Abstract

We demonstrate the suppression of soft X-ray high harmonics generated by two-color laser pulses interacting with Ne gas in a gas cell. We show that harmonic suppression can occur at the proper combination of the propagation distance and gas pressure. The physical mechanism behind is the phase mismatch between “short”-trajectory harmonics generated at the early and later times through the interplay of geometric phase, dispersion, and plasma effects. In addition, we demonstrate that the position and depth of harmonic suppression can be tuned by increasing the gas pressure. Furthermore, the suppression can be extended to other laser focusing configurations by properly scaling macroscopic parameters. Our investigation reveals a simple and novel experimental scheme purely relying on the phase mismatch for selectively controlling soft X-ray tabletop light sources without adopting the filters for applications.

© 2018 Chinese Laser Press

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2017 (6)

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).
[Crossref]

S. L. Cousin, N. Di Palo, B. Buades, S. M. Teichmann, M. Reduzzi, M. Devetta, A. Kheifets, G. Sansone, and J. Biegert, “Attosecond streaking in the water window: a new regime of attosecond pulse characterization,” Phys. Rev. X 7, 041030 (2017).
[Crossref]

G. Lerner, T. Diskon, O. Neufeld, O. Kfir, and O. Cohen, “Selective suppression of high-order harmonics within phase-matched spectral regions,” Opt. Lett. 42, 1349–1352 (2017).
[Crossref]

C. Jin, K.-H. Hong, and C. D. Lin, “Macroscopic scaling of high-order harmonics generated by two-color optimized waveforms in a hollow waveguide,” Phys. Rev. A 96, 013422 (2017).
[Crossref]

C. M. Heyl, C. L. Arnold, A. Couairon, and A. L’Huillier, “Introduction to macroscopic power scaling principles for high-order harmonic generation,” J. Phys. B 50, 013001 (2017).
[Crossref]

H.-W. Sun, P.-C. Huang, Y.-H. Tzeng, R.-T. Huang, C. D. Lin, C. Jin, and M.-C. Chen, “Extended phase matching of high harmonic generation by plasma-induced defocusing,” Optica 4, 976–981 (2017).
[Crossref]

2016 (5)

C. M. Heyl, H. Coudert-Alteirac, M. Miranda, M. Louisy, K. Kovacs, V. Tosa, E. Balogh, K. Varjú, A. L’Huillier, A. Couairon, and C. L. Arnold, “Scale-invariant nonlinear optics in gases,” Optica 3, 75–81 (2016).
[Crossref]

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

C. Jin, K.-H. Hong, and C. D. Lin, “Optimal generation of spatially coherent soft X-ray isolated attosecond pulses in a gas-filled waveguide using two-color synthesized laser pulses,” Sci. Rep. 6, 38165 (2016).
[Crossref]

B. Zhang, D. F. Gardner, M. H. Seaberg, E. R. Shanblatt, C. L. Porter, R. Karl, C. A. Mancuso, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “Ptychographic hyperspectral spectromicroscopy with an extreme ultraviolet high harmonic comb,” Opt. Express 24, 18745–18754 (2016).
[Crossref]

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

2015 (5)

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]

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent X-ray light sources,” Science 348, 530–535 (2015).
[Crossref]

F. Wang, L. He, C. Zhai, W. Shi, Q. Zhang, P. Lan, and P. Lu, “Time-dependent phase matching of high-order-harmonic generation,” Phys. Rev. A 92, 063839 (2015).
[Crossref]

C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115, 043901 (2015).
[Crossref]

Y. Huang, C. Meng, X. Wang, Z. Lü, D. Zhang, W. Chen, J. Zhao, J. Yuan, and Z. Zhao, “Joint measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules reveal angle-resolved molecular structures,” Phys. Rev. Lett. 115, 123002 (2015).
[Crossref]

2014 (7)

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zar, 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).
[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]

P. Ye, H. Teng, X.-K. He, S.-Y. Zhong, L.-F. Wang, M.-J. Zhan, W. Zhang, C.-X. Yun, and Z.-Y. Wei, “Minimizing the angular divergence of high-order harmonics by truncating the truncated Bessel beam,” Phys. Rev. A 90, 063808 (2014).
[Crossref]

A. Dubrouil, O. Hort, F. Catoire, D. Descamps, S. Petit, E. Mével, V. V. Strelkov, and E. Constant, “Spatio-spectral structures in high-order harmonic beams generated with terawatt 10-fs pulses,” Nat. Commun. 5, 4637 (2014).
[Crossref]

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).
[Crossref]

J. Rothhardt, M. Krebs, S. Hädrich, S. Demmler, J. Limpert, and A. Tünnermann, “Absorption-limited and phase-matched high harmonic generation in the tight focusing regime,” New J. Phys. 16, 033022 (2014).
[Crossref]

P. Wei, Z. Zeng, J. Jiang, J. Miao, Y. Zheng, X. Ge, C. Li, and R. Li, “Selective generation of an intense single harmonic from a long gas cell with loosely focusing optics based on a three-color laser field,” Appl. Phys. Lett. 104, 151101 (2014).
[Crossref]

2013 (4)

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).
[Crossref]

X. Ren, V. Makhija, A.-T. Le, J. Troß, S. Mondal, C. Jin, V. Kumarappan, and C. Trallero-Herrero, “Measuring the angle-dependent photoionization cross section of nitrogen using high-harmonic generation,” Phys. Rev. A 88, 043421 (2013).
[Crossref]

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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M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the Cooper minimum in molecules,” Phys. Rev. Lett. 110, 033006 (2013).
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2012 (5)

C. M. Heyl, J. Güdde, A. L’Huillier, and U. Höfer, “High-order harmonic generation with μJ laser pulses at high repetition rates,” J. Phys. B 45, 074020 (2012).
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J. B. Bertrand, H. J. Wörner, P. Hockett, D. M. Villeneuve, and P. B. Corkum, “Revealing the Cooper minimum of N2 by molecular frame high-harmonic spectroscopy,” Phys. Rev. Lett. 109, 143001 (2012).
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C. Jin, J. B. Bertrand, R. R. Lucchese, H. J. Wörner, P. B. Corkum, D. M. Villeneuve, A.-T. Le, and C. D. Lin, “Intensity dependence of multiple orbital contributions and shape resonance in high-order harmonic generation of aligned N2 molecules,” Phys. Rev. A 85, 013405 (2012).
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G. Wang, C. Jin, A.-T. Le, and C. D. Lin, “Conditions for extracting photoionization cross sections from laser-induced high-order-harmonic spectra,” Phys. Rev. A 86, 015401 (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. Hernndez-Garcia, 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 (9)

C. Jin, H. J. Wörner, V. Tosa, A. T. Le, J. B. Bertrand, R. R. Lucchese, P. B. Corkum, D. M. Villeneuve, and C. D. Lin, “Separation of target structure and medium propagation effects in high-harmonic generation,” J. Phys. B 44, 095601 (2011).
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J. P. Farrell, L. S. Spector, B. K. McFarland, P. H. Bucksbaum, M. Gühr, M. B. Gaarde, and K. J. Schafer, “Influence of phase matching on the Cooper minimum in Ar high-order harmonic spectra,” Phys. Rev. A 83, 023420 (2011).
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J. Higuet, H. Ruf, N. Thiré, R. Cireasa, E. Constant, E. Cormier, D. Descamps, E. Mével, S. Petit, B. Pons, Y. Mairesse, and B. Fabre, “High-order harmonic spectroscopy of the Cooper minimum in argon: experimental and theoretical study,” Phys. Rev. A 83, 053401 (2011).
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A. D. Shiner, B. E. Schmidt, C. Trallero-Herrero, H. J. Wörner, S. Patchkovskii, P. B. Corkum, J.-C. Kieffer, F. Légaré, and D. M. Villeneuve, “Probing collective multi-electron dynamics in xenon with high-harmonic spectroscopy,” Nat. Phys. 7, 464–467 (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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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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C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. 7, 822–826 (2011).
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2010 (2)

R. Torres, T. Siegel, L. Brugnera, I. Procino, J. G. Underwood, C. Altucci, R. Velotta, E. Springate, C. Froud, I. C. E. Turcu, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and J. P. Marangos, “Revealing molecular structure and dynamics through high-order harmonic generation driven by mid-IR fields,” Phys. Rev. A 81, 051802 (2010).
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S. Haessler, J. Caillat, W. Boutu, C. Giovanetti-Teixeira, T. Ruchon, T. Auguste, Z. Diveki, P. Breger, A. Maquet, B. Carré, R. Taeb, and P. Salières, “Attosecond imaging of molecular electronic wavepackets,” Nat. Phys. 6, 200–206 (2010).
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2009 (4)

H. J. Wörner, H. Niikura, J. B. Bertrand, P. B. Corkum, and D. M. Villeneuve, “Observation of electronic structure minima in high-harmonic generation,” Phys. Rev. Lett. 102, 103901 (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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F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
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O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460, 972–977 (2009).
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2008 (7)

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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G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, S. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M.-E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
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A. Ozawa, J. Rauschenberger, C. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and T. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100, 253901 (2008).
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C. Winterfeldt, C. Spielmann, and G. Gerber, “Colloquium: optimal control of high-harmonic generation,” Rev. Mod. Phys. 80, 117–140 (2008).
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S. Minemoto, T. Umegaki, Y. Oguchi, T. Morishita, A. T. Le, S. Watanabe, and H. Sakai, “Retrieving photorecombination cross sections of atoms from high-order harmonic spectra,” Phys. Rev. A 78, 061402 (2008).
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E. J. Takahashi, T. Kanai, Y. Nabekawa, and K. Midorikawa, “10  mJ class femtosecond optical parametric amplifier for generating soft X-ray harmonics,” Appl. Phys. Lett. 93, 041111 (2008).
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P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4, 386–389 (2008).
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2007 (2)

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3, 270–275 (2007).
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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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2005 (3)

C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci, and R. Velotta, “Controlling two-center interference in molecular high harmonic generation,” Phys. Rev. Lett. 95, 153902 (2005).
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I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94, 243901 (2005).
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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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2003 (1)

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421, 51–54 (2003).
[Crossref]

2001 (1)

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent X-ray generation,” Chem. Phys. 267, 277–289 (2001).
[Crossref]

2000 (2)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature 406, 164–166 (2000).
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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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Adams, D. E.

Agostini, P.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4, 386–389 (2008).
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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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Alharbi, A. F.

M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the Cooper minimum in molecules,” Phys. Rev. Lett. 110, 033006 (2013).
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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. Hernndez-Garcia, 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.

R. Torres, T. Siegel, L. Brugnera, I. Procino, J. G. Underwood, C. Altucci, R. Velotta, E. Springate, C. Froud, I. C. E. Turcu, S. Patchkovskii, M. Y. Ivanov, O. Smirnova, and J. P. Marangos, “Revealing molecular structure and dynamics through high-order harmonic generation driven by mid-IR fields,” Phys. Rev. A 81, 051802 (2010).
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C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci, and R. Velotta, “Controlling two-center interference in molecular high harmonic generation,” Phys. Rev. Lett. 95, 153902 (2005).
[Crossref]

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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Andriukaitis, G.

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zar, 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. Hernndez-Garcia, 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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Apolonski, A.

A. Ozawa, J. Rauschenberger, C. Gohle, M. Herrmann, D. R. Walker, V. Pervak, A. Fernandez, R. Graf, A. Apolonski, R. Holzwarth, F. Krausz, T. W. Hänsch, and T. Udem, “High harmonic frequency combs for high resolution spectroscopy,” Phys. Rev. Lett. 100, 253901 (2008).
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Arnold, C. L.

C. M. Heyl, C. L. Arnold, A. Couairon, and A. L’Huillier, “Introduction to macroscopic power scaling principles for high-order harmonic generation,” J. Phys. B 50, 013001 (2017).
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C. M. Heyl, H. Coudert-Alteirac, M. Miranda, M. Louisy, K. Kovacs, V. Tosa, E. Balogh, K. Varjú, A. L’Huillier, A. Couairon, and C. L. Arnold, “Scale-invariant nonlinear optics in gases,” Optica 3, 75–81 (2016).
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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. Hernndez-Garcia, 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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Auguste, T.

S. Haessler, J. Caillat, W. Boutu, C. Giovanetti-Teixeira, T. Ruchon, T. Auguste, Z. Diveki, P. Breger, A. Maquet, B. Carré, R. Taeb, and P. Salières, “Attosecond imaging of molecular electronic wavepackets,” Nat. Phys. 6, 200–206 (2010).
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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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Backus, S.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421, 51–54 (2003).
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R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent X-ray generation,” Chem. Phys. 267, 277–289 (2001).
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R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature 406, 164–166 (2000).
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Balciunas, T.

S. Haessler, T. Balčiunas, G. Fan, G. Andriukaitis, A. Pugžlys, A. Baltuška, T. Witting, R. Squibb, A. Zar, 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. Hernndez-Garcia, 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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Balogh, E.

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. Hernndez-Garcia, 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. Zar, 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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Bartels, R.

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent X-ray generation,” Chem. Phys. 267, 277–289 (2001).
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R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature 406, 164–166 (2000).
[Crossref]

Bartels, R. A.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421, 51–54 (2003).
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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.

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. Hernndez-Garcia, 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.

C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci, and R. Velotta, “Controlling two-center interference in molecular high harmonic generation,” Phys. Rev. Lett. 95, 153902 (2005).
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Bertrand, J. B.

J. B. Bertrand, H. J. Wörner, P. Hockett, D. M. Villeneuve, and P. B. Corkum, “Revealing the Cooper minimum of N2 by molecular frame high-harmonic spectroscopy,” Phys. Rev. Lett. 109, 143001 (2012).
[Crossref]

C. Jin, J. B. Bertrand, R. R. Lucchese, H. J. Wörner, P. B. Corkum, D. M. Villeneuve, A.-T. Le, and C. D. Lin, “Intensity dependence of multiple orbital contributions and shape resonance in high-order harmonic generation of aligned N2 molecules,” Phys. Rev. A 85, 013405 (2012).
[Crossref]

C. Jin, H. J. Wörner, V. Tosa, A. T. Le, J. B. Bertrand, R. R. Lucchese, P. B. Corkum, D. M. Villeneuve, and C. D. Lin, “Separation of target structure and medium propagation effects in high-harmonic generation,” J. Phys. B 44, 095601 (2011).
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H. J. Wörner, H. Niikura, J. B. Bertrand, P. B. Corkum, and D. M. Villeneuve, “Observation of electronic structure minima in high-harmonic generation,” Phys. Rev. Lett. 102, 103901 (2009).
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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).
[Crossref]

Bhardwaj, V. R.

M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the Cooper minimum in molecules,” Phys. Rev. Lett. 110, 033006 (2013).
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Biegert, J.

S. L. Cousin, N. Di Palo, B. Buades, S. M. Teichmann, M. Reduzzi, M. Devetta, A. Kheifets, G. Sansone, and J. Biegert, “Attosecond streaking in the water window: a new regime of attosecond pulse characterization,” Phys. Rev. X 7, 041030 (2017).
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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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Blaga, C. I.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4, 386–389 (2008).
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Boguslavskiy, A. E.

M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the Cooper minimum in molecules,” Phys. Rev. Lett. 110, 033006 (2013).
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Bougeard, M.

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Figures (9)

Fig. 1.
Fig. 1. (a) Single-atom harmonic yields with a 1.6-μm and a two-color laser pulse. The corresponding time-frequency harmonic emissions by the two-color pulse are shown in (b). (c) Macroscopic harmonic spectra (integrated over the exit plane of the gas cell and smoothed by using Bezier curve) generated by the two-color laser pulse at different gas pressures. Optimal pressure for the highest harmonic yields and the largest cutoff energy was found to be 200 Torr. The angular divergence of the far-field harmonic generated at this pressure is shown in (d). See text for other laser parameters.
Fig. 2.
Fig. 2. (a) Evolution of harmonic spectra against the propagation distance by a two-color laser pulse at the gas pressure of 400 Torr. The propagation distances are as indicated. (b) The harmonic spectrum at the exit of the gas cell calculated including both dispersion and absorption effects ( w / dis + abs ) is compared with calculations where only absorption (only abs) is included, and with calculations where neither absorption nor dispersion (no dis + abs ) is included. The absorption length versus harmonic energy for gas pressure at 400 Torr from NIST [56] is also plotted (see right-hand scale). (c), (d) Time-frequency analysis of the harmonic emissions (normalized) at r = 11    μm of the exit plane. The optical cycle (o.c.) is defined with respect to the fundamental 1.6-μm laser.
Fig. 3.
Fig. 3. Time-frequency analysis of the harmonic emissions (normalized) at r = 11    μm at different propagation planes for the gas pressure of 400 Torr including both dispersion and absorption effects. The optical cycle (o.c.) is defined with respect to the fundamental 1.6-μm laser.
Fig. 4.
Fig. 4. Evolution of macroscopic two-color harmonic spectra with the propagation distance (as indicated) for two gas pressures: (a) 50 Torr and (b) 200 Torr. (c), (d) Time-frequency analysis of macroscopic harmonic emissions (normalized) at r = 11    μm of the exit plane.
Fig. 5.
Fig. 5. Time-dependent electric fields of the two-color laser pulse at r = 11    μm for three gas pressures (a) 50 Torr, (b) 200 Torr, and (c) 400 Torr at three positions: d = 0    mm (at the entrance), d = 1    mm (in the middle), and d = 2    mm (at the exit plane of the gas cell), respectively. Enlarged figures of the electric fields are shown for the two time intervals, one at the leading edge and the other at the trailing edge of the pulse. Note that the driving field has been substantially weakened due to the geometric phase, the dispersion, and the plasma dispersion as the beam travels in space and time in the gas cell.
Fig. 6.
Fig. 6. Time-frequency analysis of harmonic emission driven by the electric field at d = 1    mm for an off-axis position, r = 11    μm (shown in Fig. 5) for three gas pressures: (a) 50 Torr, (b) 200 Torr, and (c) 400 Torr. The 120 eV harmonic emissions are lined out from (a)–(c) and replotted in (d) for the three pressures at d = 1    mm . The same plots are shown at (e)  d = 1.5    mm and (f)  d = 2    mm . One observes that each harmonic burst of “short”-trajectory electron emission changes in time depending on the gas pressure as well as the propagation distance.
Fig. 7.
Fig. 7. Macroscopic harmonic spectra (smoothed by using Bezier curve for easy comparison) generated by (a) two-color and (b) 1.6-μm laser pulses at different gas pressures.
Fig. 8.
Fig. 8. Harmonic emission (normalized at the highest peak in each figure) in the far field using the optimized two-color laser pulses. (a)–(c) are for the generation of optimal harmonics, and (d)–(f) are for the generation of suppressed harmonics. The beam waists of the 1.6-μm laser in the two-color waveforms are indicated on top of the figures. Other parameters for (a)–(f) are listed in Table 2.
Fig. 9.
Fig. 9. Total harmonic yields integrated over the radial dimension under the (a) optimal and (b) suppression conditions. Panels (a) and (b) correspond to harmonic emissions in Figs. 8(a)8(c) and in Figs. 8(d)8(f), respectively. In both (a) and (b), the ratio of the harmonic yield between top, middle, and bottom curve is 16 4 1 .

Tables (2)

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Table 1. Laser Parameters for a Two-Color Laser Pulse a

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Table 2. Macroscopic Parameters for Harmonic Emissions in Fig. 8 a

Equations (4)

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E ( t ) = E 1 A 1 ( t ) cos ( ω 1 t + ϕ 1 ) + E 2 A 2 ( t ) cos ( ω 2 t + ϕ 2 ) .
z η 2 z , w η w , l η 2 l , p p / η 2 .
Div ( ω ) Div ( ω ) / η .
S ( ω ) η 2 S ( ω ) .

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