Abstract

We propose a simple and efficient method to optimize two-color chirped laser pulses by forming a “temporal gate” for the generation of isolated attosecond pulses (IAPs) in soft X rays. We show that the generation process for higher and cutoff harmonics can be effectively limited within the temporal gate, and the harmonic emission interval can be further reduced with the help of phase-matching by only selecting the contribution from short-trajectory electrons. This two-color gating mechanism is verified by increasing the pulse duration, raising the gas pressure, and extending the target cutoff. Compared to the five-color waveform in Phys. Rev. Lett. 102, 063003 (2009) [CrossRef]  , our waveform can be used to generate the IAP in the long-duration laser pulse while the cutoff energy is higher without the reduction of harmonic yields. Our work provides an alternative temporal gating scheme for the generation of IAPs by simultaneously improving the harmonic conversion efficiency, thus making the attosecond soft X rays an intense and highly time-resolved tabletop light source for future applications.

© 2019 Chinese Laser Press

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2019 (2)

2018 (9)

Z. Chang, “Attosecond chirp compensation in water window by plasma dispersion,” Opt. Express 26, 33238–33244 (2018).
[Crossref]

M. Wendl, M. Högner, and H. Fattahi, “Theoretical study: high harmonic generation by light transients,” Appl. Sci. 8, 728 (2018).
[Crossref]

E. Neyra, F. Videla, M. F. Ciappina, J. A. Pérez-Hernández, L. Roso, and G. A. Torchia, “Synthesis of ultrashort laser pulses for high-order harmonic generation,” Phys. Rev. A 98, 013403 (2018).
[Crossref]

C. Jin and C. D. Lin, “Control of soft X-ray high harmonic spectrum by using two-color laser pulses,” Photon. Res. 6, 434–442 (2018).
[Crossref]

C. D. Lin, A. T. Le, C. Jin, and H. Wei, “Elements of the quantitative rescattering theory,” J. Phys. B 51, 104001 (2018).
[Crossref]

D. Peng, M. V. Frolov, L.-W. Pi, and A. F. Starace, “Enhancing high-order harmonic generation by sculpting waveforms with chirp,” Phys. Rev. A 97, 053414 (2018).
[Crossref]

A. S. Johnson, D. R. Austin, D. A. Wood, C. Brahms, A. Gregory, K. B. Holzner, S. Jarosch, E. W. Larsen, S. Parker, C. S. Strüber, P. Ye, J. W. G. Tisch, and J. P. Marangos, “High-flux soft X-ray harmonic generation from ionization-shaped few-cycle laser pulses,” Sci. Adv. 4, eaar3761 (2018).
[Crossref]

X. Ren, J. Li, Y. Yin, K. Zhao, A. Chew, Y. Wang, S. Hu, Y. Cheng, E. Cunningham, Y. Wu, M. Chini, and Z. Chang, “Attosecond light sources in the water window,” J. Opt. 20, 023001 (2018).
[Crossref]

Z. Hong, S. A. Rezvani, Q. Zhang, and P. Lu, “Ultrafast mid-IR laser pulses generation via chirp manipulated optical parametric amplification,” Appl. Sci. 8, 744 (2018).
[Crossref]

2017 (5)

2016 (6)

C. Jin and C. D. Lin, “Optimization of multi-color laser waveform for high-order harmonic generation,” Chin. Phys. B 25, 094213 (2016).
[Crossref]

S. M. Teichmann, F. Silva, S. L. Cousin, M. Hemmer, and J. Biegert, “0.5-keV soft X-ray attosecond continua,” Nat. Commun. 7, 11493 (2016).
[Crossref]

F. Calegari, G. Sansone, S. Stagira, C. Vozzi, and M. Nisoli, “Advances in attosecond science,” J. Phys. B 49, 062001 (2016).
[Crossref]

F. Krausz, “The birth of attosecond physics and its coming of age,” Phys. Scr. 91, 063011 (2016).
[Crossref]

B. Bódi, E. Balogh, V. Tosa, E. Goulielmakis, K. Varjú, and P. Dombi, “Attosecond pulse generation with an optimization loop in a light-field-synthesizer,” Opt. Express 24, 21957–21962 (2016).
[Crossref]

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
[Crossref]

2015 (3)

C. Jin, K.-H. Hong, and C. D. Lin, “Optimal generation of high harmonics in the water-window region by synthesizing 800-nm and mid-infrared laser pulses,” Opt. Lett. 40, 3754–3757 (2015).
[Crossref]

L.-Y. Peng, W.-C. Jiang, J.-W. Geng, W.-H. Xiong, and Q. Gong, “Tracing and controlling electronic dynamics in atoms and molecules by attosecond pulses,” Phys. Rep. 575, 1–71 (2015).
[Crossref]

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6, 6611 (2015).
[Crossref]

2014 (11)

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

C. Jin, G. Wang, H. Wei, A. T. Le, and C. D. Lin, “Waveforms for optimal sub-keV high-order harmonics with synthesized two- or three-colour laser fields,” Nat. Commun. 5, 4003 (2014).
[Crossref]

E. Balogh, B. Bódi, V. Tosa, E. Goulielmakis, K. Varjú, and P. Dombi, “Genetic optimization of attosecond-pulse generation in light-field synthesizers,” Phys. Rev. A 90, 023855 (2014).
[Crossref]

C.-H. Lu, Y.-J. Tsou, H.-Y. Chen, B.-H. Chen, Y.-C. Cheng, S.-D. Yang, M.-C. Chen, C.-C. Hsu, and A. H. Kung, “Generation of intense supercontinuum in condensed media,” Optica 1, 400–406 (2014).
[Crossref]

K.-H. Hong, C.-J. Lai, J. P. Siqueira, P. Krogen, J. Moses, C.-L. Chang, G. J. Stein, L. E. Zapata, and F. X. Kätner, “Multi-mJ, kHz, 2.1  μm optical parametric chirped-pulse amplifier and high-flux soft X-ray high-harmonic generation,” Opt. Lett. 39, 3145–3148 (2014).
[Crossref]

S. L. Cousin, F. Silva, S. Teichmann, M. Hemmer, B. Buades, and J. Biegert, “High-flux table–top soft X-ray source driven by sub-2-cycle, CEP stable, 1.85-μm 1-kHz pulses for carbon K-edge spectroscopy,” Opt. Lett. 39, 5383–5386 (2014).
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J. Solanpää, J. A. Budagosky, N. I. Shvetsov-Shilovski, A. Castro, A. Rubio, and E. Räsänen, “Optimal control of high-harmonic generation by intense few-cycle pulses,” Phys. Rev. A 90, 053402 (2014).
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C. Jin, G. Wang, A. T. Le, and C. D. Lin, “Route to optimal generation of soft X-ray high harmonics with synthesized two-color laser pulses,” Sci. Rep. 4, 7067 (2014).
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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).
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X. Wang, C. Jin, and C. D. Lin, “Coherent control of high-harmonic generation using waveform-synthesized chirped laser fields,” Phys. Rev. A 90, 023416 (2014).
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Q. Zhang, L. He, P. Lan, and P. Lu, “Shaped multi-cycle two-color laser field for generating an intense isolated XUV pulse toward 100 attoseconds,” Opt. Express 22, 13213–13233 (2014).
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2013 (2)

E. J. Takahashi, P. Lan, O. D. Mücke, Y. Nabekawa, and K. Midorikawa, “Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses,” Nat. Commun. 4, 2691 (2013).
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P. Wei, J. Miao, Z. Zeng, C. Li, X. Ge, R. Li, and Z. Xu, “Selective enhancement of a single harmonic emission in a driving laser field with subcycle waveform control,” Phys. Rev. Lett. 110, 233903 (2013).
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2012 (2)

K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37, 3891–3893 (2012).
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T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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2011 (7)

A. Wirth, M. T. 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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S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011).
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L. Feng and T. Chu, “Generation of an isolated sub-40-as pulse using two-color laser pulses: combined chirp effects,” Phys. Rev. A 84, 053853 (2011).
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H. Du and B. Hu, “Propagation effects of isolated attosecond pulse generation with a multicycle chirped and chirped-free two-color field,” Phys. Rev. A 84, 023817 (2011).
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C. Jin, A. T. Le, and C. D. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N2,” Phys. Rev. A 83, 023411 (2011).
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H.-S. Chan, Z.-M. Hsieh, W.-H. Liang, A. H. 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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C. Jin, A. T. Le, C. A. Trallero-Herrero, and C. D. Lin, “Generation of isolated attosecond pulses in the far field by spatial filtering with an intense few-cycle mid-infrared laser,” Phys. Rev. A 84, 043411 (2011).
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2010 (2)

J. Xu, B. Zeng, and Y. Yu, “Extension of harmonic cutoff in a multicycle chirped pulse combined with a chirp-free pulse,” Phys. Rev. A 82, 053822 (2010).
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J. Wu, G.-T. Zhang, C.-L. Xia, and X.-S. Liu, “Control of the high-order harmonics cutoff and attosecond pulse generation through the combination of a chirped fundamental laser and a subharmonic laser field,” Phys. Rev. A 82, 013411 (2010).
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2009 (6)

Y. Niu, Y. Xiang, Y. Qi, and S. Gong, “Single attosecond pulse generation from multicycle nonlinear chirped pulses,” Phys. Rev. A 80, 063818 (2009).
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A.-T. Le, R. R. Lucchese, S. Tonzani, T. Morishita, and C. D. Lin, “Quantitative rescattering theory for high-order harmonic generation from molecules,” Phys. Rev. A 80, 013401 (2009).
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P.-C. Li, X.-X. Zhou, G.-L. Wang, and Z.-X. Zhao, “Isolated sub-30-as pulse generation of an He+ ion by an intense few-cycle chirped laser and its high-order harmonic pulses,” Phys. Rev. A 80, 053825 (2009).
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L. E. Chipperfield, J. S. Robinson, J. W. G. Tisch, and J. P. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009).
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A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103, 073902 (2009).
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F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
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2008 (4)

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, 103906 (2008).
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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).
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M. V. Frolov, N. L. Manakov, and A. F. Starace, “Wavelength scaling of high-harmonic yield: threshold phenomena and bound state symmetry dependence,” Phys. Rev. Lett. 100, 173001 (2008).
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M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B 41, 132001 (2008).
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2007 (3)

V. S. Yakovlev, M. Ivanov, and F. Krausz, “Enhanced phase-matching for generation of soft X-ray harmonics and attosecond pulses in atomic gases,” Opt. Express 15, 15351–15364 (2007).
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J. J. Carrera and S.-I. Chu, “Extension of high-order harmonic generation cutoff via coherent control of intense few-cycle chirped laser pulses,” Phys. Rev. A 75, 033807 (2007).
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J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. Di Mauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007).
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2006 (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).
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2005 (3)

V. Tosa, H. T. Kim, I. J. Kim, and C. H. Nam, “High-order harmonic generation by chirped and self-guided femtosecond laser pulses. I. Spatial and spectral analysis,” Phys. Rev. A 71, 063807 (2005).
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X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38, 2593–2600 (2005).
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R. López-Martens, K. Varjú, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salières, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C.-G. Wahlström, and A. L’Huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94, 033001 (2005).
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2001 (3)

M. B. Gaarde, “Time-frequency representations of high order harmonics,” Opt. Express 8, 529–536 (2001).
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D. G. Lee, J.-H. Kim, K.-H. Hong, and C. H. Nam, “Coherent control of high-order harmonics with chirped femtosecond laser pulses,” Phys. Rev. Lett. 87, 243902 (2001).
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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).
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2000 (2)

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
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X. M. Tong and S.-I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61, 021802 (2000).
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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).
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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).

Agostini, P.

J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. Di Mauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007).
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Alahmed, Z. A.

A. Wirth, M. T. 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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Alisauskas, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Altucci, C.

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).
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E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
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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).

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).
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T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Aquila, A. L.

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).
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Ardana-Lamas, F.

Arpin, P.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Attwood, D. T.

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).
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Auguste, T.

J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. Di Mauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007).
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A. S. Johnson, D. R. Austin, D. A. Wood, C. Brahms, A. Gregory, K. B. Holzner, S. Jarosch, E. W. Larsen, S. Parker, C. S. Strüber, P. Ye, J. W. G. Tisch, and J. P. Marangos, “High-flux soft X-ray harmonic generation from ionization-shaped few-cycle laser pulses,” Sci. Adv. 4, eaar3761 (2018).
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Avaldi, L.

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).
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Azzeer, A. M.

A. Wirth, M. T. 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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Balciunas, 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).
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T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Balcou, P.

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).
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Balogh, E.

B. Bódi, E. Balogh, V. Tosa, E. Goulielmakis, K. Varjú, and P. Dombi, “Attosecond pulse generation with an optimization loop in a light-field-synthesizer,” Opt. Express 24, 21957–21962 (2016).
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E. Balogh, B. Bódi, V. Tosa, E. Goulielmakis, K. Varjú, and P. Dombi, “Genetic optimization of attosecond-pulse generation in light-field synthesizers,” Phys. Rev. A 90, 023855 (2014).
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Baltuska, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Baltuška, 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).
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Bandulet, H.-C.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103, 073902 (2009).
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Baykusheva, D.

Y. Pertot, C. Schmidt, M. Matthews, A. Chauvet, M. Huppert, V. Svoboda, A. von Conta, A. Tehlar, D. Baykusheva, J.-P. Wolf, and H. J. Wörner, “Time-resolved X-ray absorption spectroscopy with a water window high-harmonic source,” Science 355, 264–267 (2017).
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Becker, A.

C. Hernández-García, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, L. Plaja, A. Becker, and A. Jaron-Becker, “Isolated broadband attosecond pulse generation with near- and mid-infrared driver pulses via time-gated phase matching,” Opt. Express 25, 11855–11866 (2017).
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M.-C. Chen, C. Mancuso, C. Hernández-García, F. Dollar, B. Galloway, D. Popmintchev, P.-C. Huang, B. Walker, L. Plaja, A. A. Jaron-Becker, A. Becker, M. M. Murnane, H. C. Kapteyn, and T. Popmintchev, “Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers,” Proc. Natl. Acad. Sci. USA 111, E2361–E2367 (2014).
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T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Benedetti, E.

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).
[Crossref]

Bergues, B.

Bhardwaj, S.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011).
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Biegert, J.

S. M. Teichmann, F. Silva, S. L. Cousin, M. Hemmer, and J. Biegert, “0.5-keV soft X-ray attosecond continua,” Nat. Commun. 7, 11493 (2016).
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F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6, 6611 (2015).
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S. L. Cousin, F. Silva, S. Teichmann, M. Hemmer, B. Buades, and J. Biegert, “High-flux table–top soft X-ray source driven by sub-2-cycle, CEP stable, 1.85-μm 1-kHz pulses for carbon K-edge spectroscopy,” Opt. Lett. 39, 5383–5386 (2014).
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Birge, J. R.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5, 475–479 (2011).
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Bódi, B.

B. Bódi, E. Balogh, V. Tosa, E. Goulielmakis, K. Varjú, and P. Dombi, “Attosecond pulse generation with an optimization loop in a light-field-synthesizer,” Opt. Express 24, 21957–21962 (2016).
[Crossref]

E. Balogh, B. Bódi, V. Tosa, E. Goulielmakis, K. Varjú, and P. Dombi, “Genetic optimization of attosecond-pulse generation in light-field synthesizers,” Phys. Rev. A 90, 023855 (2014).
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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).
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Brahms, C.

A. S. Johnson, D. R. Austin, D. A. Wood, C. Brahms, A. Gregory, K. B. Holzner, S. Jarosch, E. W. Larsen, S. Parker, C. S. Strüber, P. Ye, J. W. G. Tisch, and J. P. Marangos, “High-flux soft X-ray harmonic generation from ionization-shaped few-cycle laser pulses,” Sci. Adv. 4, eaar3761 (2018).
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Brown, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref]

Bruzzese, R.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61, 063801 (2000).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Laser waveforms (red lines) of (a) five-color field in Ref. [31] and (b) optimized two-color chirped field. In (a) and (b), the excursion distances of the classical electrons are shown (blue dashed lines), leading to the cutoff harmonics (maximum electron kinetic energies indicated), and the green shadow marks the effective waveform. (c)–(e) The waveforms of two-color chirped fields are extended for longer laser durations of 16, 24, and 32 fs. The green regions show the temporal gate for the generation of continuous high harmonics, leading to IAPs. (o.c. means the optical cycle of an 800-nm laser.)
Fig. 2.
Fig. 2. Comparison of (a) single-atom and (b) macroscopic high-harmonic spectra by using single-color laser (800 nm), five-color field (from Ref. [31]), and two-color chirped field [shown in Fig. 1(c)]. Laser duration is fixed at 16 fs for all driving fields. For the macroscopic calculations, a 1-mm-long gas jet is located 0.5 mm after laser focus, the gas pressure is 10 Torr (distributed uniformly in the jet), and the beam waist is assumed as 50 μm for all colors. For three cases, the single-atom waveforms are only formed in the center of the gas jet, and the harmonic spectra in (b) are thus normalized according to the individual input pulse energy for easy comparison. Time-frequency pictures of harmonic emission and the temporal profiles of attosecond pulses with (c)–(e) two-color chirped and (f)–(h) five-color fields.
Fig. 3.
Fig. 3. Harmonic spectra, time-frequency analysis of harmonic emission, and temporal profiles of attosecond pulses, similar to Fig. 2. However, the driving lasers are replaced by the two-color chirped fields with durations of 24 and 32 fs [as plotted in Figs. 1(d) and 1(e)]. (c)–(e) 24 fs and (f)–(h) 32 fs. In (e) and (h), the IAPs with durations of 240 and 200 as are obtained by synthesized high-harmonics in the same photon energy region of 130–219 eV.
Fig. 4.
Fig. 4. (a) Macroscopic harmonic spectra with the two-color chirped field at different gas pressures of 10, 50, and 100 Torr. The pulse duration is 16 fs, and other macroscopic conditions are the same as those in Fig. 2. Time-frequency wavelet analysis of harmonic emission and the generation of IAPs at (b), (c) 50 Torr and (d), (e) 100 Torr. In (c) and (e), 200-as single attosecond pulses are generated by synthesized high-harmonics in slightly different photon-energy regions.
Fig. 5.
Fig. 5. (a) Optimized two-color chirped laser pulse (using parameters in Table 2) with laser duration of 8 fs when the target cutoff energy is set as 330 eV; (b) extended waveform for the laser duration of 16 fs. The green areas indicate the temporal gate for the generation of soft X-ray harmonics and IAPs. (o.c. is the optical cycle of the 800-nm laser.) (c) Single-atom harmonic spectra by using optimized waveforms with different preset cutoff energies, showing that the cutoff energy is extended with the decrease of harmonic yields; (d) macroscopic harmonic spectrum with the two-color chirped waveforms (800  nm+1600  nm) as shown in (b). In the calculation, a 1-mm-long gas jet is located 3.5 mm after the laser focus, the gas pressure is 10 Torr (distributed uniformly in the jet), and the beam waist is assumed as 40 μm for two colors. (e), (f) Time-frequency analysis of harmonic emission; and (g) time profile of IAP with high harmonics in the photon-energy range of 169–245 eV.

Tables (2)

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Table 1. Optimized Laser Parameters for the Two-Color Waveform at Different Runsa

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Table 2. Optimized Laser Parameters for the Two-Color Waveform at Different Runsa

Equations (9)

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E(t)=E1A1(t)cos(ω1t+α1t2+ϕ1)+E2A2(t)cos(ω2t+α2t2+ϕ2).
D(ω)=W(ω)d(ω),
F=ωminωmaxω4|D(ω)|2dω.
2E1(r,z,t)1c22E1(r,z,t)t2=μ0Jabs(r,z,t)t+ω02c2(1ηeff2)E1(r,z,t),
2Eh(r,z,t)1c22Eh(r,z,t)t2=μ02P(r,z,t)t2,
A(t,ω)=Eh(τ)wt,ω(τ)dτ,
W(x)=(1/ν)eixex2/2ν2.
|Anear(t,ω)|2=02πrdr|Eh(r,τ)wt,ω(τ)dτ|2.
Inear(t)=02πrdr|ω1ω2Eh(r,ω)eiωtdω|2.

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