Abstract

Above-threshold ionization of rare-gas atoms by a bicircular field with its two components counterrotating is theoretically investigated by means of the improved strong-field approximation. Both direct and rescattered electrons are considered and the quantum orbits that lead into a specific final state are calculated and depicted. The angle-dependent spectrum reflects the discrete rotational symmetry of the bicircular field. The backward-scattering contributions are very similar to those generated by a linearly polarized field; several such contributions are rotated one versus the other by the symmetry angle of the discrete rotational symmetry. The forward-scattering contributions dramatically affect the velocity map at comparatively low momenta. The direct-electron spectrum observes reflection symmetry about several symmetry axes determined by the field symmetry. This is broken by rescattering.

© 2016 Optical Society of America

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References

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2015 (12)

D. B. Milošević, “High-order harmonic generation by a bichromatic elliptically polarized field: conservation of angular momentum,” J. Phys. B. 48, 171001 (2015).
[Crossref]

D. B. Milošević, “Circularly polarized high harmonics generated by a bicircular field from inert atomic gases in the p state: A tool for exploring chirality-sensitive processes,” Phys. Rev. A. 92, 043827 (2015).
[Crossref]

L. Medišauskas, J. Wragg, H. van der Hart, and M. Yu. Ivanov, “Generating isolated elliptically polarized attosecond pulses using bichromatic counterrotating circularly polarized laser fields,” Phys. Rev. Lett. 115, 153001 (2015).
[Crossref]

T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. Dorney, C. Chen, O. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
[Crossref] [PubMed]

S. Odžak and D. B. Milošević, “Bicircular-laser-field-assisted electron-ion radiative recombination,” Phys. Rev. A. 92, 053416 (2015).
[Crossref]

G. Lambert, B. Vodungbo, J. Gautier, B. Mahieu, V. Malka, S. Sebban, P. Zeitoun, J. Luning, J. Perron, A. Andreev, S. Stremoukhov, F. Ardana-Lamas, A. Dax, C. P. Hauri, A. Sardinha, and M. Fajardo, “Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources,” Nat. Commun. 6, 6167 (2015).
[Crossref] [PubMed]

F. Willems, C. T. L. Smeenk, N. Zhavoronkov, O. Kornilov, I. Radu, M. Schmidhauer, M. Hanke, C. von KorffSchmising, M. J. J. Vrakking, and S. Eisebitt, “Probing ultrafast spin dynamics with high-harmonic magnetic circular dichroism spectroscopy,” Phys. Rev. A. 92, 220405 (2015).

W. Becker and D. B. Milošević, “Above-threshold ionization for very low electron energy,” J. Phys. B. 48, 151001 (2015).
[Crossref]

C. A. Mancuso, D. D. Hickstein, P. Grychtol, R. Knut, O. Kfir, X. M. Tong, F. Dollar, D. Zusin, M. Gopalakrishnan, C. Gentry, E. Turgut, J. L. Ellis, M.-C. Chen, A. Fleischer, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Strong-field ionization with two-color circularly polarized laser fields,” Phys. Rev. A. 91, 031402 (2015).
[Crossref]

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

D. B. Milošević, “Generation of elliptically polarized attosecond pulse trains,” Opt. Lett. 40, 2381–2384 (2015).
[Crossref]

W. Becker and D. B. Milošević, “Quantum-orbit theory of low-energy above-threshold ionization on and off axis,” Chin. Opt. Lett. 13, 070006 (2015).
[Crossref]

2014 (8)

A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, “Spin angular momentum and tunable polarization in high-harmonic generation,” Nat. Photonics 8, 543–549 (2014).
[Crossref]

E. Pisanty and M. Ivanov, “High-harmonic generation: taking control of polarization,” Nat. Photonics 8, 501–503 (2014).
[Crossref]

E. Pisanty, S. Sukiasyan, and M. Ivanov, “Spin conservation in high-order-harmonic generation using bicircular fields,” Phys. Rev. A. 90, 043829 (2014).
[Crossref]

D. B. Milošević, “Low-frequency approximation for above-threshold ionization by a laser pulse: Low-energy forward rescattering,” Phys. Rev. A 90, 063423 (2014).
[Crossref]

M. Möller, F. Meyer, A. M. Sayler, G. G. Paulus, M. F. Kling, B. E. Schmidt, W. Becker, and D. B. Milošević, “Off-axis low-energy structures in above-threshold ionization,” Phys. Rev. A. 90, 023412 (2014).
[Crossref]

W. Becker, S. P. Goreslavski, D. B. Milošević, and G. G. Paulus, “Low-energy rescattering in laser-induced ionization,” J. Phys. B. 47, 204022 (2014).
[Crossref]

C. von KorffSchmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovanella, J. Perron, B. Vodungho, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging ultrafast demagnetization dynamics after a spatially localized optical excitation,” Phys. Rev. Lett. 112, 217203 (2014).
[Crossref]

D. B. Milošević, “Forward- and backward-scattering quantum orbits in above-threshold ionization,” Phys. Rev. A. 90, 063414 (2014).
[Crossref]

2013 (2)

D. B. Milošević, “Reexamination of the improved strong-field approximation: Low-energy structures in the above-threshold-ionization spectra for short-range potentials,” Phys. Rev. A. 88, 023417 (2013).
[Crossref]

X. Y. Lai, C. L. Wang, Y. J. Chen, Z. L. Hu, W. Quan, X. J. Liu, J. Chen, Y. Cheng, Z. Z. Xu, and W. Becker, “Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases,” Phys. Rev. Lett. 110, 043002 (2013).
[Crossref] [PubMed]

2012 (4)

P. Agostini and L. F. DiMauro, “Atomic and molecular ionization dynamics in strong laser fields: from optical to x-rays,” Adv. At. Mol. Opt. Phys. 61, 117–158 (2012).
[Crossref]

P. A. Korneev, S. V. Popruzhenko, S. P. Goreslavski, W. Becker, G. G. Paulus, B. Fetić, and D. B. Milošević, “Interference structure of above-threshold ionization versus above-threshold detachment,” New. J. Phys. 14, 055019 (2012).
[Crossref]

C. Y. Wu, Y. D. Yang, Y. Q. Liu, Q. H. Gong, M. Wu, X. Liu, X. L. Hao, W. D. Li, X. T. He, and J. Chen, “Characteristic spectrum of very low-energy photoelectron from above-threshold ionization in the tunneling regime,” Phys. Rev. Lett. 109, 043001 (2012).
[Crossref] [PubMed]

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F. DiMauro, and C. D. Lin, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature (London) 483, 194–197 (2012).
[Crossref]

2011 (1)

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Dörner, and U. Keller, “Timing the release in sequential double ionization,” Nat. Phys. 7, 428–433 (2011).
[Crossref]

2010 (3)

F. Mauger, C. Chandre, and T. Uzer, “Recollisions and correlated double ionization with circularly polarized light,” Phys. Rev. Lett. 105, 083002 (2010).
[Crossref] [PubMed]

X. Wang and J. H. Eberly, “Elliptical polarization and probability of double ionization,” Phys. Rev. Lett. 105, 083001 (2010).
[Crossref] [PubMed]

C. D. Lin, A.-T. Le, Z. Chen, T. Morishita, and R. Lucchese, “Strong-field rescattering physics — self-imaging of a molecule by its own electrons,” J. Phys. B. 43, 122001 (2010).
[Crossref]

2009 (3)

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

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[Crossref]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[Crossref] [PubMed]

2008 (2)

E. Hasović, A. Kramo, and D. B. Milošević, “Energy- and angle-resolved photoelectron spectra of above-threshold ionization and detachment,” Eur. Phys. J. Spec. Top. 160, 205–216 (2008).
[Crossref]

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[Crossref] [PubMed]

2007 (2)

D. B. Milošević, E. Hasović, M. Busuladžić, A. Gazibegović-Busuladžić, and W. Becker, “Intensity-dependent enhancements in high-order above-threshold ionization,” Phys. Rev. A. 76, 053410 (2007).
[Crossref]

A. Kramo, E. Hasović, D. B. Milošević, and W. Becker, “Above-threshold detachment by a two-color bicircular laser field,” Laser Phys. Lett. 4, 279–286 (2007).
[Crossref]

2006 (1)

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B. 39, R203–R262 (2006).
[Crossref]

2005 (2)

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401 (2005).
[Crossref] [PubMed]

D. B. Milošević and W. Becker, “Attosecond pulse generation by bicircular fields: from pulse trains to a single pulse,” J. Mod. Opt. 52, 233–241 (2005).
[Crossref]

2004 (1)

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by x-ray spectro-holography,” Nature (London) 432, 885–888 (2004).
[Crossref]

2003 (2)

F. Ceccherini, D. Bauer, and F. Cornolti, “Harmonic generation by atoms in circularly polarized two-color laser fields with coplanar polarizations and commensurate frequencies,” Phys. Rev. A. 68, 053402 (2003).
[Crossref]

A. D. Bandrauk and H. Z. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: orientation effects,” Phys. Rev. A. 68, 043408 (2003).
[Crossref]

2002 (2)

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

D. B. Milošević and W. Becker, “Role of long quantum orbits in high-order harmonic generation,” Phys. Rev. A. 66, 063417 (2002).
[Crossref]

2001 (2)

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292, 902–905 (2001).
[Crossref]

D. B. Milošević, W. Becker, R. Kopold, and W. Sandner, “High-harmonic generation by a bichromatic bicircular laser field,” Laser Phys. 11, 165–168 (2001).

2000 (5)

D. B. Milošević and W. Becker, “Attosecond pulse trains with unusual nonlinear polarization,” Phys. Rev. A. 62011403 (2000).
[Crossref]

D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A. 61, 063403 (2000).
[Crossref]

R. Kopold, W. Becker, and M. Kleber, “Quantum path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
[Crossref]

R. Kopold, D. B. Milošević, and W. Becker, “Rescattering processes for elliptical polarization: a quantum trajectory analysis,” Phys. Rev. Lett. 84, 3831–3834 (2000).
[Crossref] [PubMed]

D. B. Milošević and W. Sandner, “Extreme-ultraviolet harmonic generation near 13 nm with a two-color elliptically polarized laser field,” Opt. Lett. 25, 1532–1534 (2000).
[Crossref]

1995 (3)

T. Zuo and A. D. Bandrauk, “High-order harmonic generation in intense laser and magnetic fields,” J. Nonlinear Opt. Phys. Mat. 4, 533–546 (1995).
[Crossref]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A. 51, R3414–R3417 (1995).
[Crossref] [PubMed]

S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A. 52, 2262–2278 (1995).
[Crossref] [PubMed]

1994 (2)

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
[Crossref] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. 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] [PubMed]

1993 (1)

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

1988 (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B. 21, L31–L35 (1988).
[Crossref]

Agostini, P.

P. Agostini and L. F. DiMauro, “Atomic and molecular ionization dynamics in strong laser fields: from optical to x-rays,” Adv. At. Mol. Opt. Phys. 61, 117–158 (2012).
[Crossref]

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F. DiMauro, and C. D. Lin, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature (London) 483, 194–197 (2012).
[Crossref]

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[Crossref]

Andreev, A.

G. Lambert, B. Vodungbo, J. Gautier, B. Mahieu, V. Malka, S. Sebban, P. Zeitoun, J. Luning, J. Perron, A. Andreev, S. Stremoukhov, F. Ardana-Lamas, A. Dax, C. P. Hauri, A. Sardinha, and M. Fajardo, “Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources,” Nat. Commun. 6, 6167 (2015).
[Crossref] [PubMed]

Ardana-Lamas, F.

G. Lambert, B. Vodungbo, J. Gautier, B. Mahieu, V. Malka, S. Sebban, P. Zeitoun, J. Luning, J. Perron, A. Andreev, S. Stremoukhov, F. Ardana-Lamas, A. Dax, C. P. Hauri, A. Sardinha, and M. Fajardo, “Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources,” Nat. Commun. 6, 6167 (2015).
[Crossref] [PubMed]

Balcou, Ph.

M. Lewenstein, Ph. Balcou, M. Yu. 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] [PubMed]

Baltuška, A.

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401 (2005).
[Crossref] [PubMed]

Bandrauk, A. D.

A. D. Bandrauk and H. Z. Lu, “Controlling harmonic generation in molecules with intense laser and static magnetic fields: orientation effects,” Phys. Rev. A. 68, 043408 (2003).
[Crossref]

T. Zuo and A. D. Bandrauk, “High-order harmonic generation in intense laser and magnetic fields,” J. Nonlinear Opt. Phys. Mat. 4, 533–546 (1995).
[Crossref]

Bandulet, H. C.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[Crossref] [PubMed]

Bauer, D.

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B. 39, R203–R262 (2006).
[Crossref]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401 (2005).
[Crossref] [PubMed]

F. Ceccherini, D. Bauer, and F. Cornolti, “Harmonic generation by atoms in circularly polarized two-color laser fields with coplanar polarizations and commensurate frequencies,” Phys. Rev. A. 68, 053402 (2003).
[Crossref]

Becker, A.

T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. Dorney, C. Chen, O. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
[Crossref] [PubMed]

Becker, W.

W. Becker and D. B. Milošević, “Quantum-orbit theory of low-energy above-threshold ionization on and off axis,” Chin. Opt. Lett. 13, 070006 (2015).
[Crossref]

W. Becker and D. B. Milošević, “Above-threshold ionization for very low electron energy,” J. Phys. B. 48, 151001 (2015).
[Crossref]

W. Becker, S. P. Goreslavski, D. B. Milošević, and G. G. Paulus, “Low-energy rescattering in laser-induced ionization,” J. Phys. B. 47, 204022 (2014).
[Crossref]

M. Möller, F. Meyer, A. M. Sayler, G. G. Paulus, M. F. Kling, B. E. Schmidt, W. Becker, and D. B. Milošević, “Off-axis low-energy structures in above-threshold ionization,” Phys. Rev. A. 90, 023412 (2014).
[Crossref]

X. Y. Lai, C. L. Wang, Y. J. Chen, Z. L. Hu, W. Quan, X. J. Liu, J. Chen, Y. Cheng, Z. Z. Xu, and W. Becker, “Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases,” Phys. Rev. Lett. 110, 043002 (2013).
[Crossref] [PubMed]

P. A. Korneev, S. V. Popruzhenko, S. P. Goreslavski, W. Becker, G. G. Paulus, B. Fetić, and D. B. Milošević, “Interference structure of above-threshold ionization versus above-threshold detachment,” New. J. Phys. 14, 055019 (2012).
[Crossref]

A. Kramo, E. Hasović, D. B. Milošević, and W. Becker, “Above-threshold detachment by a two-color bicircular laser field,” Laser Phys. Lett. 4, 279–286 (2007).
[Crossref]

D. B. Milošević, E. Hasović, M. Busuladžić, A. Gazibegović-Busuladžić, and W. Becker, “Intensity-dependent enhancements in high-order above-threshold ionization,” Phys. Rev. A. 76, 053410 (2007).
[Crossref]

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B. 39, R203–R262 (2006).
[Crossref]

D. B. Milošević and W. Becker, “Attosecond pulse generation by bicircular fields: from pulse trains to a single pulse,” J. Mod. Opt. 52, 233–241 (2005).
[Crossref]

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuška, E. Goulielmakis, F. Krausz, D. B. Milošević, D. Bauer, W. Becker, and G. G. Paulus, “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401 (2005).
[Crossref] [PubMed]

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: from classical features to quantum effects,” Adv. At. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

D. B. Milošević and W. Becker, “Role of long quantum orbits in high-order harmonic generation,” Phys. Rev. A. 66, 063417 (2002).
[Crossref]

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292, 902–905 (2001).
[Crossref]

D. B. Milošević, W. Becker, R. Kopold, and W. Sandner, “High-harmonic generation by a bichromatic bicircular laser field,” Laser Phys. 11, 165–168 (2001).

D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A. 61, 063403 (2000).
[Crossref]

R. Kopold, D. B. Milošević, and W. Becker, “Rescattering processes for elliptical polarization: a quantum trajectory analysis,” Phys. Rev. Lett. 84, 3831–3834 (2000).
[Crossref] [PubMed]

D. B. Milošević and W. Becker, “Attosecond pulse trains with unusual nonlinear polarization,” Phys. Rev. A. 62011403 (2000).
[Crossref]

R. Kopold, W. Becker, and M. Kleber, “Quantum path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
[Crossref]

S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A. 52, 2262–2278 (1995).
[Crossref] [PubMed]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A. 51, R3414–R3417 (1995).
[Crossref] [PubMed]

Blaga, C. I.

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F. DiMauro, and C. D. Lin, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature (London) 483, 194–197 (2012).
[Crossref]

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[Crossref]

Busuladžic, M.

D. B. Milošević, E. Hasović, M. Busuladžić, A. Gazibegović-Busuladžić, and W. Becker, “Intensity-dependent enhancements in high-order above-threshold ionization,” Phys. Rev. A. 76, 053410 (2007).
[Crossref]

Capotondi, F.

C. von KorffSchmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovanella, J. Perron, B. Vodungho, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging ultrafast demagnetization dynamics after a spatially localized optical excitation,” Phys. Rev. Lett. 112, 217203 (2014).
[Crossref]

Carré, B.

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292, 902–905 (2001).
[Crossref]

Carva, K.

T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. Dorney, C. Chen, O. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
[Crossref] [PubMed]

Catoire, F.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[Crossref]

Ceccherini, F.

F. Ceccherini, D. Bauer, and F. Cornolti, “Harmonic generation by atoms in circularly polarized two-color laser fields with coplanar polarizations and commensurate frequencies,” Phys. Rev. A. 68, 053402 (2003).
[Crossref]

Chandre, C.

F. Mauger, C. Chandre, and T. Uzer, “Recollisions and correlated double ionization with circularly polarized light,” Phys. Rev. Lett. 105, 083002 (2010).
[Crossref] [PubMed]

Chen, C.

T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. Dorney, C. Chen, O. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
[Crossref] [PubMed]

Chen, J.

X. Y. Lai, C. L. Wang, Y. J. Chen, Z. L. Hu, W. Quan, X. J. Liu, J. Chen, Y. Cheng, Z. Z. Xu, and W. Becker, “Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases,” Phys. Rev. Lett. 110, 043002 (2013).
[Crossref] [PubMed]

C. Y. Wu, Y. D. Yang, Y. Q. Liu, Q. H. Gong, M. Wu, X. Liu, X. L. Hao, W. D. Li, X. T. He, and J. Chen, “Characteristic spectrum of very low-energy photoelectron from above-threshold ionization in the tunneling regime,” Phys. Rev. Lett. 109, 043001 (2012).
[Crossref] [PubMed]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[Crossref] [PubMed]

Chen, M.-C.

C. A. Mancuso, D. D. Hickstein, P. Grychtol, R. Knut, O. Kfir, X. M. Tong, F. Dollar, D. Zusin, M. Gopalakrishnan, C. Gentry, E. Turgut, J. L. Ellis, M.-C. Chen, A. Fleischer, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Strong-field ionization with two-color circularly polarized laser fields,” Phys. Rev. A. 91, 031402 (2015).
[Crossref]

Chen, S. G.

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[Crossref] [PubMed]

Chen, Y. J.

X. Y. Lai, C. L. Wang, Y. J. Chen, Z. L. Hu, W. Quan, X. J. Liu, J. Chen, Y. Cheng, Z. Z. Xu, and W. Becker, “Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases,” Phys. Rev. Lett. 110, 043002 (2013).
[Crossref] [PubMed]

Chen, Z.

C. D. Lin, A.-T. Le, Z. Chen, T. Morishita, and R. Lucchese, “Strong-field rescattering physics — self-imaging of a molecule by its own electrons,” J. Phys. B. 43, 122001 (2010).
[Crossref]

Cheng, Y.

X. Y. Lai, C. L. Wang, Y. J. Chen, Z. L. Hu, W. Quan, X. J. Liu, J. Chen, Y. Cheng, Z. Z. Xu, and W. Becker, “Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases,” Phys. Rev. Lett. 110, 043002 (2013).
[Crossref] [PubMed]

W. Quan, Z. Lin, M. Wu, H. Kang, H. Liu, X. Liu, J. Chen, J. Liu, X. T. He, S. G. Chen, H. Xiong, L. Guo, H. Xu, Y. Fu, Y. Cheng, and Z. Z. Xu, “Classical aspects in above-threshold ionization with a midinfrared strong laser field,” Phys. Rev. Lett. 103, 093001 (2009).
[Crossref] [PubMed]

Cirelli, C.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, R. Dörner, and U. Keller, “Timing the release in sequential double ionization,” Nat. Phys. 7, 428–433 (2011).
[Crossref]

Cohen, O.

C. A. Mancuso, D. D. Hickstein, P. Grychtol, R. Knut, O. Kfir, X. M. Tong, F. Dollar, D. Zusin, M. Gopalakrishnan, C. Gentry, E. Turgut, J. L. Ellis, M.-C. Chen, A. Fleischer, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Strong-field ionization with two-color circularly polarized laser fields,” Phys. Rev. A. 91, 031402 (2015).
[Crossref]

T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. Dorney, C. Chen, O. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015).
[Crossref] [PubMed]

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, “Spin angular momentum and tunable polarization in high-harmonic generation,” Nat. Photonics 8, 543–549 (2014).
[Crossref]

Colosimo, P.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5, 335–338 (2009).
[Crossref]

Comtois, D.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[Crossref] [PubMed]

Corkum, P. B.

M. Meckel, D. Comtois, D. Zeidler, A. Staudte, D. Pavičić, H. C. Bandulet, H. Pépin, J. C. Kieffer, R. Dörner, D. M. Villeneuve, and P. B. Corkum, “Laser-induced electron tunneling and diffraction,” Science 320, 1478–1482 (2008).
[Crossref] [PubMed]

M. Lewenstein, Ph. Balcou, M. Yu. 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] [PubMed]

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

Cornolti, F.

F. Ceccherini, D. Bauer, and F. Cornolti, “Harmonic generation by atoms in circularly polarized two-color laser fields with coplanar polarizations and commensurate frequencies,” Phys. Rev. A. 68, 053402 (2003).
[Crossref]

Dax, A.

G. Lambert, B. Vodungbo, J. Gautier, B. Mahieu, V. Malka, S. Sebban, P. Zeitoun, J. Luning, J. Perron, A. Andreev, S. Stremoukhov, F. Ardana-Lamas, A. Dax, C. P. Hauri, A. Sardinha, and M. Fajardo, “Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources,” Nat. Commun. 6, 6167 (2015).
[Crossref] [PubMed]

DiChiara, A. D.

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F. DiMauro, and C. D. Lin, “Imaging ultrafast molecular dynamics with laser-induced electron diffraction,” Nature (London) 483, 194–197 (2012).
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Figures (7)

Fig. 1
Fig. 1 Electric field vector E(t) (black solid line) and the corresponding vectors A(t) (red dashed line) and its integral α(t) (cyan dot-dashed line) of the ω–2ω bicircular laser field (5). The various symbols and their colors refer to the instants of ionization (I) and rescattering (R) of certain quantum orbits that are identified in Fig. 6 by the solid lines and discussed in this context. The arrows indicate the temporal evolution of the field vectors.
Fig. 2
Fig. 2 The differential ionization rate (in a.u.) of Ne atoms, presented in false colors in the electron momentum plane for ionization by a bicircular ω–2ω laser field with equal intensity of both components I1 = I2 = 2×1014 W/cm2 and the fundamental wavelength of 800 nm (Up1 = 0.4392 a.u., 20 U p 1 = 2.964 a . u .). The results are obtained by numerical integration of the direct SFA matrix element. The false color scale is logarithmic for the right panel and linear and normalized to 1 for the left panel.
Fig. 3
Fig. 3 The logarithm of the differential ionization rate for the same parameters as in Fig. 2. The ISFA result (4) is obtained by two-dimensional numerical integration and using four 2p Slater-type orbitals to represent the ground state of the Ne atom.
Fig. 4
Fig. 4 The logarithm of the differential ionization rate for the same parameters as in Fig. 2, but for the ω–3ω field. In the left panel the coherent sum of the SFA and ISFA results is shown, while in the right panel only the ISFA result (4) is presented. The scale is logarithmic and the results are normalized to 1 in each panel separately.
Fig. 5
Fig. 5 Comparison of the differential ionization rates as function of the electron energy (in units of the ponderomotive energy of the ω field component) for the same parameters as in Fig. 3 and emission into the angle θ = 50°. The results obtained by numerical integration are presented by the black solid line with the circles, while the coherent sum of the contributions of 14 saddle-point solutions is represented by the solid red line with squares. The contributions of the divergent solutions (dashed lines) are neglected after the corresponding cutoff values. The partial contributions of each of the 14 solutions (α,β,m) are presented separately, as denoted. The spectrum that includes both the direct and the rescattered electron, obtained by numerical integration, is represented by small diamonds and denoted by D + R.
Fig. 6
Fig. 6 Electron trajectories for some of the quantum-orbit solutions presented in Fig. 5. The electron energies for the presented pairs α = ±1 of solutions are 10Up1 for solutions (β,m) = (1,0) and (2,0), 7Up1 for solutions (3, 0), and 9Up1 for solutions (1, 1). The ionization and rescattering times of the depicted orbits can be identified in Fig. 1.
Fig. 7
Fig. 7 Same as in Fig. 3 but obtained using the saddle-point method with the solutions (α,β,m) = (±1,1,0) (upper left panel), and the forward-scattering solutions (ν,μ) = (1,0) (upper right panel) and (ν,μ) = (±1,1) (lower left panel). In the lower right panel the coherent sum of all above-mentioned contributions is presented.

Equations (9)

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M p i ( t , t ) = ψ p ( t ) | U ( t , t ) | ψ i ( t ) ,
M p i ( t , t ) = M p i D ( t , t ) + M p i R ( t , t ) ,
M p i D ( t , t ) = i t t d τ ψ p ( t ) | U L ( t , τ ) V L ( τ ) | ψ i ( τ ) ,
M p i R ( t , t ) = ( i ) 2 t t d τ τ t d τ ψ p ( t ) | U L ( t , τ ) × V ( r ) U ( τ , τ ) V L ( τ ) | ψ i ( τ ) .
E ( t ) = i ( E 1 e ^ + e i r ω t + E 2 e ^ e i s ω t ) / 2 + c . c . ,
( t r t 0 ) k = t 0 t r d t A ( t ) ,
[ k + A ( t 0 ) ] 2 / 2 = I p ,
[ k + A ( t r ) ] 2 / 2 = [ p + A ( t r ) ] 2 / 2 ,
r ( s ) ( t ) = { ( t t 0 s ) k s + α ( t ) α ( t 0 s ) , ( t t r s ) p + α ( t ) α ( t r s ) ,

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