Abstract

The optical Kerr effect, and the nonlinear polarization in general, represents an important light-matter interaction governing many regimes encountered in the nonlinear optics. We reason that in the context of optical filamentation one should distinguish the third-order Kerr effect occurring at relatively low light intensities from the effective Kerr nonlinearity relevant to higher intensity. While many properties of filaments can be captured well with a third-order nonlinear polarization model with a nonlinear index chosen somewhat higher than the true nonlinear index operative at low intensities, our comparative simulations indicate that some filamentation aspects carry significant signatures from the higher-order nonlinearity.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

J. K. Wahlstrand, S. Zahedpour, A. Bahl, M. Kolesik, and H. M. Milchberg, “Bound-electron nonlinearity beyond the ionization threshold,” Phys. Rev. Lett. 120, 183901 (2018).
[Crossref] [PubMed]

M. Nesrallah, A. Hakami, G. Bart, C. R. McDonald, C. Varin, and T. Brabec, “Measuring the Kerr nonlinearity via seeded Kerr instability amplification: conceptual analysis,” Opt. Express 26, 7646–7654 (2018).
[Crossref] [PubMed]

A. Nguyen, P. González de Alaiza Martínez, I. Thiele, S. Skupin, and L. Bergé, “Broadband terahertz radiation from two-color mid- and far-infrared laser filaments in air,” Phys. Rev. A 97, 063839 (2018).
[Crossref]

2017 (5)

A. Bahl, J. K. Wahlstrand, S. Zahedpour, H. Milchberg, and M. Kolesik, “Nonlinear optical polarization response and plasma generation in noble gases: Comparison of MESA models to experiments,” Phys. Rev. A 96, 043867 (2017).
[Crossref]

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

J. Doussot, G. Karras, F. Billard, P. Béjot, and O. Faucher, “Resonantly enhanced filamentation in gases,” Optica 4, 764–769 (2017).
[Crossref]

R. Šuminas, G. Tamošauskas, G. Valiulis, V. Jukna, A. Couairon, and A. Dubietis, “Multi-octave spanning nonlinear interactions induced by femtosecond filamentation in polycrystalline znse,” Appl. Phys. Lett. 110, 241106 (2017).
[Crossref]

R. Šuminas, G. Tamošauskas, V. Jukna, A. Couairon, and A. Dubietis, “Second-order cascading-assisted filamentation and controllable supercontinuum generation in birefringent crystals,” Opt. Express 25, 6746–6756 (2017).
[Crossref] [PubMed]

2016 (6)

N. Garejev, V. Jukna, G. Tamošauskas, M. Veličkė, R. Šuminas, A. Couairon, and A. Dubietis, “Odd harmonics-enhanced supercontinuum in bulk solid-state dielectric medium,” Opt. Express 24, 17060–17068 (2016).
[Crossref] [PubMed]

M. Hofmann and C. Brée, “Adiabatic Floquet model for the optical response in femtosecond filaments,” J. Phys. B: At. Mol. Opt. Phys. 49, 205004 (2016).
[Crossref]

A. Bahl, E. M. Wright, and M. Kolesik, “Nonlinear optical response of noble gases via the metastable electronic state approach,” Phys. Rev. A 94, 023850 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, M. V. Rozhko, A. Pugžlys, A. B. Fedotov, V. Y. Panchenko, A. Baltuška, and A. M. Zheltikov, “Angle-resolved multioctave supercontinua from mid-infrared laser filaments,” Opt. Lett. 41, 3479–3482 (2016).
[Crossref] [PubMed]

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

2015 (12)

A. V. Mitrofanov, A. A. Voronin, S. I. Mitryukovskiy, D. A. Sidorov-Biryukov, A. Pugžlys, G. Andriukaitis, T. Flöry, E. A. Stepanov, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared-to-mid-ultraviolet supercontinuum enhanced by third-to-fifteenth odd harmonics,” Opt. Lett. 40, 2068–2071 (2015).
[Crossref] [PubMed]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

A. Bahl, J. M. Brown, E. M. Wright, and M. Kolesik, “Assessment of the metastable electronic state approach as a microscopically self-consistent description for the nonlinear response of atoms,” Opt. Lett. 40, 4987–4990 (2015).
[Crossref] [PubMed]

M. Hofmann and C. Brée, “Femtosecond filamentation by intensity clamping at a Freeman resonance,” Phys. Rev. A 92, 013813 (2015).
[Crossref]

J. Doussot, P. Béjot, G. Karras, F. Billard, and O. Faucher, “Phase control of two-color filamentation,” J. Phys. B: Atom. Mol. Opt. Phys. 48, 184005 (2015).
[Crossref]

L. Wang and W. Lin, “The impact of the varied nonlinear refractive index of higher-order Kerr effect on the laser pulse’s propagation,” Optik - Int. J. for Light. Electron Opt. 126, 5387–5391 (2015).
[Crossref]

L. Su-Yu, G. Fu-Ming, Y. Yu-Jun, and J. Ming-Xing, “Defocusing role in femtosecond filamentation: Higher-order Kerr effect or plasma effect?” Chin. Phys. B 24, 114207 (2015).
[Crossref]

M. Hofmann and C. Brée, “Femtosecond filamentation by intensity clamping at a Freeman resonance,” Phys. Rev. A 92, 013813 (2015).
[Crossref]

E. Lorin, M. Lytova, A. Memarian, and A. D. Bandrauk, “Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell — Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model,” J. Phys. A: Math. Theor. 48, 105201 (2015).
[Crossref]

A. A. Lanin, A. A. Voronin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Multioctave, sub-two-cycle supercontinua from self-compressing, self-focusing soliton transients in a solid,” Opt. Lett. 40, 974–977 (2015).
[Crossref] [PubMed]

H. Liang, P. Krogen, R. Grynko, O. Novak, C.-L. Chang, G. J. Stein, D. Weerawarne, B. Shim, F. X. Kärtner, and K.-H. Hong, “Three-octave-spanning supercontinuum generation and sub-two-cycle self-compression of mid-infrared filaments in dielectrics,” Opt. Lett. 40, 1069–1072 (2015).
[Crossref] [PubMed]

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114, 093901 (2015).
[Crossref] [PubMed]

2014 (7)

M. Tarazkar, D. A. Romanov, and R. J. Levis, “High-order nonlinear refractive indices for He, Ne, Kr, and Xe atoms,” Phys. Rev. A 90, 062514 (2014).
[Crossref]

M. Tarazkar, D. A. Romanov, and R. J. Levis, “Higher-order nonlinearity of refractive index: The case of argon,” The J. Chem. Phys. 140, 214316 (2014).
[Crossref] [PubMed]

D. Wang and Y. Leng, “Measuring high-order Kerr effects of noble gases based on spectral analysis,” Opt. Commun. 328, 41–48 (2014).
[Crossref]

T. C. Rensink, T. M. Antonsen, J. P. Palastro, and D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

M. Kolesik, J.M. Brown, A. Teleki, P. Jakobsen, J.V. Moloney, and E. M. Wright, “Metastable electronic states and nonlinear response for high-intensity optical pulses,” Optica 1, 323 (2014).
[Crossref]

A. Gorodetsky, A. D. Koulouklidis, M. Massaouti, and S. Tzortzakis, “Physics of the conical broadband terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. A 89, 033838 (2014).
[Crossref]

S. I. Mitryukovskiy, Y. Liu, B. Prade, A. Houard, and A. Mysyrowicz, “Coherent interaction between the terahertz radiation emitted by filaments in air,” Laser Phys. 24, 094009 (2014).
[Crossref]

2013 (2)

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

A. Nath, J. A. Dharmadhikari, A. K. Dharmadhikari, and D. Mathur, “Seventh-harmonic generation from tightly focused 2 um ultrashort pulses in air,” Opt. Lett. 38, 2560–2562 (2013).
[Crossref] [PubMed]

2012 (4)

G. O. Ariunbold, P. Polynkin, and J. V. Moloney, “Third and fifth harmonic generation by tightly focused femtosecond pulses at 2.2 μm wavelength in air,” Opt. Express 20, 1662–1667 (2012).
[Crossref] [PubMed]

E. Lorin, S. Chelkowski, E. Zaoui, and A. Bandrauk, “Maxwell–Schrödinger–Plasma (MASP) model for laser– molecule interactions: Towards an understanding of filamentation with intense ultrashort pulses,” Phys. D 241, 1059–1071 (2012).
[Crossref]

D. Kartashov, S. Ališauskas, A. Pugzdžlys, A. A. Voronin, A. M. Zheltikov, and A. Baltuška, “Third- and fifth-harmonic generation by mid-infrared ultrashort pulses:beyond the fifth-order nonlinearity,” Opt. Lett. 37, 2268–2270 (2012).
[Crossref] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett. 109, 113904 (2012).
[Crossref] [PubMed]

2011 (5)

C. Brée, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref] [PubMed]

Z. Wang, C. Zhang, J. Liu, R. Li, and Z. Xu, “Femtosecond filamentation in argon and higher-order nonlinearities,” Opt. Lett. 36, 2336–2338 (2011).
[Crossref] [PubMed]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[Crossref] [PubMed]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, and M. Kolesik, “Practitioner‘s guide to laser pulse propagation models and simulation,” The Eur. Phys. J. Special Top. 199, 5–76 (2011).
[Crossref]

J. M. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[Crossref]

2010 (5)

C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Laser Phys. 20, 1107–1113 (2010).
[Crossref]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[Crossref]

O. I. Tolstikhin, T. Morishita, and S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: One-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18, 3011–3012 (2010).
[Crossref]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2007 (4)

E. Lorin, S. Chelkowski, and A. Bandrauk, “A numerical Maxwell-Schrödinger model for intense laser-mater interaction and propagation,” Comp. Phys. Commun. 177, 908–932 (2007).
[Crossref]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 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, 1633–1713 (2007).
[Crossref]

M. A. Porras, A. Dubietis, A. Matijošius, R. Piskarskas, F. Bragheri, A. Averchi, and P. D. Trapani, “Characterization of conical emission of light filaments in media with anomalous dispersion,” J. Opt. Soc. Am. B 24, 581–584 (2007).
[Crossref]

2005 (1)

2004 (1)

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

2001 (2)

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

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

1964 (1)

E.R. Peck and D.J. Fisher, “Dispersion of Argon,” J. Opt. Soc. Am. 54, 1326 (1964).
[Crossref]

Abjean, R.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” 25, 395 (1981).

Aközbek, N.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Ališauskas, S.

Andreeva, V. A.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Andriukaitis, G.

Antonsen, T. M.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, and D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Ariunbold, G. O.

Averchi, A.

Bahl, A.

J. K. Wahlstrand, S. Zahedpour, A. Bahl, M. Kolesik, and H. M. Milchberg, “Bound-electron nonlinearity beyond the ionization threshold,” Phys. Rev. Lett. 120, 183901 (2018).
[Crossref] [PubMed]

A. Bahl, J. K. Wahlstrand, S. Zahedpour, H. Milchberg, and M. Kolesik, “Nonlinear optical polarization response and plasma generation in noble gases: Comparison of MESA models to experiments,” Phys. Rev. A 96, 043867 (2017).
[Crossref]

A. Bahl, E. M. Wright, and M. Kolesik, “Nonlinear optical response of noble gases via the metastable electronic state approach,” Phys. Rev. A 94, 023850 (2016).
[Crossref]

A. Bahl, J. M. Brown, E. M. Wright, and M. Kolesik, “Assessment of the metastable electronic state approach as a microscopically self-consistent description for the nonlinear response of atoms,” Opt. Lett. 40, 4987–4990 (2015).
[Crossref] [PubMed]

Baltuška, A.

Bandrauk, A.

E. Lorin, S. Chelkowski, E. Zaoui, and A. Bandrauk, “Maxwell–Schrödinger–Plasma (MASP) model for laser– molecule interactions: Towards an understanding of filamentation with intense ultrashort pulses,” Phys. D 241, 1059–1071 (2012).
[Crossref]

E. Lorin, S. Chelkowski, and A. Bandrauk, “A numerical Maxwell-Schrödinger model for intense laser-mater interaction and propagation,” Comp. Phys. Commun. 177, 908–932 (2007).
[Crossref]

Bandrauk, A. D.

E. Lorin, M. Lytova, A. Memarian, and A. D. Bandrauk, “Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell — Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model,” J. Phys. A: Math. Theor. 48, 105201 (2015).
[Crossref]

Bart, G.

Becker, A.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Béjot, P.

J. Doussot, G. Karras, F. Billard, P. Béjot, and O. Faucher, “Resonantly enhanced filamentation in gases,” Optica 4, 764–769 (2017).
[Crossref]

J. Doussot, P. Béjot, G. Karras, F. Billard, and O. Faucher, “Phase control of two-color filamentation,” J. Phys. B: Atom. Mol. Opt. Phys. 48, 184005 (2015).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[Crossref] [PubMed]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Bergé, L.

A. Nguyen, P. González de Alaiza Martínez, I. Thiele, S. Skupin, and L. Bergé, “Broadband terahertz radiation from two-color mid- and far-infrared laser filaments in air,” Phys. Rev. A 97, 063839 (2018).
[Crossref]

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Laser Phys. 20, 1107–1113 (2010).
[Crossref]

L. Bergé, “Self-compression of 2 μm laser filaments,” Opt. Express 16, 21529–21543 (2008).
[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, 1633–1713 (2007).
[Crossref]

Bideau-Mehu, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” 25, 395 (1981).

Billard, F.

J. Doussot, G. Karras, F. Billard, P. Béjot, and O. Faucher, “Resonantly enhanced filamentation in gases,” Optica 4, 764–769 (2017).
[Crossref]

J. Doussot, P. Béjot, G. Karras, F. Billard, and O. Faucher, “Phase control of two-color filamentation,” J. Phys. B: Atom. Mol. Opt. Phys. 48, 184005 (2015).
[Crossref]

Bowden, C.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Brabec, T.

Bragheri, F.

Brambilla, E.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, and M. Kolesik, “Practitioner‘s guide to laser pulse propagation models and simulation,” The Eur. Phys. J. Special Top. 199, 5–76 (2011).
[Crossref]

Brée, C.

M. Hofmann and C. Brée, “Adiabatic Floquet model for the optical response in femtosecond filaments,” J. Phys. B: At. Mol. Opt. Phys. 49, 205004 (2016).
[Crossref]

M. Hofmann and C. Brée, “Femtosecond filamentation by intensity clamping at a Freeman resonance,” Phys. Rev. A 92, 013813 (2015).
[Crossref]

M. Hofmann and C. Brée, “Femtosecond filamentation by intensity clamping at a Freeman resonance,” Phys. Rev. A 92, 013813 (2015).
[Crossref]

C. Brée, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref] [PubMed]

C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Laser Phys. 20, 1107–1113 (2010).
[Crossref]

Brown, J. M.

A. Bahl, J. M. Brown, E. M. Wright, and M. Kolesik, “Assessment of the metastable electronic state approach as a microscopically self-consistent description for the nonlinear response of atoms,” Opt. Lett. 40, 4987–4990 (2015).
[Crossref] [PubMed]

J. M. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[Crossref]

Brown, J.M.

Chang, C.-L.

Chelkowski, S.

E. Lorin, S. Chelkowski, E. Zaoui, and A. Bandrauk, “Maxwell–Schrödinger–Plasma (MASP) model for laser– molecule interactions: Towards an understanding of filamentation with intense ultrashort pulses,” Phys. D 241, 1059–1071 (2012).
[Crossref]

E. Lorin, S. Chelkowski, and A. Bandrauk, “A numerical Maxwell-Schrödinger model for intense laser-mater interaction and propagation,” Comp. Phys. Commun. 177, 908–932 (2007).
[Crossref]

Chen, S.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

Cheng, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett. 109, 113904 (2012).
[Crossref] [PubMed]

Chin, S.

W. Liu and S. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13, 5750–5755 (2005).
[Crossref] [PubMed]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Chin, S. L.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

S. L. Chin, Femtosecond Laser Filamentation (Springer, 2009).

Corti, T.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, and M. Kolesik, “Practitioner‘s guide to laser pulse propagation models and simulation,” The Eur. Phys. J. Special Top. 199, 5–76 (2011).
[Crossref]

Couairon, A.

R. Šuminas, G. Tamošauskas, G. Valiulis, V. Jukna, A. Couairon, and A. Dubietis, “Multi-octave spanning nonlinear interactions induced by femtosecond filamentation in polycrystalline znse,” Appl. Phys. Lett. 110, 241106 (2017).
[Crossref]

R. Šuminas, G. Tamošauskas, V. Jukna, A. Couairon, and A. Dubietis, “Second-order cascading-assisted filamentation and controllable supercontinuum generation in birefringent crystals,” Opt. Express 25, 6746–6756 (2017).
[Crossref] [PubMed]

N. Garejev, V. Jukna, G. Tamošauskas, M. Veličkė, R. Šuminas, A. Couairon, and A. Dubietis, “Odd harmonics-enhanced supercontinuum in bulk solid-state dielectric medium,” Opt. Express 24, 17060–17068 (2016).
[Crossref] [PubMed]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, and M. Kolesik, “Practitioner‘s guide to laser pulse propagation models and simulation,” The Eur. Phys. J. Special Top. 199, 5–76 (2011).
[Crossref]

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

Demircan, A.

C. Brée, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref] [PubMed]

C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Laser Phys. 20, 1107–1113 (2010).
[Crossref]

Dharmadhikari, A. K.

Dharmadhikari, J. A.

Doussot, J.

J. Doussot, G. Karras, F. Billard, P. Béjot, and O. Faucher, “Resonantly enhanced filamentation in gases,” Optica 4, 764–769 (2017).
[Crossref]

J. Doussot, P. Béjot, G. Karras, F. Billard, and O. Faucher, “Phase control of two-color filamentation,” J. Phys. B: Atom. Mol. Opt. Phys. 48, 184005 (2015).
[Crossref]

Dubietis, A.

Esaulkov, M. N.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Faucher, O.

Fedotov, A. B.

Fisher, D.J.

E.R. Peck and D.J. Fisher, “Dispersion of Argon,” J. Opt. Soc. Am. 54, 1326 (1964).
[Crossref]

Flöry, T.

Fu-Ming, G.

L. Su-Yu, G. Fu-Ming, Y. Yu-Jun, and J. Ming-Xing, “Defocusing role in femtosecond filamentation: Higher-order Kerr effect or plasma effect?” Chin. Phys. B 24, 114207 (2015).
[Crossref]

Gaeta, A. L.

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114, 093901 (2015).
[Crossref] [PubMed]

Gao, X.

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114, 093901 (2015).
[Crossref] [PubMed]

Garejev, N.

González de Alaiza Martínez, P.

A. Nguyen, P. González de Alaiza Martínez, I. Thiele, S. Skupin, and L. Bergé, “Broadband terahertz radiation from two-color mid- and far-infrared laser filaments in air,” Phys. Rev. A 97, 063839 (2018).
[Crossref]

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Gordon, D. F.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, and D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Gorodetsky, A.

A. Gorodetsky, A. D. Koulouklidis, M. Massaouti, and S. Tzortzakis, “Physics of the conical broadband terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. A 89, 033838 (2014).
[Crossref]

Grynko, R.

Guern, Y.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” 25, 395 (1981).

Hakami, A.

He, P.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

He, X.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

Henin, S.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Hertz, E.

Hofmann, M.

M. Hofmann and C. Brée, “Adiabatic Floquet model for the optical response in femtosecond filaments,” J. Phys. B: At. Mol. Opt. Phys. 49, 205004 (2016).
[Crossref]

M. Hofmann and C. Brée, “Femtosecond filamentation by intensity clamping at a Freeman resonance,” Phys. Rev. A 92, 013813 (2015).
[Crossref]

M. Hofmann and C. Brée, “Femtosecond filamentation by intensity clamping at a Freeman resonance,” Phys. Rev. A 92, 013813 (2015).
[Crossref]

Hong, K.-H.

Houard, A.

S. I. Mitryukovskiy, Y. Liu, B. Prade, A. Houard, and A. Mysyrowicz, “Coherent interaction between the terahertz radiation emitted by filaments in air,” Laser Phys. 24, 094009 (2014).
[Crossref]

Ivanov, M.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

Ivanov, M. Y.

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

Jakobsen, P.

Johannin-Gilles, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7–140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” 25, 395 (1981).

Jukna, V.

Karras, G.

J. Doussot, G. Karras, F. Billard, P. Béjot, and O. Faucher, “Resonantly enhanced filamentation in gases,” Optica 4, 764–769 (2017).
[Crossref]

J. Doussot, P. Béjot, G. Karras, F. Billard, and O. Faucher, “Phase control of two-color filamentation,” J. Phys. B: Atom. Mol. Opt. Phys. 48, 184005 (2015).
[Crossref]

Kartashov, D.

Kärtner, F. X.

Kasparian, J.

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[Crossref] [PubMed]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

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, 1633–1713 (2007).
[Crossref]

Kolesik, M.

J. K. Wahlstrand, S. Zahedpour, A. Bahl, M. Kolesik, and H. M. Milchberg, “Bound-electron nonlinearity beyond the ionization threshold,” Phys. Rev. Lett. 120, 183901 (2018).
[Crossref] [PubMed]

A. Bahl, J. K. Wahlstrand, S. Zahedpour, H. Milchberg, and M. Kolesik, “Nonlinear optical polarization response and plasma generation in noble gases: Comparison of MESA models to experiments,” Phys. Rev. A 96, 043867 (2017).
[Crossref]

A. Bahl, E. M. Wright, and M. Kolesik, “Nonlinear optical response of noble gases via the metastable electronic state approach,” Phys. Rev. A 94, 023850 (2016).
[Crossref]

A. Bahl, J. M. Brown, E. M. Wright, and M. Kolesik, “Assessment of the metastable electronic state approach as a microscopically self-consistent description for the nonlinear response of atoms,” Opt. Lett. 40, 4987–4990 (2015).
[Crossref] [PubMed]

M. Kolesik, J.M. Brown, A. Teleki, P. Jakobsen, J.V. Moloney, and E. M. Wright, “Metastable electronic states and nonlinear response for high-intensity optical pulses,” Optica 1, 323 (2014).
[Crossref]

J. M. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[Crossref]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, and M. Kolesik, “Practitioner‘s guide to laser pulse propagation models and simulation,” The Eur. Phys. J. Special Top. 199, 5–76 (2011).
[Crossref]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[Crossref]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

Kosareva, O. G.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Koulouklidis, A. D.

A. Gorodetsky, A. D. Koulouklidis, M. Massaouti, and S. Tzortzakis, “Physics of the conical broadband terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. A 89, 033838 (2014).
[Crossref]

Krogen, P.

Lanin, A. A.

Lavorel, B.

Leng, Y.

D. Wang and Y. Leng, “Measuring high-order Kerr effects of noble gases based on spectral analysis,” Opt. Commun. 328, 41–48 (2014).
[Crossref]

Levis, R. J.

M. Tarazkar, D. A. Romanov, and R. J. Levis, “Higher-order nonlinearity of refractive index: The case of argon,” The J. Chem. Phys. 140, 214316 (2014).
[Crossref] [PubMed]

M. Tarazkar, D. A. Romanov, and R. J. Levis, “High-order nonlinear refractive indices for He, Ne, Kr, and Xe atoms,” Phys. Rev. A 90, 062514 (2014).
[Crossref]

Li, R.

Liang, H.

Lin, W.

L. Wang and W. Lin, “The impact of the varied nonlinear refractive index of higher-order Kerr effect on the laser pulse’s propagation,” Optik - Int. J. for Light. Electron Opt. 126, 5387–5391 (2015).
[Crossref]

Liu, J.

Liu, W.

Liu, Y.

S. I. Mitryukovskiy, Y. Liu, B. Prade, A. Houard, and A. Mysyrowicz, “Coherent interaction between the terahertz radiation emitted by filaments in air,” Laser Phys. 24, 094009 (2014).
[Crossref]

Lorin, E.

E. Lorin, M. Lytova, A. Memarian, and A. D. Bandrauk, “Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell — Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model,” J. Phys. A: Math. Theor. 48, 105201 (2015).
[Crossref]

E. Lorin, S. Chelkowski, E. Zaoui, and A. Bandrauk, “Maxwell–Schrödinger–Plasma (MASP) model for laser– molecule interactions: Towards an understanding of filamentation with intense ultrashort pulses,” Phys. D 241, 1059–1071 (2012).
[Crossref]

E. Lorin, S. Chelkowski, and A. Bandrauk, “A numerical Maxwell-Schrödinger model for intense laser-mater interaction and propagation,” Comp. Phys. Commun. 177, 908–932 (2007).
[Crossref]

Loriot, V.

Lotti, A.

J. M. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[Crossref]

Lu, X.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

Lytova, M.

E. Lorin, M. Lytova, A. Memarian, and A. D. Bandrauk, “Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell — Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model,” J. Phys. A: Math. Theor. 48, 105201 (2015).
[Crossref]

Majus, D.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, and M. Kolesik, “Practitioner‘s guide to laser pulse propagation models and simulation,” The Eur. Phys. J. Special Top. 199, 5–76 (2011).
[Crossref]

Makarov, V. A.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Massaouti, M.

A. Gorodetsky, A. D. Koulouklidis, M. Massaouti, and S. Tzortzakis, “Physics of the conical broadband terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. A 89, 033838 (2014).
[Crossref]

Mathur, D.

Matijošius, A.

McDonald, C. R.

Memarian, A.

E. Lorin, M. Lytova, A. Memarian, and A. D. Bandrauk, “Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell — Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model,” J. Phys. A: Math. Theor. 48, 105201 (2015).
[Crossref]

Milchberg, H.

A. Bahl, J. K. Wahlstrand, S. Zahedpour, H. Milchberg, and M. Kolesik, “Nonlinear optical polarization response and plasma generation in noble gases: Comparison of MESA models to experiments,” Phys. Rev. A 96, 043867 (2017).
[Crossref]

Milchberg, H. M.

J. K. Wahlstrand, S. Zahedpour, A. Bahl, M. Kolesik, and H. M. Milchberg, “Bound-electron nonlinearity beyond the ionization threshold,” Phys. Rev. Lett. 120, 183901 (2018).
[Crossref] [PubMed]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett. 109, 113904 (2012).
[Crossref] [PubMed]

Ming-Xing, J.

L. Su-Yu, G. Fu-Ming, Y. Yu-Jun, and J. Ming-Xing, “Defocusing role in femtosecond filamentation: Higher-order Kerr effect or plasma effect?” Chin. Phys. B 24, 114207 (2015).
[Crossref]

Mitrofanov, A. V.

Mitryukovskiy, S. I.

Mitryukovsky, S. I.

Moloney, J. V.

G. O. Ariunbold, P. Polynkin, and J. V. Moloney, “Third and fifth harmonic generation by tightly focused femtosecond pulses at 2.2 μm wavelength in air,” Opt. Express 20, 1662–1667 (2012).
[Crossref] [PubMed]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

Moloney, J.V.

Morales, F.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

Morishita, T.

O. I. Tolstikhin, T. Morishita, and S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: One-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

Mysyrowicz, A.

S. I. Mitryukovskiy, Y. Liu, B. Prade, A. Houard, and A. Mysyrowicz, “Coherent interaction between the terahertz radiation emitted by filaments in air,” Laser Phys. 24, 094009 (2014).
[Crossref]

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

Nath, A.

Nesrallah, M.

Nguyen, A.

A. Nguyen, P. González de Alaiza Martínez, I. Thiele, S. Skupin, and L. Bergé, “Broadband terahertz radiation from two-color mid- and far-infrared laser filaments in air,” Phys. Rev. A 97, 063839 (2018).
[Crossref]

Novak, O.

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, 1633–1713 (2007).
[Crossref]

Oral, E.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Palastro, J. P.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, and D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Panchenko, V. Y.

Panov, N. A.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Patchkovskii, S.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

Peck, E.R.

E.R. Peck and D.J. Fisher, “Dispersion of Argon,” J. Opt. Soc. Am. 54, 1326 (1964).
[Crossref]

Piskarskas, R.

Polynkin, P.

Porras, M. A.

Prade, B.

S. I. Mitryukovskiy, Y. Liu, B. Prade, A. Houard, and A. Mysyrowicz, “Coherent interaction between the terahertz radiation emitted by filaments in air,” Laser Phys. 24, 094009 (2014).
[Crossref]

Pugzdžlys, A.

Pugžlys, A.

Ramírez-Góngora, O. d. J.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. d. J. Ramírez-Góngora, and M. Kolesik, “Practitioner‘s guide to laser pulse propagation models and simulation,” The Eur. Phys. J. Special Top. 199, 5–76 (2011).
[Crossref]

Rensink, T. C.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, and D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Richter, M.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

Romanov, D. A.

M. Tarazkar, D. A. Romanov, and R. J. Levis, “High-order nonlinear refractive indices for He, Ne, Kr, and Xe atoms,” Phys. Rev. A 90, 062514 (2014).
[Crossref]

M. Tarazkar, D. A. Romanov, and R. J. Levis, “Higher-order nonlinearity of refractive index: The case of argon,” The J. Chem. Phys. 140, 214316 (2014).
[Crossref] [PubMed]

Rozhko, M. V.

Shim, B.

Shipilo, D. E.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Shkurinov, A. P.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Sidorov-Biryukov, D. A.

Skupin, S.

A. Nguyen, P. González de Alaiza Martínez, I. Thiele, S. Skupin, and L. Bergé, “Broadband terahertz radiation from two-color mid- and far-infrared laser filaments in air,” Phys. Rev. A 97, 063839 (2018).
[Crossref]

C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Laser Phys. 20, 1107–1113 (2010).
[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, 1633–1713 (2007).
[Crossref]

Smirnova, O.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

Solyankin, P. M.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Stein, G. J.

Steinmeyer, G.

C. Brée, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
[Crossref] [PubMed]

C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Laser Phys. 20, 1107–1113 (2010).
[Crossref]

Stepanov, E. A.

Šuminas, R.

Su-Yu, L.

L. Su-Yu, G. Fu-Ming, Y. Yu-Jun, and J. Ming-Xing, “Defocusing role in femtosecond filamentation: Higher-order Kerr effect or plasma effect?” Chin. Phys. B 24, 114207 (2015).
[Crossref]

Tamošauskas, G.

Tarazkar, M.

M. Tarazkar, D. A. Romanov, and R. J. Levis, “Higher-order nonlinearity of refractive index: The case of argon,” The J. Chem. Phys. 140, 214316 (2014).
[Crossref] [PubMed]

M. Tarazkar, D. A. Romanov, and R. J. Levis, “High-order nonlinear refractive indices for He, Ne, Kr, and Xe atoms,” Phys. Rev. A 90, 062514 (2014).
[Crossref]

Teleki, A.

M. Kolesik, J.M. Brown, A. Teleki, P. Jakobsen, J.V. Moloney, and E. M. Wright, “Metastable electronic states and nonlinear response for high-intensity optical pulses,” Optica 1, 323 (2014).
[Crossref]

J. M. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[Crossref]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[Crossref]

Teng, H.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

Thiele, I.

A. Nguyen, P. González de Alaiza Martínez, I. Thiele, S. Skupin, and L. Bergé, “Broadband terahertz radiation from two-color mid- and far-infrared laser filaments in air,” Phys. Rev. A 97, 063839 (2018).
[Crossref]

Tolstikhin, O. I.

O. I. Tolstikhin, T. Morishita, and S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: One-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

Trapani, P. D.

Tzortzakis, S.

A. Gorodetsky, A. D. Koulouklidis, M. Massaouti, and S. Tzortzakis, “Physics of the conical broadband terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. A 89, 033838 (2014).
[Crossref]

Valiulis, G.

R. Šuminas, G. Tamošauskas, G. Valiulis, V. Jukna, A. Couairon, and A. Dubietis, “Multi-octave spanning nonlinear interactions induced by femtosecond filamentation in polycrystalline znse,” Appl. Phys. Lett. 110, 241106 (2017).
[Crossref]

Varin, C.

Velicke, M.

Vieillard, T.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Vijayalakshmi, K.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Voronin, A. A.

Wahlstrand, J. K.

J. K. Wahlstrand, S. Zahedpour, A. Bahl, M. Kolesik, and H. M. Milchberg, “Bound-electron nonlinearity beyond the ionization threshold,” Phys. Rev. Lett. 120, 183901 (2018).
[Crossref] [PubMed]

A. Bahl, J. K. Wahlstrand, S. Zahedpour, H. Milchberg, and M. Kolesik, “Nonlinear optical polarization response and plasma generation in noble gases: Comparison of MESA models to experiments,” Phys. Rev. A 96, 043867 (2017).
[Crossref]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “High field optical nonlinearity and the Kramers-Kronig relations,” Phys. Rev. Lett. 109, 113904 (2012).
[Crossref] [PubMed]

Wang, D.

D. Wang and Y. Leng, “Measuring high-order Kerr effects of noble gases based on spectral analysis,” Opt. Commun. 328, 41–48 (2014).
[Crossref]

Wang, L.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

L. Wang and W. Lin, “The impact of the varied nonlinear refractive index of higher-order Kerr effect on the laser pulse’s propagation,” Optik - Int. J. for Light. Electron Opt. 126, 5387–5391 (2015).
[Crossref]

Wang, Z.

Watanabe, S.

O. I. Tolstikhin, T. Morishita, and S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: One-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

Weerawarne, D.

Weerawarne, D. L.

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114, 093901 (2015).
[Crossref] [PubMed]

Wei, Z.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

Wolf, J.-P.

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[Crossref] [PubMed]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

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, 1633–1713 (2007).
[Crossref]

Wright, E. M.

A. Bahl, E. M. Wright, and M. Kolesik, “Nonlinear optical response of noble gases via the metastable electronic state approach,” Phys. Rev. A 94, 023850 (2016).
[Crossref]

A. Bahl, J. M. Brown, E. M. Wright, and M. Kolesik, “Assessment of the metastable electronic state approach as a microscopically self-consistent description for the nonlinear response of atoms,” Opt. Lett. 40, 4987–4990 (2015).
[Crossref] [PubMed]

M. Kolesik, J.M. Brown, A. Teleki, P. Jakobsen, J.V. Moloney, and E. M. Wright, “Metastable electronic states and nonlinear response for high-intensity optical pulses,” Optica 1, 323 (2014).
[Crossref]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[Crossref]

Xi, T.

L. Wang, X. Lu, H. Teng, T. Xi, S. Chen, P. He, X. He, and Z. Wei, “Carrier-envelope phase-dependent electronic conductivity in an air filament driven by few-cycle laser pulses,” Phys. Rev. A 94, 013827 (2016).
[Crossref]

Xu, Z.

Yudin, G. L.

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

Yu-Jun, Y.

L. Su-Yu, G. Fu-Ming, Y. Yu-Jun, and J. Ming-Xing, “Defocusing role in femtosecond filamentation: Higher-order Kerr effect or plasma effect?” Chin. Phys. B 24, 114207 (2015).
[Crossref]

Zahedpour, S.

J. K. Wahlstrand, S. Zahedpour, A. Bahl, M. Kolesik, and H. M. Milchberg, “Bound-electron nonlinearity beyond the ionization threshold,” Phys. Rev. Lett. 120, 183901 (2018).
[Crossref] [PubMed]

A. Bahl, J. K. Wahlstrand, S. Zahedpour, H. Milchberg, and M. Kolesik, “Nonlinear optical polarization response and plasma generation in noble gases: Comparison of MESA models to experiments,” Phys. Rev. A 96, 043867 (2017).
[Crossref]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

Zaoui, E.

E. Lorin, S. Chelkowski, E. Zaoui, and A. Bandrauk, “Maxwell–Schrödinger–Plasma (MASP) model for laser– molecule interactions: Towards an understanding of filamentation with intense ultrashort pulses,” Phys. D 241, 1059–1071 (2012).
[Crossref]

Zhang, C.

Zheltikov, A. M.

Appl. Phys. B (1)

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. Bowden, and S. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B 73, 287–290 (2001).
[Crossref]

Appl. Phys. Lett. (1)

R. Šuminas, G. Tamošauskas, G. Valiulis, V. Jukna, A. Couairon, and A. Dubietis, “Multi-octave spanning nonlinear interactions induced by femtosecond filamentation in polycrystalline znse,” Appl. Phys. Lett. 110, 241106 (2017).
[Crossref]

Chin. Phys. B (1)

L. Su-Yu, G. Fu-Ming, Y. Yu-Jun, and J. Ming-Xing, “Defocusing role in femtosecond filamentation: Higher-order Kerr effect or plasma effect?” Chin. Phys. B 24, 114207 (2015).
[Crossref]

Comp. Phys. Commun. (1)

E. Lorin, S. Chelkowski, and A. Bandrauk, “A numerical Maxwell-Schrödinger model for intense laser-mater interaction and propagation,” Comp. Phys. Commun. 177, 908–932 (2007).
[Crossref]

J. Opt. Soc. Am. (1)

E.R. Peck and D.J. Fisher, “Dispersion of Argon,” J. Opt. Soc. Am. 54, 1326 (1964).
[Crossref]

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

J. Phys. A: Math. Theor. (1)

E. Lorin, M. Lytova, A. Memarian, and A. D. Bandrauk, “Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell — Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model,” J. Phys. A: Math. Theor. 48, 105201 (2015).
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J. Phys. B: At. Mol. Opt. Phys. (2)

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Figures (6)

Fig. 1
Fig. 1 a) Induced nonlinear dipole moment, Pnl(F), in Argon and Krypton in atomic units. b) Normalized effective nonlinear index as a function of the cycle-averaged intensity. These curves are derived from those shown in panel a); their deviations from the unity (horizontal line) can be attributed to a combination of higher-order nonlinear effects.
Fig. 2
Fig. 2 Peak intensity versus the propagation distance for increasing initial pulse energy, with the results for models F, E, and T shown from left to right. The range of initial pulse energies shown in these maps is from 0.1 mJ to 5.7 mJ, and the propagation distances are shown between 1m and 2m (with the linear focus at 1.5m in Argon). The peak intensities become clamped at about 80TW/cm2 for the higher pulse energies.
Fig. 3
Fig. 3 Peak-intensity location, measured as the distance from the lens, as a function of the initial-pulse peak intensity. These examples are for Argon and focal length of f = 150 cm in a) and f = 400 cm in b). The peak power corresponding to critical power for self-focusing collapse in a CW-beam is reached for a peak intensity of about 98TW/cm2. The shapes of these curves reflect a complex competition between self-focusing, diffraction, chromatic dispersion, and de-focusing by free electrons.
Fig. 4
Fig. 4 Quantity Z75 for characterization of the steepness of the filamentation onset as observed in the on-axis peak intensity. The set of curves were obtained by varying the initial energy of the pulse. For each curve, its maximum was identified, and the location (red dots) was found at which 75 percent of the maximal intensity occurred for the first time. Z75 reflects mainly the properties of the self-focusing pulse, and thus characterizes the shape of the leading edge of the filament. These simulation were executed for Argon (and f = 150cm) with the MESA-based model which will be referred to as the “full” model.
Fig. 5
Fig. 5 Quantity Z75 for Argon (a) and Krypton (b) and a focal length of f = 150cm. Outcomes for the three different versions of the nonlinear polarization model are depicted with different symbols. Higher values (longer distance) for a fixed intensity (horizontal axis) mean that the self-focusing accelerates more before the start of the filament proper. The panels demonstrate the same qualitative behavior in two different noble gases. Similar results are obtained for other species.
Fig. 6
Fig. 6 Z75 for a filament in Argon and four different focal lengths of 50cm (a), 100cm (b), 300cm (c), and 400cm (d). In all cases, model E (diamonds) with the effective Kerr coefficient equal to that measured in experiments is closer to the reference model F (circles) with full response than the simulation with the true value of the nonlinear index (squares).

Equations (6)

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z E ^ ( k , ω , z ) = i K z ( ω , k ) E ^ + i ω 2 2 0 c 2 K z P ^ ω 2 0 c 2 K z J ^ ,
K z ( ω , k ) = ω 2 ( ω ) c 2 k 2 .
P ( t ) = e a P nl F ( t ) ) ,
d d t ρ ( t ) = 2 ( N a ρ ( t ) ) Im { E g ( F ( t ) ) } and d d t J ( t ) = e 2 m ρ ( t ) E ( t ) +
P = e a N a P nl ( E ) = 0 n b Δ χ ( E ) E = 2 0 n b n 2 eff ( I ) IE ,
n 2 T n 2 eff ( F = 0 ) .

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