Abstract

The canonical framework of optical physics connects the validity of perturbative nonlinear optics to the smallness of the optical driver field E compared to a characteristic field Eat that acts on electrons in an atom, a molecule, or a crystal lattice. However, in a vast area of strong-field optical science, the borderline between perturbative and nonperturbative nonlinear optics is defined as γ ~1, where γ is the Keldysh parameter. Not only is this criterion frequency-dependent, in a stark contrast with E/Eat ~1, but it also often dictates much weaker fields at which the perturbative treatment is still valid, leading to a dramatic shrinkage in the convergence radius of perturbation-theory expansions. Here, we identify the physics behind the gap between the E/Eat ~1 and γ ~1 conditions as the limits of perturbative nonlinear optics. We argue that, while the criterion E/Eat << 1 sets a universal upper-bound limit on the validity of perturbative nonlinear optics and its central concept of nonlinear-optical susceptibilities, optical nonlinearities related to photoionization pathways become nonperturbative in much weaker optical fields, with the limits of a perturbative treatment defined by the Keldysh parameter γ rather than the E/Eat ratio.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Multioctave supercontinua and subcycle lightwave electronics [Invited]

Aleksei Zheltikov
J. Opt. Soc. Am. B 36(2) A168-A182 (2019)

Solvable approximate model for the harmonic radiation from atoms subjected to oscillatory electric fields

L. C. Biedenharn, G. A. Rinker, and Johndale C. Solem
J. Opt. Soc. Am. B 6(2) 221-227 (1989)

Nonperturbative treatments of nonresonant multiphoton ionization of the hydrogen atom: weak-field limit

F. Trombetta, S. Basile, and G. Ferrante
J. Opt. Soc. Am. B 6(4) 554-559 (1989)

References

  • View by:
  • |
  • |
  • |

  1. N. Bloembergen, Nonlinear Optics (New York: W.A. Benjamin, 1965).
  2. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, Orlando, 2008).
  3. Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York, 1984).
  4. L. V. Keldysh, “Ionization in Field of a Strong Electromagnetic Wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1952 (1964).
  5. N. B. Delone and V. P. Krainov, Multiphoton Processes in Atoms (Berlin, New York: Springer-Verlag, 1994).
  6. S. V. Popruzhenko, “Keldysh theory of strong field ionization: history, applications, difficulties and perspectives,” J. Phys. B 47(20), 204001 (2014).
    [Crossref]
  7. A. M. Zheltikov, “Keldysh photoionization theory: through the barriers,” Phys. Uspekhi 60(11), 1087–1120 (2017).
    [Crossref]
  8. M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, and Van Stryland EW, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
    [Crossref] [PubMed]
  9. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
    [Crossref]
  10. D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
    [Crossref]
  11. B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984).
    [Crossref]
  12. H. S. Brandi and C. B. de Araujo, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. (Paris) C,  16, 5929–5936 (1983).
  13. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
    [Crossref]
  14. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
    [Crossref]
  15. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Oxford: Butterworth-Heinemann, 1991).
  16. J. J. Sakurai and J. J. Napolitano, Modern Quantum Mechanics, 2nd ed. (Addison Wesley, New York, 2010)
  17. D. M. Volkov, “Über eine Klasse von Lösungen der Diracschen Gleichung,” Z. Phys. 94(3-4), 250–260 (1935).
    [Crossref]
  18. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of Atoms in an Alternating Electric Field,” Sov. Phys. JETP 23, 924–939 (1966).
  19. N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
    [Crossref]
  20. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
    [Crossref] [PubMed]
  21. A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
    [Crossref] [PubMed]
  22. A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
    [Crossref]
  23. A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
    [Crossref]
  24. A. M. Zheltikov, “Laser-induced filaments in the mid-infrared,” J. Phys. At. Mol. Opt. Phys. 50(9), 092001 (2017).
    [Crossref]
  25. A. I. Baz, Y. B. Zeldovich, and A. M. Perelomov, Rasseyanie, Reaktsii i Raspady v Nerelyativistskoi Kvantovoi Mekhanike, 2nd ed. (Moscow: Nauka, 1971) [Scattering, Reactions and Decay in Nonrelativistic Quantum Mechanics (Jerusalem: Israel Program for Scientific Translations, 1969)].
  26. P. L. Kapitza, “Dynamic stability of the pendulum with vibrating suspension point,” Sov. Phys. JETP 21, 588–597 (1951).
  27. P. L. Kapitza, “A pendulum with vibrating point of suspension,” Sov. Phys. Usp. 44, 7–29 (1951).
    [Crossref]
  28. L. D. Landau and E. M. Lifshitz, Mechanics (New York, Pergamon, 1960).
  29. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
    [Crossref] [PubMed]
  30. P. Balcou, A. S. Dederichs, M. B. Gaarde, and A. L’Huillier, “Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields,” J. Phys. At. Mol. Opt. Phys. 32(12), 2973–2989 (1999).
    [Crossref]
  31. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
    [Crossref]
  32. P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
    [Crossref]
  33. J. E. Sipe and E. Ghahramani, “Nonlinear optical response of semiconductors in the independent-particle approximation,” Phys. Rev. B Condens. Matter 48(16), 11705–11722 (1993).
    [Crossref] [PubMed]
  34. C. Aversa, J. E. Sipe, M. Sheik-Bahae, E. W. Van Stryland, and Van Stryland EW, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
    [Crossref] [PubMed]
  35. G. L. Yudin and M. Yu. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64(1), 013409 (2001).
    [Crossref]
  36. P. A. Zhokhov and A. M. Zheltikov, “Field-cycle-resolved photoionization in solids,” Phys. Rev. Lett. 113(13), 133903 (2014).
    [Crossref] [PubMed]
  37. E. E. Serebryannikov and A. M. Zheltikov, “Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle,” Phys. Rev. Lett. 113(4), 043901 (2014).
    [Crossref] [PubMed]
  38. S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
    [Crossref]
  39. O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
    [Crossref]
  40. G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
    [Crossref] [PubMed]
  41. T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
    [Crossref] [PubMed]
  42. A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
    [Crossref]

2017 (6)

A. M. Zheltikov, “Keldysh photoionization theory: through the barriers,” Phys. Uspekhi 60(11), 1087–1120 (2017).
[Crossref]

N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. M. Zheltikov, “Laser-induced filaments in the mid-infrared,” J. Phys. At. Mol. Opt. Phys. 50(9), 092001 (2017).
[Crossref]

P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
[Crossref]

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
[Crossref]

2016 (1)

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

2015 (3)

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

2014 (4)

P. A. Zhokhov and A. M. Zheltikov, “Field-cycle-resolved photoionization in solids,” Phys. Rev. Lett. 113(13), 133903 (2014).
[Crossref] [PubMed]

E. E. Serebryannikov and A. M. Zheltikov, “Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle,” Phys. Rev. Lett. 113(4), 043901 (2014).
[Crossref] [PubMed]

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

S. V. Popruzhenko, “Keldysh theory of strong field ionization: history, applications, difficulties and perspectives,” J. Phys. B 47(20), 204001 (2014).
[Crossref]

2012 (1)

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

2011 (1)

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

2009 (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

2007 (2)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

2001 (1)

G. L. Yudin and M. Yu. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64(1), 013409 (2001).
[Crossref]

1999 (1)

P. Balcou, A. S. Dederichs, M. B. Gaarde, and A. L’Huillier, “Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields,” J. Phys. At. Mol. Opt. Phys. 32(12), 2973–2989 (1999).
[Crossref]

1994 (1)

C. Aversa, J. E. Sipe, M. Sheik-Bahae, E. W. Van Stryland, and Van Stryland EW, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

1993 (2)

J. E. Sipe and E. Ghahramani, “Nonlinear optical response of semiconductors in the independent-particle approximation,” Phys. Rev. B Condens. Matter 48(16), 11705–11722 (1993).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

1992 (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

1990 (1)

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, and Van Stryland EW, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

1984 (1)

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984).
[Crossref]

1983 (1)

H. S. Brandi and C. B. de Araujo, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. (Paris) C,  16, 5929–5936 (1983).

1966 (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of Atoms in an Alternating Electric Field,” Sov. Phys. JETP 23, 924–939 (1966).

1964 (1)

L. V. Keldysh, “Ionization in Field of a Strong Electromagnetic Wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1952 (1964).

1951 (2)

P. L. Kapitza, “Dynamic stability of the pendulum with vibrating suspension point,” Sov. Phys. JETP 21, 588–597 (1951).

P. L. Kapitza, “A pendulum with vibrating point of suspension,” Sov. Phys. Usp. 44, 7–29 (1951).
[Crossref]

1935 (1)

D. M. Volkov, “Über eine Klasse von Lösungen der Diracschen Gleichung,” Z. Phys. 94(3-4), 250–260 (1935).
[Crossref]

Abanador, P. M.

P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
[Crossref]

Agostini, P.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Ališauskas, S.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Andriukaitis, G.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Arpin, P.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Aversa, C.

C. Aversa, J. E. Sipe, M. Sheik-Bahae, E. W. Van Stryland, and Van Stryland EW, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

Balciunas, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Balcou, P.

P. Balcou, A. S. Dederichs, M. B. Gaarde, and A. L’Huillier, “Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields,” J. Phys. At. Mol. Opt. Phys. 32(12), 2973–2989 (1999).
[Crossref]

Baltuška, A.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Becker, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Brabec, T.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

Brandi, H. S.

H. S. Brandi and C. B. de Araujo, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. (Paris) C,  16, 5929–5936 (1983).

Brown, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Chen, M.-C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Corkum, P. B.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

Couairon, A.

N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
[Crossref]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

de Araujo, C. B.

H. S. Brandi and C. B. de Araujo, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. (Paris) C,  16, 5929–5936 (1983).

Dederichs, A. S.

P. Balcou, A. S. Dederichs, M. B. Gaarde, and A. L’Huillier, “Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields,” J. Phys. At. Mol. Opt. Phys. 32(12), 2973–2989 (1999).
[Crossref]

DiChiara, A. D.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

DiMauro, L. F.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Fedotov, A. B.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

Flöry, T.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

Gaarde, M. B.

P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
[Crossref]

P. Balcou, A. S. Dederichs, M. B. Gaarde, and A. L’Huillier, “Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields,” J. Phys. At. Mol. Opt. Phys. 32(12), 2973–2989 (1999).
[Crossref]

Gaeta, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Garg, M.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Ghahramani, E.

J. E. Sipe and E. Ghahramani, “Nonlinear optical response of semiconductors in the independent-particle approximation,” Phys. Rev. B Condens. Matter 48(16), 11705–11722 (1993).
[Crossref] [PubMed]

Ghimire, S.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Golde, D.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Goulielmakis, E.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Guizard, S.

N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
[Crossref]

Hagan, D. J.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, and Van Stryland EW, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

Hammond, T. J.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

Hassan, M. Th.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Hernández-García, C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Hohenleutner, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Huber, R.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Hutchings, D. C.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

Huttner, U.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

Ivanov, M. Yu.

G. L. Yudin and M. Yu. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64(1), 013409 (2001).
[Crossref]

Jaron-Becker, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Kapitza, P. L.

P. L. Kapitza, “Dynamic stability of the pendulum with vibrating suspension point,” Sov. Phys. JETP 21, 588–597 (1951).

P. L. Kapitza, “A pendulum with vibrating point of suspension,” Sov. Phys. Usp. 44, 7–29 (1951).
[Crossref]

Kapteyn, H. C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Kasparian, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Keldysh, L. V.

L. V. Keldysh, “Ionization in Field of a Strong Electromagnetic Wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1952 (1964).

Kira, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Koch, S. W.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Krausz, F.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

Kruchinin, S. Yu.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

L’Huillier, A.

P. Balcou, A. S. Dederichs, M. B. Gaarde, and A. L’Huillier, “Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields,” J. Phys. At. Mol. Opt. Phys. 32(12), 2973–2989 (1999).
[Crossref]

Lange, C.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Langer, F.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Lanin, A. A.

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
[Crossref]

Légaré, F.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

Lopata, K.

P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
[Crossref]

Luu, T. T.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Mauger, F.

P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
[Crossref]

McDonald, C. R.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

Meier, T.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Meshchankin, D. V.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

Mitrofanov, A. V.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

Mitryukovsky, S. I.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

Moulet, A.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Mücke, O. D.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Murnane, M. M.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Panchenko, V. Ya.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of Atoms in an Alternating Electric Field,” Sov. Phys. JETP 23, 924–939 (1966).

Plaja, L.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Popmintchev, D.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Popmintchev, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of Atoms in an Alternating Electric Field,” Sov. Phys. JETP 23, 924–939 (1966).

Popruzhenko, S. V.

S. V. Popruzhenko, “Keldysh theory of strong field ionization: history, applications, difficulties and perspectives,” J. Phys. B 47(20), 204001 (2014).
[Crossref]

Povarnitsyn, M. E.

N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
[Crossref]

Pugžlys, A.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Reis, D. A.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Rozhko, M. V.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

Schafer, K. J.

P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
[Crossref]

Schmidt, B. E.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

Schrauth, S. E.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Schubert, O.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Serebryannikov, E. E.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

E. E. Serebryannikov and A. M. Zheltikov, “Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle,” Phys. Rev. Lett. 113(4), 043901 (2014).
[Crossref] [PubMed]

Shcheblanov, N. S.

N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
[Crossref]

Sheik-Bahae, M.

C. Aversa, J. E. Sipe, M. Sheik-Bahae, E. W. Van Stryland, and Van Stryland EW, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, and Van Stryland EW, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

Shim, B.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Shumakova, V.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

Sidorov-Biryukov, D. A.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

Sipe, J. E.

C. Aversa, J. E. Sipe, M. Sheik-Bahae, E. W. Van Stryland, and Van Stryland EW, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

J. E. Sipe and E. Ghahramani, “Nonlinear optical response of semiconductors in the independent-particle approximation,” Phys. Rev. B Condens. Matter 48(16), 11705–11722 (1993).
[Crossref] [PubMed]

Sistrunk, E.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Stepanov, E. A.

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

Terekhin, P. N.

N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
[Crossref]

Terent’ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of Atoms in an Alternating Electric Field,” Sov. Phys. JETP 23, 924–939 (1966).

Thiré, N.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

Urbanek, B.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Vampa, G.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

Van Stryland, E. W.

C. Aversa, J. E. Sipe, M. Sheik-Bahae, E. W. Van Stryland, and Van Stryland EW, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, and Van Stryland EW, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

Volkov, D. M.

D. M. Volkov, “Über eine Klasse von Lösungen der Diracschen Gleichung,” Z. Phys. 94(3-4), 250–260 (1935).
[Crossref]

Voronin, A. A.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

Wherrett, B. S.

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984).
[Crossref]

Wolf, J.-P.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Yudin, G. L.

G. L. Yudin and M. Yu. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64(1), 013409 (2001).
[Crossref]

Zheltikov, A. M.

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. M. Zheltikov, “Laser-induced filaments in the mid-infrared,” J. Phys. At. Mol. Opt. Phys. 50(9), 092001 (2017).
[Crossref]

A. M. Zheltikov, “Keldysh photoionization theory: through the barriers,” Phys. Uspekhi 60(11), 1087–1120 (2017).
[Crossref]

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

E. E. Serebryannikov and A. M. Zheltikov, “Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle,” Phys. Rev. Lett. 113(4), 043901 (2014).
[Crossref] [PubMed]

P. A. Zhokhov and A. M. Zheltikov, “Field-cycle-resolved photoionization in solids,” Phys. Rev. Lett. 113(13), 133903 (2014).
[Crossref] [PubMed]

Zhokhov, P. A.

P. A. Zhokhov and A. M. Zheltikov, “Field-cycle-resolved photoionization in solids,” Phys. Rev. Lett. 113(13), 133903 (2014).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

J. Opt. Soc. Am. B (1)

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984).
[Crossref]

J. Phys. (Paris) C (1)

H. S. Brandi and C. B. de Araujo, “Multiphonon absorption coefficients in solids: a universal curve,” J. Phys. (Paris) C,  16, 5929–5936 (1983).

J. Phys. At. Mol. Opt. Phys. (3)

A. M. Zheltikov, “Laser-induced filaments in the mid-infrared,” J. Phys. At. Mol. Opt. Phys. 50(9), 092001 (2017).
[Crossref]

P. Balcou, A. S. Dederichs, M. B. Gaarde, and A. L’Huillier, “Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields,” J. Phys. At. Mol. Opt. Phys. 32(12), 2973–2989 (1999).
[Crossref]

P. M. Abanador, F. Mauger, K. Lopata, M. B. Gaarde, and K. J. Schafer, “Semiclassical modeling of high-order harmonic generation driven by an elliptically polarized laser field: the role of recolliding periodic orbits,” J. Phys. At. Mol. Opt. Phys. 50(3), 035601 (2017).
[Crossref]

J. Phys. B (1)

S. V. Popruzhenko, “Keldysh theory of strong field ionization: history, applications, difficulties and perspectives,” J. Phys. B 47(20), 204001 (2014).
[Crossref]

Nat. Photonics (1)

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Nat. Phys. (1)

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Nature (2)

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref] [PubMed]

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref] [PubMed]

Opt. Quantum Electron. (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

Optica (3)

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, M. V. Rozhko, D. A. Sidorov-Biryukov, A. B. Fedotov, A. Pugžlys, V. Shumakova, S. Ališauskas, A. Baltuška, and A. M. Zheltikov, “Self-compression of high-peak-power mid-infrared pulses in anomalously dispersive air,” Optica 4(11), 1405–1408 (2017).
[Crossref]

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (2017).
[Crossref]

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

Phys. Rev. A (1)

G. L. Yudin and M. Yu. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64(1), 013409 (2001).
[Crossref]

Phys. Rev. A (Coll. Park) (1)

N. S. Shcheblanov, M. E. Povarnitsyn, P. N. Terekhin, S. Guizard, and A. Couairon, “Nonlinear photoionization of transparent solids: A nonperturbative theory obeying selection rules,” Phys. Rev. A (Coll. Park) 96(6), 063410 (2017).
[Crossref]

Phys. Rev. B Condens. Matter (2)

J. E. Sipe and E. Ghahramani, “Nonlinear optical response of semiconductors in the independent-particle approximation,” Phys. Rev. B Condens. Matter 48(16), 11705–11722 (1993).
[Crossref] [PubMed]

C. Aversa, J. E. Sipe, M. Sheik-Bahae, E. W. Van Stryland, and Van Stryland EW, “Third-order optical nonlinearities in semiconductors: The two-band model,” Phys. Rev. B Condens. Matter 50(24), 18073–18082 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

P. A. Zhokhov and A. M. Zheltikov, “Field-cycle-resolved photoionization in solids,” Phys. Rev. Lett. 113(13), 133903 (2014).
[Crossref] [PubMed]

E. E. Serebryannikov and A. M. Zheltikov, “Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle,” Phys. Rev. Lett. 113(4), 043901 (2014).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, and Van Stryland EW, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

Phys. Uspekhi (1)

A. M. Zheltikov, “Keldysh photoionization theory: through the barriers,” Phys. Uspekhi 60(11), 1087–1120 (2017).
[Crossref]

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Rev. Mod. Phys. (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

Sci. Rep. (1)

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5(1), 8368 (2015).
[Crossref] [PubMed]

Science (1)

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugžlys, A. Baltuška, 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(6086), 1287–1291 (2012).
[Crossref] [PubMed]

Sov. Phys. JETP (2)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of Atoms in an Alternating Electric Field,” Sov. Phys. JETP 23, 924–939 (1966).

P. L. Kapitza, “Dynamic stability of the pendulum with vibrating suspension point,” Sov. Phys. JETP 21, 588–597 (1951).

Sov. Phys. Usp. (1)

P. L. Kapitza, “A pendulum with vibrating point of suspension,” Sov. Phys. Usp. 44, 7–29 (1951).
[Crossref]

Z. Phys. (1)

D. M. Volkov, “Über eine Klasse von Lösungen der Diracschen Gleichung,” Z. Phys. 94(3-4), 250–260 (1935).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

L. V. Keldysh, “Ionization in Field of a Strong Electromagnetic Wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1952 (1964).

Other (8)

N. B. Delone and V. P. Krainov, Multiphoton Processes in Atoms (Berlin, New York: Springer-Verlag, 1994).

N. Bloembergen, Nonlinear Optics (New York: W.A. Benjamin, 1965).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, Orlando, 2008).

Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York, 1984).

L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Oxford: Butterworth-Heinemann, 1991).

J. J. Sakurai and J. J. Napolitano, Modern Quantum Mechanics, 2nd ed. (Addison Wesley, New York, 2010)

L. D. Landau and E. M. Lifshitz, Mechanics (New York, Pergamon, 1960).

A. I. Baz, Y. B. Zeldovich, and A. M. Perelomov, Rasseyanie, Reaktsii i Raspady v Nerelyativistskoi Kvantovoi Mekhanike, 2nd ed. (Moscow: Nauka, 1971) [Scattering, Reactions and Decay in Nonrelativistic Quantum Mechanics (Jerusalem: Israel Program for Scientific Translations, 1969)].

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1 Nonlinear response of (a) bound-state electrons, (b) recolliding photoelectrons, and (c) photoelectrons in the outgoing wave packet. The perturbative regime: (d) a representative Feynman diagram of the perturbative nonlinear-optical response and (e) a photon diagram of multiphoton ionization. Nonperturbative nonlinear-optical response: (f) tunneling of bound-state electrons, (g) recolliding electron trajectories, and (h) photoelectron trajectories in the outgoing electron wave packet (top) and bursts of photoionization probabilities in the γ < 1 regime.

Equations (49)

Equations on this page are rendered with MathJax. Learn more.

P= χ ( 1 ) E+ χ ( 2 ) :EE+ χ ( 3 ) EEE+,
E/ E at <<1,
E at = m 1/2 ( 2 I p ) 3/2 e
γ={ ω ( 2m I p ) 1/2 eE for atoms ω ( m E g ) 1/2 eE for solids
i ψ( r,t ) t =Hψ( r,t )
H= H 0 +V( r,t )
H 0 = 2 2m 2 + U 0 ( r )
ψ( r,t )= n a n ( t ) ϕ n ( r )exp( i ε n t )
H 0 ϕ n = ε n ϕ n
| V mn |<<| ε m ε n |
V mn = ϕ m V ϕ n dr
V=eEr
ψ p ( r,t )=exp{ i P( t )r/ i/ ( 2m ) 0 t [ P( θ ) ] 2 dθ }
E( t )= E 0 cos( ωt )
P( t )=p+e ω 1 E 0 sin( ωt )
w( p,t )= ψ p * ( r,t )V( r,t ) ψ 0 ( r )dr
w K = 2π | L( p ) | 2 n δ( I 0 + p 2 2m + e 2 E 0 2 4m ω 2 nω ) d 3 p ( 2π ) 3
L( p )= 1 2π dξW( p+ e E 0 ω ξ )exp{ i ω 0 ξ [ I 0 + 1 2m ( p+ e E 0 ω u ) 2 ] du ( 1 u 2 ) 1/2 }
I 0 + 1 2m ( p+ e E 0 ω sinωt ) 2 =0
w K =Q( γ, I 0 ,ω )exp{ ξ( γ, I 0 ,ω ) }
ξ( γ, I 0 ,ω )= 2 ω I 0 ( 1+ 1 2 γ 2 )[ sin h 1 γγ ( 1+ γ 2 ) 1/2 1+2 γ 2 ]
w K exp{ ( 4/3 ) ( 2m ) 1/2 I 0 3/2 ( e E 0 ) 1 ( 1 γ 2 / 10 ) }
ψ( r,t )= ψ b ( r,t )+ ψ f ( r,t )
j= 2im ( ψ ψ ψ ),r
j= P ph / t
ψ( r,t )= t d t 1 d r 1 G( r,t; r 1 , t 1 ) U 0 ( r 1 )ψ( r 1 , t 1 )
[ i t + 2 2m 2 V( r,t ) ]G( r,t; r 1 , t 1 )=δ( t t 1 )δ( r r 1 )
G( r,t; r 1 , t 1 )=iΘ( t t 1 ) dp ψ p ( r 1 , t 1 ) ψ p ( r,t )
K( r,t; r 1 , t 1 )=G( r,t; r 1 , t 1 ) U 0 ( r 1 )
ψ( r,t )= ϕ 0 ( r )exp( i I p t )at t
ψ( r,t )= 1 ( 2π ) 3/2 dpM( p )exp[ i ( pr p 2 2m t ) ]
M( p )= i ( 2π ) 3/2 d t 1 exp[ i S( p, t 1 ) ] d r 1 exp[ i P( t 1 ) r 1 ] V 0 ( r 1 ) ψ 0 ( r 1 )
S( p,t )= 1 2m t 1 [ P 2 ( θ ) 2m + I p ]dθ
M( p )= i ( 2π ) 3/2 d t 1 e d r 1 exp{ i [ P( t 1 ) r 1 +S( p, t 1 ) ] } E( t 1 ) r 1 ψ 0 ( r 1 )
H= P 2 2m + U 0 (r)
H ¯ = p 2 2m + U q + U 0 (r)
U q = e 2 E 0 2 4m ω 2
m r ¨ = r U( r,t )
U( r,t )= U 0 ( r )+V( r,t )
r( t )=q( t )+ξ( t )
r ¯ ( t )=q( t )
U 0 q U 0 +ξ( t ) q 2 U 0
m q ¨ +m ξ ¨ q U 0 ξ q 2 U 0 +f+ξ q f
m ξ ¨ f
ξ f m ω 2
m q ¨ q U 0 f q f ¯ m ω 2
m q ¨ q U eff
U eff = U 0 + f 2 ¯ 2m ω 2
U eff = U 0 + e 2 E 0 2 4m ω 2

Metrics