IAPs. (a) Measured and (b) calculated spatial-spectral interferograms over ±5-fs delay regions. The negative delay corresponds to IAP1 (top beam split by the BSM) later than IAP2 (bottom beam split by the BSM), and vice versa for the positive delay. The signal in (a) accumulates 30,000 laser shots each delay step, which is averaged for 30 measurements.
Fig. 3.
Fig. 3. Normalized intensity I(ω)/I0(ω) of spectral interferogram with IAP. Spectral interferograms I0(ω) and I(ω) correspond to zero delay and delays from −1 to −6 fs over photon energy regions of 32–38 eV, respectively. The maximum contrast ratio is approximately 70%.
Fig. 4.
Fig. 4. Spectral-delay interferogram with IAP. (a) Measured spectral-delay interferogram. The delay step is 12 as. The signal accumulates 6,000 laser shots each delay step, which is averaged for 17 measurements. The periodic temporal oscillations correspond to 103–159 as over the bandwidth of 26–40 eV. (b) Spectral-spectral interferogram after Fourier transformation for delay axis in (a). AC components appear in ±26–40-eV regions, in addition to the DC component around zero photon energy.
Fig. 5.
Fig. 5. Delay and beam position stabilities with IAP. (a) Measured spatial-spectral interferogram for a delay of −3.2 fs. (b) Top: lineout spectra integrated spatial area of ±13.5 µm in (a). The signal accumulates 3,000 laser shots every spectrum. Bottom: delay and relative phase jitters between IAPs extracted from the upper figure through the Fourier analysis. The root mean square (rms) values of the delay and relative phase jitter measured over 30 min. are 2.6-as and 172-mrad, respectively. (c) Top: beam profiles integrated photon energy regions over 36–50 eV in (a). The signal accumulates 3,000 laser shots in every profile, which is synchronized for taking data of (b). Bottom: Gaussian fitted peak value for beam profiles. The beam center position stability measured over 30 min corresponds to 0.2-µm rms.
Fig. 6.
Fig. 6. IAP spectrum and first-order interferometric autocorrelation. (a) The blue solid line shows the measured IAP spectrum at zero delay between IAPs. The Fourier-transform-limited pulse estimated from the spectrum has 257-as duration. (b) Measured first-order interferometric autocorrelation trace (red filled circles and solid line), which was observed without a diffraction grating. The delay step is 12 as. The inset shows the trace enlarged over the ±5-fs region. The blue dashed line is the spectrum reconstructed from (a) through inverse Fourier transformation. The estimated coherence time from the measured trace is 386 as. Error bars in (a) and (b) represent the root mean square (rms) over 15 measurements.
Fig. 7.
Fig. 7. Calculated spatial beam intensity profile and phase with spatially split IAPs. (a) Beam intensity profile of input IAPs (IAP1 for top beam and IAP2 for bottom beam). The (x1,y1) coordinate corresponds to the space on the first Mo/Si mirror after the BSM in the experiment. The input IAP beam radius (before beam splitting) was 563 µm. (b) Images of focused beam intensity profiles (left) and spatial phases (middle), which were numerically calculated based on diffraction theory [30]. The (x2,y2) coordinate corresponds to the space on the XCCD camera in the experiment. The image transfer of 8.5 times magnification is already considered for images of focused beam intensity profiles and spatial phases. The right graphs show lineout beam intensity profiles (red solid line) and spatial phases (blue dashed line) at the space x2=0 µm in left and middle images. The upper and lower images and graphs correspond to IAP1 (top beam) and IAP2 (bottom beam), respectively.

Equations (1)

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E ~ ( x 2 , y 2 , t ) = f ( t ) | U ~ 1 ( x 2 , y 2 ) | e i φ 1 ( x 2 , y 2 ) + f ( t τ ) | U ~ 2 ( x 2 , y 2 ) | e i φ 2 ( x 2 , y 2 ) e i Δ ϕ ,

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