Abstract

Temporal characterization of a laser pulse is an essential task in many applications. Temporal characterization methods that are currently available support only a limited spectral bandwidth without information on the carrier-envelope phase (CEP) of the laser pulse or require complicated equipment in a vacuum environment. Here we demonstrate that an arbitrary time-dependent laser field can be directly sampled using subcycle tunneling ionization in a gaseous medium or in air. The subcycle ionization is used as a fast temporal gate for the direct sampling of the laser field. This unique approach enables the complete temporal characterization of the laser field, including its CEP, for a broad spectral range in ambient air, providing a universal tool for the precise measurement of the laser field.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. Z. Chen, Y. Liang, D. H. Madison, and C. D. Lin, “Strong-field nonsequential double ionization of Ar and Ne,” Phys. Rev. A 84, 023414 (2011).
    [Crossref]
  25. W. P. Putnam, R. G. Hobbs, P. D. Keathley, K. K. Berggren, and F. X. Kärtner, “Optical-field-controlled photoemission from plasmonic nanoparticles,” Nat. Phys. 13, 335–339 (2017).
    [Crossref]
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    [Crossref]

2017 (2)

W. P. Putnam, R. G. Hobbs, P. D. Keathley, K. K. Berggren, and F. X. Kärtner, “Optical-field-controlled photoemission from plasmonic nanoparticles,” Nat. Phys. 13, 335–339 (2017).
[Crossref]

K. T. Kim, K. Kim, and T. J. Hammond, “Phase retrieval approach for an accurate reconstruction of an arbitrary optical waveform in the petahertz optical oscilloscope,” J. Phys. B 50, 024002 (2017).
[Crossref]

2016 (2)

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref]

A. S. Wyatt, T. Witting, A. Schiavi, D. Fabris, P. Matia-Hernando, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Attosecond sampling of arbitrary optical waveforms,” Optica 3, 303–310 (2016).
[Crossref]

2014 (3)

I. A. Ivanov, “Evolution of the transverse photoelectron-momentum distribution for atomic ionization driven by a laser pulse with varying ellipticity,” Phys. Rev. A 90, 013418 (2014).
[Crossref]

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8, 178–186 (2014).
[Crossref]

F. Krausz and M. I. Stockman, “Attosecond metrology: From electron capture to future signal processing,” Nat. Photonics 8, 205–213 (2014).
[Crossref]

2013 (3)

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493, 70–74 (2013).
[Crossref]

K. T. Kim, C. Zhang, A. D. Shiner, B. E. Schmidt, F. Légaré, D. M. Villeneuve, and P. B. Corkum, “Petahertz optical oscilloscope,” Nat. Photonics 7, 958–962 (2013).
[Crossref]

2012 (1)

2011 (1)

Z. Chen, Y. Liang, D. H. Madison, and C. D. Lin, “Strong-field nonsequential double ionization of Ar and Ne,” Phys. Rev. A 84, 023414 (2011).
[Crossref]

2007 (1)

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

2004 (2)

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys.-Usp. 47, 855–885 (2004).
[Crossref]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref]

2003 (1)

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

2001 (2)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref]

1998 (1)

1994 (1)

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref]

1993 (2)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[Crossref]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

1982 (1)

A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions formed by multiphoton absorption processes in the continuum,” Phys. Rev. Lett. 48, 1814–1817 (1982).
[Crossref]

1966 (1)

A. M. Perelemov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307 (1965).

Agostini, P.

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref]

Alonso, B.

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

Apalkov, V.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493, 70–74 (2013).
[Crossref]

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Apolonski, A.

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

Arnold, C. L.

Baltuska, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref]

Baltuška, A.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

Barth, J. V.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493, 70–74 (2013).
[Crossref]

Berggren, K. K.

W. P. Putnam, R. G. Hobbs, P. D. Keathley, K. K. Berggren, and F. X. Kärtner, “Optical-field-controlled photoemission from plasmonic nanoparticles,” Nat. Phys. 13, 335–339 (2017).
[Crossref]

Bothschafter, E. M.

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref]

Cavalieri, A. L.

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

Chang, Z.

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8, 178–186 (2014).
[Crossref]

Chen, Z.

Z. Chen, Y. Liang, D. H. Madison, and C. D. Lin, “Strong-field nonsequential double ionization of Ar and Ne,” Phys. Rev. A 84, 023414 (2011).
[Crossref]

Chini, M.

M. Chini, K. Zhao, and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses,” Nat. Photonics 8, 178–186 (2014).
[Crossref]

Corkum, P.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref]

Corkum, P. B.

K. T. Kim, C. Zhang, A. D. Shiner, B. E. Schmidt, F. Légaré, D. M. Villeneuve, and P. B. Corkum, “Petahertz optical oscilloscope,” Nat. Photonics 7, 958–962 (2013).
[Crossref]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref]

Crespo, H.

De Silvestri, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

DiMauro, L. F.

B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, “Precision measurement of strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref]

Drescher, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref]

Ernstorfer, R.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493, 70–74 (2013).
[Crossref]

Fabris, D.

Fiess, M.

M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Fordell, T.

Garg, M.

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref]

Gerster, D.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature 493, 70–74 (2013).
[Crossref]

Gohle, C.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

Goulielmakis, E.

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref]

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

Grasbon, F.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref]

Guggenmos, A.

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref]

Hammond, T. J.

K. T. Kim, K. Kim, and T. J. Hammond, “Phase retrieval approach for an accurate reconstruction of an arbitrary optical waveform in the petahertz optical oscilloscope,” J. Phys. B 50, 024002 (2017).
[Crossref]

Hänsch, T. W.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

Heinzmann, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305, 1267–1269 (2004).
[Crossref]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref]

Hentschel, M.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001).
[Crossref]

Hobbs, R. G.

W. P. Putnam, R. G. Hobbs, P. D. Keathley, K. K. Berggren, and F. X. Kärtner, “Optical-field-controlled photoemission from plasmonic nanoparticles,” Nat. Phys. 13, 335–339 (2017).
[Crossref]

Hofstetter, M.

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. (a) Tunneling ionization is illustrated. The part of the wavefunction (blue line) tunnels through the deformed potential barrier (red line). (b) The instantaneous ionization rate w(t) (blue line) and its derivative with respect to the field strength w(t)=dw/dE|E=EF(t) (dotted line) calculated using the ADK ionization model for a He atom are shown. The fundamental laser pulse (center wavelength: 800 nm, duration: 3.9 fs in the FWHM, peak intensity: 1×1014  W/cm2) used in the calculations is shown with the red line. (c) The numeral calculations were performed using the TDSE model in 3D. The fundamental pulse shown in (b) and the broadband signal pulse (blue line) were used in the calculation. The modulation of the ionization yield δN/N0 obtained by solving the TDSE calculations is shown (red line). The modulation amplitude of the ionization yield for the same signal intensity is different for different wavelengths, as shown with the dashed line in (d). The modulation, after calibrating the spectral response (see Section S1.3 of Supplement 1), is shown as the green line. (d) The spectral amplitude (thick lines) and phase (thin lines) of the original (blue) and the calculated (red) pulses from the modulation of the ionization yield are shown. The spectral response of the TIPTOE measurement is shown with the dashed line (see Section S1.3 of Supplement 1).
Fig. 2.
Fig. 2. Incident laser pulse is separated into two pulses: the fundamental pulse EF and the signal pulse ES. The fundamental pulse is divided into two identical pulses again by a beam splitter (BS2). One of these components is superposed with the signal pulse by another beam splitter (BS3). A part of the fundamental (730 nm, 5 fs pulses) or second-harmonic (355 nm) pulse can be selected as a signal pulse since the pulses are temporally separated. In the reference channel, the ionization yield N0 is measured using only the fundamental pulse. In the signal channel, the ionization yield N0+δN is measured using the fundamental and signal pulses. The details of the setup are provided in Section 4 (Methods).
Fig. 3.
Fig. 3. (a), (b) ADK ionization rates calculated for Ar atoms using a 5 fs Gaussian (a) cosine or (b) sine pulse with an intensity of 1×1014  W/cm2. The ionization rates obtained only with the fundamental field EF are represented by solid red lines, while those obtained with the fundamental field EF and the second-harmonic signal field ES are shown with solid blue lines. In each case, the intensity of the second-harmonic field was 0.1% of the intensity of the fundamental field. (c) Results of ab initio calculations performed using the fundamental and second-harmonic signal pulses and different fundamental pulse CEPs ϕFCEP. (d) Experimentally obtained total ionization yields corresponding to different CEPs. The ionization yields from Ar atoms (5 mbar) were obtained using the fundamental pulse (duration: 5 fs, center wavelength: 730 nm, peak intensity: 1×1014  W/cm2) and the second-harmonic signal pulse (duration: 100  fs, center wavelength: 355 nm). Nine cases corresponding to fundamental pulse CEPs ranging from 1.60π to 2.43π are represented by solid lines. The depicted ionization yields were obtained after narrow bandpass filtering (solid lines) and low-pass filtering (dots). (e) Comparison of the amplitude modulation results of the ab initio calculations (red line) and the experiments (blue boxes) for different CEPs.
Fig. 4.
Fig. 4. Experiments were performed with few-cycle laser pulses. The intensity of the fundamental pulse was 1×1014  W/cm2. The signal intensity was 1×1011  W/cm2. The modulation of the ionization yield was obtained in the Ar-filled chamber (5 mar). (a) Signal pulse measurements for different CEPs ϕSCEP are shown. The color code shows the modulation of the ionization yield. (b), (c) The experimental data (δN/N0) for cosine (b) and sine (c) signal pulses are shown (dots). The signal pulses (solid lines) and their envelopes (dashed lines) obtained after the spectral filtering from 500 nm to 1 μm are shown.
Fig. 5.
Fig. 5. (a)–(c) TIPTOE and petahertz optical oscilloscope (PO) measurements for signal pulses with different chirp conditions. In the TIPTOE measurements, the ionization yield from Xe atoms (5 mbar) was measured using the fundamental pulse (duration: 5 fs, center wavelength: 730 nm, intensity: 3×1013  W/cm2). The dispersion of the signal pulse was controlled using a glass wedge to obtain (a) positively chirped, (b) chirp-free, and (c) negatively chirped pulses. The color plot at the top of each panel shows the spatial distribution of the harmonic radiation measured in the PO. In each case, the signal pulse was estimated based on the modulation of the spatial distribution. The signal electric fields measured using the PO method ESPO (τ) are shown with blue lines in (a)–(c), while those obtained using the TIPTOE method δN/N0 are represented by red lines. The spectral filtering was applied to both the PO and TIPTOE results from 500 nm to 1 μm. (d)–(f) Spectral amplitudes (lower lines) and phases (upper lines) acquired using the PO (blue lines) and TIPTOE (red lines) methods for (d) positively chirped, (e) chirp-free, and (f) negatively chirped pulses. The spectral amplitudes measured with a grating-based optical spectrometer are shown with black lines for comparison in (d)–(f). The phase modulation caused by the chirp mirrors is marked with red arrows in (e).
Fig. 6.
Fig. 6. (a) GDDs obtained for different glass thicknesses in air (blue) and in Ar (red) are shown. (b) The temporal profiles obtained at the chirp-free cases [marked with the arrows in (a)] for 1 bar air (blue) and 5 mbar Ar (red) are compared. (c) The spectral amplitudes for the pulses shown in (b) are shown for 1 bar air (thick blue) and 5 mbar Ar (thick red). The spectral amplitude measured with a spectrometer is shown (thick black). The spectral phases are shown for air (thin blue) and Ar (thin red). The spectral filtering is applied from 500 nm to 1 μm.

Equations (2)

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δN(τ)m=,1,0,1,amES(τ+mTF2).
δN(τ)ES(τ).

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