Abstract

Advances in the generation of ultrashort laser pulses, and the emergence of new research areas such as attosecond science, nanoplasmonics, coherent control, and multidimensional spectroscopy, have led to the need for a new class of ultrafast metrology that can measure the electric field of complex optical waveforms spanning the ultraviolet to the infrared. Important examples of such waveforms are those produced by spectral control of ultrabroad bandwidth pulses, or by Fourier synthesis. These are typically tailored for specific purposes, such as to increase the photon energy and flux of high-harmonic radiation, or to control dynamical processes by steering electron dynamics on subcycle time scales. These applications demand a knowledge of the full temporal evolution of the field. Conventional pulse measurement techniques that provide estimates of the relative temporal or spectral phase are unsuited to measure such waveforms. Here we experimentally demonstrate a new, all-optical method for directly measuring the electric field of arbitrary ultrafast optical waveforms. Our method is based on high-harmonic generation (HHG) driven by a field that is the collinear superposition of the waveform to be measured with a stronger probe laser pulse. As the delay between the pulses is varied, we show that the field of the unknown waveform is mapped to energy shifts in the high-harmonic spectrum, allowing a direct, accurate, and rapid retrieval of the electric field with subcycle temporal resolution at the location of the HHG.

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  44. http://dx.doi.org/10.5287/bodleian:pv7DopPz7 .

2015 (4)

C.-S. Yang, C.-H. Lin, A. Zaytsev, K.-C. Teng, T.-H. Her, and C.-L. Pan, “Femtosecond laser ablation of polymethylmethacrylate via dual-color synthesized waveform,” Appl. Phys. Lett. 106, 051902 (2015).
[Crossref]

O. Mucke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kartner, “Toward waveform nonlinear optics using multimillijoule sub-cycle waveform synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015).
[Crossref]

T. Luu, M. Garg, S. Y. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521, 498–502 (2015).
[Crossref]

P. G. de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref]

2014 (1)

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zaïr, J. W. G. Tisch, J. P. Marangos, and L. E. Chipperfield, “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X 4, 021028 (2014).

2013 (2)

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

A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photon. Rev. 7, 385–407 (2013).
[Crossref]

2012 (4)

M. Miranda, C. L. Arnold, T. Fordell, F. Silva, B. Alonso, R. Weigand, A. L’Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the D-scan technique,” Opt. Express 20, 18732–18743 (2012).
[Crossref]

T. Witting, F. Frank, W. Okell, C. Arrell, J. Marangos, and J. Tisch, “Sub-4-fs laser pulse characterization by spatially resolved spectral shearing interferometry and attosecond streaking,” J. Phys. B 45, 074014 (2012).
[Crossref]

M. T. Hassan, A. Wirth, I. Grguraš, A. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, “Attosecond photonics: synthesis and control of light transients,” Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

F. Frank, C. Arrell, T. Witting, W. A. Okell, J. McKenna, J. S. Robinson, C. A. Haworth, D. Austin, H. Teng, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref]

2011 (4)

T. Witting, F. Frank, C. A. Arrell, W. A. Okell, J. P. Marangos, and J. W. Tisch, “Characterization of high-intensity sub-4-fs laser pulses using spatially encoded spectral shearing interferometry,” Opt. Lett. 36, 1680–1682 (2011).
[Crossref]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[Crossref]

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334, 195–200 (2011).
[Crossref]

H.-S. Chan, Z.-M. Hsieh, W.-H. Liang, A. Kung, C.-K. Lee, C.-J. Lai, R.-P. Pan, and L.-H. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331, 1165–1168 (2011).
[Crossref]

2010 (1)

2009 (5)

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
[Crossref]

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

L. Chipperfield, J. Robinson, J. Tisch, and J. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009).
[Crossref]

T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34, 881–883 (2009).
[Crossref]

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

2007 (1)

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. Tisch, “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nat. Phys. 3, 52–57 (2007).
[Crossref]

2006 (1)

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne mixing of laser fields for temporal gating of high-order harmonic generation,” Phys. Rev. Lett. 97, 163901 (2006).
[Crossref]

2005 (1)

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005).
[Crossref]

2004 (2)

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

V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29, 775–777 (2004).
[Crossref]

2003 (2)

D. Keusters, H.-S. Tan, P. O’Shea, E. Zeek, R. Trebino, and W. S. Warren, “Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components,” J. Opt. Soc. Am. B 20, 2226–2237 (2003).
[Crossref]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. 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]

2002 (3)

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

C. Dorrer and I. A. Walmsley, “Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction,” J. Opt. Soc. Am. B 19, 1019–1029 (2002).
[Crossref]

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[Crossref]

2001 (2)

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[Crossref]

R. J. Levis, G. M. Menkir, and H. Rabitz, “Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses,” Science 292, 709–713 (2001).
[Crossref]

1998 (3)

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
[Crossref]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[Crossref]

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

1996 (1)

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref]

1993 (1)

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

1992 (1)

E. Potter, J. Herek, S. Pedersen, Q. Liu, and A. Zewail, “Femtosecond laser control of a chemical reaction,” Nature 355, 66–68 (1992).
[Crossref]

1986 (1)

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541–546 (1986).
[Crossref]

1984 (1)

Abel, M. J.

T. Pfeifer, L. Gallmann, M. J. Abel, P. M. Nagel, D. M. Neumark, and S. R. Leone, “Heterodyne mixing of laser fields for temporal gating of high-order harmonic generation,” Phys. Rev. Lett. 97, 163901 (2006).
[Crossref]

Alahmed, Z. A.

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334, 195–200 (2011).
[Crossref]

Alonso, B.

Andriukaitis, G.

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zaïr, J. W. G. Tisch, J. P. Marangos, and L. E. Chipperfield, “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X 4, 021028 (2014).

Arnold, C. L.

Arrell, C.

T. Witting, F. Frank, W. Okell, C. Arrell, J. Marangos, and J. Tisch, “Sub-4-fs laser pulse characterization by spatially resolved spectral shearing interferometry and attosecond streaking,” J. Phys. B 45, 074014 (2012).
[Crossref]

F. Frank, C. Arrell, T. Witting, W. A. Okell, J. McKenna, J. S. Robinson, C. A. Haworth, D. Austin, H. Teng, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref]

Arrell, C. A.

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Austin, D.

F. Frank, C. Arrell, T. Witting, W. A. Okell, J. McKenna, J. S. Robinson, C. A. Haworth, D. Austin, H. Teng, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref]

Austin, D. R.

Azzeer, A. M.

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334, 195–200 (2011).
[Crossref]

Babushkin, I.

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Spielmann, C.

Squibb, R.

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zaïr, J. W. G. Tisch, J. P. Marangos, and L. E. Chipperfield, “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X 4, 021028 (2014).

Strehle, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[Crossref]

Suda, A.

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[Crossref]

Südmeyer, T.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Tamaki, Y.

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[Crossref]

Tan, H.-S.

Teng, H.

F. Frank, C. Arrell, T. Witting, W. A. Okell, J. McKenna, J. S. Robinson, C. A. Haworth, D. Austin, H. Teng, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref]

Teng, K.-C.

C.-S. Yang, C.-H. Lin, A. Zaytsev, K.-C. Teng, T.-H. Her, and C.-L. Pan, “Femtosecond laser ablation of polymethylmethacrylate via dual-color synthesized waveform,” Appl. Phys. Lett. 106, 051902 (2015).
[Crossref]

Tisch, J.

T. Witting, F. Frank, W. Okell, C. Arrell, J. Marangos, and J. Tisch, “Sub-4-fs laser pulse characterization by spatially resolved spectral shearing interferometry and attosecond streaking,” J. Phys. B 45, 074014 (2012).
[Crossref]

L. Chipperfield, J. Robinson, J. Tisch, and J. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009).
[Crossref]

Tisch, J. W.

T. Witting, F. Frank, C. A. Arrell, W. A. Okell, J. P. Marangos, and J. W. Tisch, “Characterization of high-intensity sub-4-fs laser pulses using spatially encoded spectral shearing interferometry,” Opt. Lett. 36, 1680–1682 (2011).
[Crossref]

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. Tisch, “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nat. Phys. 3, 52–57 (2007).
[Crossref]

Tisch, J. W. G.

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zaïr, J. W. G. Tisch, J. P. Marangos, and L. E. Chipperfield, “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X 4, 021028 (2014).

F. Frank, C. Arrell, T. Witting, W. A. Okell, J. McKenna, J. S. Robinson, C. A. Haworth, D. Austin, H. Teng, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref]

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

Travers, J. C.

Trebino, R.

D. Keusters, H.-S. Tan, P. O’Shea, E. Zeek, R. Trebino, and W. S. Warren, “Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components,” J. Opt. Soc. Am. B 20, 2226–2237 (2003).
[Crossref]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Udem, T.

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. 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]

Uiberacker, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. 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, Ch. 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]

Villeneuve, D.

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

Vorobyev, A. Y.

A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photon. Rev. 7, 385–407 (2013).
[Crossref]

Walmsley, I. A.

Warren, W. S.

Weigand, R.

Westerwalbesloh, Th.

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

Wirth, A.

M. T. Hassan, A. Wirth, I. Grguraš, A. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, “Attosecond photonics: synthesis and control of light transients,” Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334, 195–200 (2011).
[Crossref]

Witting, T.

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zaïr, J. W. G. Tisch, J. P. Marangos, and L. E. Chipperfield, “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X 4, 021028 (2014).

T. Witting, F. Frank, W. Okell, C. Arrell, J. Marangos, and J. Tisch, “Sub-4-fs laser pulse characterization by spatially resolved spectral shearing interferometry and attosecond streaking,” J. Phys. B 45, 074014 (2012).
[Crossref]

F. Frank, C. Arrell, T. Witting, W. A. Okell, J. McKenna, J. S. Robinson, C. A. Haworth, D. Austin, H. Teng, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref]

T. Witting, F. Frank, C. A. Arrell, W. A. Okell, J. P. Marangos, and J. W. Tisch, “Characterization of high-intensity sub-4-fs laser pulses using spatially encoded spectral shearing interferometry,” Opt. Lett. 36, 1680–1682 (2011).
[Crossref]

D. R. Austin, T. Witting, and I. A. Walmsley, “Resolution of the relative phase ambiguity in spectral shearing interferometry of ultrashort pulses,” Opt. Lett. 35, 1971–1973 (2010).
[Crossref]

T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34, 881–883 (2009).
[Crossref]

Wohlleben, W.

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[Crossref]

Xu, L.

Yakovlev, V.

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

Yakovlev, V. S.

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334, 195–200 (2011).
[Crossref]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. 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]

Yang, C.-S.

C.-S. Yang, C.-H. Lin, A. Zaytsev, K.-C. Teng, T.-H. Her, and C.-L. Pan, “Femtosecond laser ablation of polymethylmethacrylate via dual-color synthesized waveform,” Appl. Phys. Lett. 106, 051902 (2015).
[Crossref]

Yang, Y.

O. Mucke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kartner, “Toward waveform nonlinear optics using multimillijoule sub-cycle waveform synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015).
[Crossref]

Ye, H.

O. Mucke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kartner, “Toward waveform nonlinear optics using multimillijoule sub-cycle waveform synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015).
[Crossref]

Yudin, G. L.

J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
[Crossref]

Zaïr, A.

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zaïr, J. W. G. Tisch, J. P. Marangos, and L. E. Chipperfield, “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X 4, 021028 (2014).

Zaytsev, A.

C.-S. Yang, C.-H. Lin, A. Zaytsev, K.-C. Teng, T.-H. Her, and C.-L. Pan, “Femtosecond laser ablation of polymethylmethacrylate via dual-color synthesized waveform,” Appl. Phys. Lett. 106, 051902 (2015).
[Crossref]

Zeek, E.

Zeidler, D.

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[Crossref]

Zewail, A.

E. Potter, J. Herek, S. Pedersen, Q. Liu, and A. Zewail, “Femtosecond laser control of a chemical reaction,” Nature 355, 66–68 (1992).
[Crossref]

Zhang, C.

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

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. B (1)

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, “High harmonic generation in a gas-filled hollow-core photonic crystal fiber,” Appl. Phys. B 97, 369–373 (2009).
[Crossref]

Appl. Phys. Lett. (1)

C.-S. Yang, C.-H. Lin, A. Zaytsev, K.-C. Teng, T.-H. Her, and C.-L. Pan, “Femtosecond laser ablation of polymethylmethacrylate via dual-color synthesized waveform,” Appl. Phys. Lett. 106, 051902 (2015).
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Chem. Phys. Lett. (1)

P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541–546 (1986).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

O. Mucke, S. Fang, G. Cirmi, G. M. Rossi, S.-H. Chia, H. Ye, Y. Yang, R. Mainz, C. Manzoni, P. Farinello, G. Cerullo, and F. X. Kartner, “Toward waveform nonlinear optics using multimillijoule sub-cycle waveform synthesizers,” IEEE J. Sel. Top. Quantum Electron. 21, 8700712 (2015).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

T. Witting, F. Frank, W. Okell, C. Arrell, J. Marangos, and J. Tisch, “Sub-4-fs laser pulse characterization by spatially resolved spectral shearing interferometry and attosecond streaking,” J. Phys. B 45, 074014 (2012).
[Crossref]

Laser Photon. Rev. (1)

A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photon. Rev. 7, 385–407 (2013).
[Crossref]

Nat. Photonics (1)

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

Nat. Phys. (1)

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. Tisch, “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nat. Phys. 3, 52–57 (2007).
[Crossref]

Nature (4)

T. Luu, M. Garg, S. Y. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521, 498–502 (2015).
[Crossref]

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. 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]

E. Potter, J. Herek, S. Pedersen, Q. Liu, and A. Zewail, “Femtosecond laser control of a chemical reaction,” Nature 355, 66–68 (1992).
[Crossref]

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
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Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (3)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref]

Y. Mairesse and F. Quéré, “Frequency-resolved optical gating for complete reconstruction of attosecond bursts,” Phys. Rev. A 71, 011401 (2005).
[Crossref]

N. H. Shon, A. Suda, Y. Tamaki, and K. Midorikawa, “High-order harmonic and attosecond pulse generations: bulk media versus hollow waveguides,” Phys. Rev. A 63, 063806 (2001).
[Crossref]

Phys. Rev. Lett. (5)

L. Chipperfield, J. Robinson, J. Tisch, and J. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009).
[Crossref]

P. G. de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
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J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88, 173903 (2002).
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Phys. Rev. X (1)

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zaïr, J. W. G. Tisch, J. P. Marangos, and L. E. Chipperfield, “Optimization of quantum trajectories driven by strong-field waveforms,” Phys. Rev. X 4, 021028 (2014).

Rev. Mod. Phys. (1)

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

Rev. Sci. Instrum. (3)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

M. T. Hassan, A. Wirth, I. Grguraš, A. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, “Attosecond photonics: synthesis and control of light transients,” Rev. Sci. Instrum. 83, 111301 (2012).
[Crossref]

F. Frank, C. Arrell, T. Witting, W. A. Okell, J. McKenna, J. S. Robinson, C. A. Haworth, D. Austin, H. Teng, I. A. Walmsley, J. P. Marangos, and J. W. G. Tisch, “Invited review article: technology for attosecond science,” Rev. Sci. Instrum. 83, 071101 (2012).
[Crossref]

Science (6)

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

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334, 195–200 (2011).
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H.-S. Chan, Z.-M. Hsieh, W.-H. Liang, A. Kung, C.-K. Lee, C.-J. Lai, R.-P. Pan, and L.-H. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331, 1165–1168 (2011).
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A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
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R. J. Levis, G. M. Menkir, and H. Rabitz, “Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses,” Science 292, 709–713 (2001).
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A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
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Other (1)

http://dx.doi.org/10.5287/bodleian:pv7DopPz7 .

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Figures (7)

Fig. 1.
Fig. 1. Basic working principle of ARIES, demonstrated here by SFA calculations of HHG in Ne for a 3.5 fs probe pulse centered at a wavelength of 800 nm with a peak intensity of 5×1014  Wcm2, and a continuous-wave (CW) test waveform at 800 nm with a relative intensity Itp/Ipp=0.1%. (a) CEP-stabilized few-cycle probe pulse and (b) corresponding HHG spectrum. (c) Constructive interference with a CW test waveform and (d) resulting HHG spectrum. (e) Destructive interference with a CW test waveform and (f) resulting HHG spectrum. The same probe pulse (blue) was used in (a)–(f); the test waveform (red) in (c) and (e) has been magnified by a factor of 5× for clarity. In (b), (d), and (f), the spectral positions of the cutoff (dotted vertical lines) are calculated by using the corresponding shaded regions (black, probe only; red, constructive interference; blue, destructive interference). (g) Simulated ARIES scan for a complex test waveform that comprises a linearly chirped section with a frequency sweep from ωtp=0.05ωpp1.0ωpp and a sawtooth section of frequency ωtp=0.5ωpp. Only the scan near the cut-off region is shown. The HHG spectrum as a function of delay between the probe and test pulses shows modulations of the cut-off that accurately map the TP electric-field waveform (dotted black curve, scaled in amplitude to match the maximum cut-off shift).
Fig. 2.
Fig. 2. Experimental apparatus used for demonstrating ARIES. (a) Setup used for electric-field measurements of 800 nm TPs. The PP and TP are produced in a Mach–Zehnder interferometer by injecting CEP-stable, few-cycle pulses from an amplified Ti:sapphire laser system with hollow core fiber (HCF) and chirped mirror compressor (Comp). Beam splitters BS1 and BS2 are 10% reflective. The adjustable iris (I) in the TP arm is used to control the TP intensity, and the fused silica wedges (W) in the TP arm are used to control the TP CEP and chirp. A delay stage in the PP arm is used to control the relative delay, τ, between the pulses. After the Mach–Zehnder interferometer, the collinear beams are sent into a HHG chamber, where they are focused into a gas jet (GJ). The generated harmonics are spectrally analyzed in an XUV spectrometer that uses a flat-field grating (G). The HHG spectrum is detected on a microchannel plate detector (MCP) readout by a CCD camera. (b) Setup used for electric-field measurements of 400 nm TPs. A portion of the laser pulse is split off at beam splitter BS before the HCF, and used to generate a second-harmonic TP in a BBO SHG crystal. The polarization of the second-harmonic pulse is rotated by 90° with a half-wave plate and combined with the few-cycle PP at a dichroic beam combiner (BC). Due to the long path length in this setup, the relative delay was actively stabilized.
Fig. 3.
Fig. 3. ARIES measurements of few-cycle TP waveforms with varying CEP, demonstrating its field sensitivity. (a), (c), (e), (g), and (i) are measured ARIES scans for five different TP CEP values spanning a range of 2π. The black lines are the center of masses of the HHG cutoff as a function of delay. The corresponding field retrievals are replotted in (b), (d), (f), (h), and (j) as thick blue curves with the pulse envelopes plotted as dotted red lines. (k) Retrieved TP CEP values (blue circles) as a function of fused silica insertion obtained over a larger wedge scan range corresponding to 8π CEP phase variation. The solid line is a linear fit to the data points, with the shaded red region marking the 95% confidence interval. The CEP is defined as the mean wavelength times the temporal difference between the peak of the electric field and peak of the pulse envelope. The green points mark the wedge positions of the waveforms plotted in (b), (d), (f), (h), and (j); the retrieved CEP values are 0.2π, 0.5π, 1.2π, 1.4π, and 1.8π, respectively.
Fig. 4.
Fig. 4. (a) Retrieved waveforms for long-range TP wedge scan. The colors of the curves are related to the instantaneous frequency to show the pulse chirp (red corresponding to lower frequencies, blue to higher frequencies). The fused silica insertions relative to the zero dispersion wedge position are (I) 0.3 mm, (II) 0.15 mm, (III) 0 mm, (IV) 0.15  mm, (V) 0.3  mm, (VI) 0.45  mm, (VII) 0.6  mm, and (VIII) 0.75  mm. (b) Spectral phase curves for the retrieved waveforms minus the spectral phase of the near-Fourier-limited pulse corresponding to (I) to (VIII), in same order as in (a). The curves have been offset for clarity. The dashed lines are the calculated phase curves from the known fused silica insertion. (c) The thin red curve is the average of the waveforms in (a), after numerical compensation of the known dispersion. The shaded region represents the mean ±1 standard deviation. (d) Retrieved TP spectrum from ARIES (filled red line) and TP spectrum measured using SEA-F-SPIDER (dashed magenta curve).
Fig. 5.
Fig. 5. ARIES measurement of a UV second-harmonic TP with a center wavelength of 400  nm. (a) The retrieved TP waveform (blue curve) and the PP waveform measured by SPIDER (red curve). (b) Magnified view of the central portion of (a). (c) Retrieved TP spectrum (blue curve) and the TP spectrum measured by a spectrometer (magenta dashed curve).
Fig. 6.
Fig. 6. ARIES amplitude response (i.e., maximum cut-off energy shift) for a 5×1014  Wcm2, 3.5 fs, 800 nm probe pulse and CW test waveform with Itp/Ipp=0.1% as a function of the TP frequency. Filled blue curve: response calculated from SFA simulations. Red curve: response calculated from numerically integrating the classical equation of motion [Eq. (1)]. Dotted green curve: classical approximation given by [Eq. (4)]. The right vertical axis shows the absolute shift in photon energy; the left vertical axis shows the relative response scaled to unity for the SFA simulations at ωtp=ωpp. The PP spectrum is shown by the gray-filled dashed black curve.
Fig. 7.
Fig. 7. SFA simulations of ARIES using multicycle PPs. The PPs are centered at wavelength of 800 nm with peak intensity fixed at 5×1014  Wcm2. The positively chirped TP is 7.7 fs in duration and centered at 800 nm, with peak intensity 0.1% of the PP. ARIES traces for (a) a 4 fs and (b) a 24 fs PP. (c),(d) ARIES reconstructions of the TP electric field (black points) compared to the TP field used in the calculation (red lines) corresponding to (a) and (b), respectively. (e) ARIES reconstruction error as a function of PP pulse duration (see text for details).

Equations (6)

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v=emtitr(Epp(t)+Etp(tτ))dt=vpp+vtp,
ϵ=12m(vpp+vtp)212mvpp2+mvppvtp,
ΔϵmaxmvppvtpE^ppE^tpωppωtp,
Δϵmax2ϵpp(max)E^tpE^ppωppωtp.
Δϵmax/eV4ϵpp(max)/eV(λtp/μm)(E^tp/(V/Å)),
σϵmax(CEP)ϵmax4ln2N/2(σCEPωppτpp)2,

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