Abstract

Heating of conduction-band electrons is one of the major processes of energy absorption and transfer in high-intensity ultrafast laser–solid interactions. It is frequently simulated by assuming a high rate of electron-particle collisions. We explore the approximation of low-rate electron–phonon collisions based on the Vinogradov equation for the intraband absorption rate by conduction-band electrons performing laser-driven oscillations. Band-structure modification by the ponderomotive energy of the ultrafast oscillations is taken into account. The Vinogradov equation combined with the Keldysh formula for the interband transition rate delivers a highly nonequilibrium energy distribution of the conduction electrons. Reported results suggest a substantial revision of the traditional models of ultrafast free-carrier heating by intense laser pulses.

© 2018 Optical Society of America

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2018 (2)

E. G. Gamaly and A. V. Rode, “Ultrafast re-structuring of the electronic landscape of transparent dielectrics: new material states (Die-Met),” Appl. Phys. A 124, 278 (2018).
[Crossref]

V. Gruzdev and O. Sergaeva, “Ultrafast modification of band structure of wide-band-gap solids by ultrashort pulses of laser-driven electron oscillations,” Phys. Rev. B 98, 115202 (2018).
[Crossref]

2017 (1)

B. Rethfeld, D. S. Ivanov, M. E. Garcia, and S. I. Anisimov, “Modelling ultrafast laser ablation,” J. Phys. D 50, 193001 (2017).
[Crossref]

2016 (3)

M. Sun, J. Zhu, and Z. Lin, “Modeling of ablation threshold dependence on pulse duration for dielectrics with ultrashort pulsed laser,” Opt. Eng. 56, 011026 (2016).
[Crossref]

M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
[Crossref]

E. Chowdhury, K. R. P. Kafka, D. R. Austin, K. Werner, N. Talisa, B. Ma, C. I. Blaga, L. F. DiMauro, H. Li, and A. Yi, “Ultra-fast bandgap photonics in mid-IR wavelengths,” Proc. SPIE 9835, 983519 (2016).
[Crossref]

2014 (7)

G. Marchetti, M. Hodgson, and I. D’Amico, “Spin decoherence in n-type GaAs: the effectiveness of the third-body rejection method for electron-electron scattering,” J. Appl. Phys. 116, 163702 (2014).
[Crossref]

G. Marchetti, M. Hodgson, J. McHugh, R. Chantrell, and I. D’Amico, “Spin relaxation in GaAs: importance of electron-electron interactions,” Materials 7, 2795–2814 (2014).
[Crossref]

V. E. Gruzdev, “Fundamental mechanisms of laser damage of dielectric crystals by ultrashort pulse: ionization dynamics for the Keldysh model,” Opt. Eng. 53, 122515 (2014).
[Crossref]

J. R. Gulley and T. E. Lanier, “Model for ultrashort laser pulse-induced ionization dynamics in transparent solids,” Phys. Rev. B 90, 155119 (2014).
[Crossref]

J. Liao and J. R. Gulley, “Time and frequency control of ultrafast plasma generation in dielectrics,” J. Opt. Soc. Am. B 31, 2973–2980 (2014).
[Crossref]

D. G. Papazoglou, D. Abdollahpour, and S. Tzortzakis, “Ultrafast electron and material dynamics following femtosecond filamentation induced excitation of transparent solids,” Appl. Phys. A 114, 161–168 (2014).
[Crossref]

V. E. Gruzdev, V. L. Komolov, and S. G. Przhibel’skií, “Ionization of nanoparticles by supershort moderate-intensity laser pulses,” J. Opt. Technol. 81, 256–261 (2014).
[Crossref]

2013 (3)

P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76, 036502 (2013).
[Crossref]

A. Mouskeftaras, S. Guizard, N. Fedorov, and S. Klimentov, “Mechanisms of femtosecond laser ablation of dielectrics revealed by double pump-probe experiment,” Appl. Phys. A 110, 709–715 (2013).
[Crossref]

C. Mezel, G. Duchateau, G. Geneste, and B. Siberchicot, “A model for multiphoton absorption in dielectric materials induced by short laser pulses at moderate intensities,” J. Phys. Condens. Matter 25, 235501 (2013).
[Crossref]

2012 (2)

A. Bourgeade and G. Duchateau, “Time-dependent ionization models designed for intense and short laser pulse propagation in dielectric materials,” Phys. Rev. E 85, 056403 (2012).
[Crossref]

J. R. Gulley, S. W. Winkler, W. M. Dennis, C. M. Liebig, and R. Stoian, “Interaction of ultrashort-laser pulses with induced undercritical plasmas in fused silica,” Phys. Rev. A 85, 013808 (2012).
[Crossref]

2011 (3)

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Légaré, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84, 094104 (2011).
[Crossref]

H. Dachraoui, C. Oberer, and U. Heinzmann, “Femtosecond crystallographic experiment in wide-bandgap LiF crystal,” Opt. Express 19, 2797–2804 (2011).
[Crossref]

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, 138–141 (2011).
[Crossref]

2009 (1)

B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79, 155424 (2009).
[Crossref]

2007 (1)

V. E. Gruzdev, “Photoionization rate in wide band-gap crystals,” Phys. Rev. B 75, 205106 (2007).
[Crossref]

2006 (5)

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, A. El-Khamhawy, and D. von der Linde, “Multiphoton ionization in dielectrics: comparison of circular and linear polarization,” Phys. Rev. Lett. 97, 237403 (2006).
[Crossref]

S. Winkler, I. Burakov, R. Stoian, N. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi, and I. Hertel, “Transient response of dielectric materials exposed to ultrafast laser radiation,” Appl. Phys. A 84, 413–422 (2006).
[Crossref]

T. Q. Jia, H. X. Chen, M. Huang, F. L. Zhao, X. X. Li, S. Z. Xu, H. Y. Sun, D. H. Feng, C. B. Li, X. F. Wang, R. X. Li, Z. Z. Xu, X. K. He, and H. Kuroda, “Ultraviolet-infrared femtosecond laser-induced damage in fused silica and CaF2 crystals,” Phys. Rev. B 73, 054105 (2006).
[Crossref]

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: plasma generation versus chromatic dispersion,” Physica D 220, 14–30 (2006).
[Crossref]

B. Rethfeld, “Free-electron generation in laser-irradiated dielectrics,” Phys. Rev. B 73, 035101 (2006).
[Crossref]

2005 (2)

B. N. Yatsenko, H. Bachau, A. N. Belsky, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, and A. N. Vasil’ev, “Creation of high energy electronic excitations in inorganic insulators by intense femtosecond laser pulses,” Phys. Status Solidi C 2, 240–243 (2005).
[Crossref]

X. Liu, R. Stock, and W. Rudolph, “Ballistic electron transport in Au films,” Phys. Rev. B 72, 195431 (2005).
[Crossref]

2004 (4)

V. E. Gruzdev, “Analysis of the transparent-crystal ionization model developed by L. V. Keldysh,” J. Opt. Technol. 71, 504–508 (2004).
[Crossref]

A. Belsky, H. Bachau, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, A. Vasil’ev, and B. Yatsenko, “Observation of high energy photoelectrons from solids at moderate laser intensity,” Appl. Phys. B 78, 989–994 (2004).
[Crossref]

B. Rethfeld, “Unified model for the free-electron avalanche in laser-irradiated dielectrics,” Phys. Rev. Lett. 92, 187401 (2004).
[Crossref]

S. Mao, F. Quéré, S. Guizard, X. Mao, R. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys. A 79, 1695–1709 (2004).
[Crossref]

2002 (2)

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601 (2002).
[Crossref]

S. R. Vatsya and S. K. Nikumb, “Modeling of laser-induced avalanche in dielectrics,” J. Appl. Phys. 91, 344–351 (2002).
[Crossref]

2000 (5)

A. Kaiser, B. Rethfeld, M. Vicanek, and G. Simon, “Microscopic processes in dielectrics under irradiation by subpicosecond laser pulses,” Phys. Rev. B 61, 11437–11450 (2000).
[Crossref]

T. Apostolova and Y. Hahn, “Modeling of laser-induced breakdown in dielectrics with subpicosecond pulses,” J. Appl. Phys. 88, 1024–1034 (2000).
[Crossref]

N. Del Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallée, “Nonequilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[Crossref]

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251, 237–258 (2000).
[Crossref]

P. B. Allen, “Misbehaviour in metals,” Nature 405, 1007–1008 (2000).
[Crossref]

1997 (1)

P. Martin, S. Guizard, P. Daguzan, G. Petite, P. D’Oliveira, P. Meynadier, and M. Perdrix, “Subpicosecond study of carrier trapping dynamics in wide-band-gap crystals,” Phys. Rev. B 55, 5799–5810 (1997).
[Crossref]

1996 (2)

S. Guizard, P. D’Oliveira, P. Daguzan, P. Martin, P. Meynadier, and G. Petite, “Time-resolved studies of carriers dynamics in wide band gap materials,” Nucl. Instrum. Methods Phys. Res. Sect. B 116, 43–48 (1996).
[Crossref]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).
[Crossref]

1995 (2)

S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. D. Santos, and A. Antonnetti, “Contrasted behaviour of an electron gas in MgO, Al2O3 and SiO2,” Europhys. Lett. 29, 401–406 (1995).
[Crossref]

B. B. Hu, E. A. de Souza, W. H. Knox, J. E. Cunningham, M. C. Nuss, A. V. Kuznetsov, and S. L. Chuang, “Identifying the distinct phases of carrier transport in semiconductors with 10  fs resolution,” Phys. Rev. Lett. 74, 1689–1692 (1995).
[Crossref]

1994 (1)

D. Arnold, E. Cartier, and D. J. DiMaria, “Theory of high-field electron transport and impact ionization in silicon dioxide,” Phys. Rev. B 49, 10278–10297 (1994).
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1993 (1)

L. Rota, P. Lugli, T. Elsaesser, and J. Shah, “Ultrafast thermalization of photoexcited carriers in polar semiconductors,” Phys. Rev. B 47, 4226–4237 (1993).
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1992 (2)

D. Arnold, E. Cartier, and D. J. DiMaria, “Acoustic-phonon runaway and impact ionization by hot electrons in silicon dioxide,” Phys. Rev. B 45, 1477–1480 (1992).
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D. Arnold and E. Cartier, “Theory of laser-induced free-electron heating and impact ionization in wide-band-gap solids,” Phys. Rev. B 46, 15102–15115 (1992).
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1988 (1)

P. C. Becker, H. L. Fragnito, C. H. BritoCruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
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1985 (1)

J. A. Kash, J. C. Tsang, and J. M. Hvam, “Subpicosecond time-resolved Raman spectroscopy of LO phonons in GaAs,” Phys. Rev. Lett. 54, 2151–2154 (1985).
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1976 (1)

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1975 (3)

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A. S. Epifanov, “Avalanche ionization induced in solid transparent dielectrics by strong laser pulses,” Sov. Phys. JETP 40, 897–902 (1975).

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1970 (1)

E. M. Epshtein, “Scattering of electrons by phonons in a strong radiation field,” Sov. Phys. Solid State 11, 2213–2217 (1970).

1969 (1)

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1965 (1)

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1964 (1)

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1957 (1)

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L. D. Landau, “Kinetic equation in the case of a Coulomb interaction,” Sov. Phys. JETP 7, 203–209 (1937).

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B. Rethfeld, D. S. Ivanov, M. E. Garcia, and S. I. Anisimov, “Modelling ultrafast laser ablation,” J. Phys. D 50, 193001 (2017).
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S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. D. Santos, and A. Antonnetti, “Contrasted behaviour of an electron gas in MgO, Al2O3 and SiO2,” Europhys. Lett. 29, 401–406 (1995).
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T. Apostolova and Y. Hahn, “Modeling of laser-induced breakdown in dielectrics with subpicosecond pulses,” J. Appl. Phys. 88, 1024–1034 (2000).
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D. Arnold, E. Cartier, and D. J. DiMaria, “Theory of high-field electron transport and impact ionization in silicon dioxide,” Phys. Rev. B 49, 10278–10297 (1994).
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D. Arnold, E. Cartier, and D. J. DiMaria, “Acoustic-phonon runaway and impact ionization by hot electrons in silicon dioxide,” Phys. Rev. B 45, 1477–1480 (1992).
[Crossref]

D. Arnold and E. Cartier, “Theory of laser-induced free-electron heating and impact ionization in wide-band-gap solids,” Phys. Rev. B 46, 15102–15115 (1992).
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S. Winkler, I. Burakov, R. Stoian, N. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi, and I. Hertel, “Transient response of dielectric materials exposed to ultrafast laser radiation,” Appl. Phys. A 84, 413–422 (2006).
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N. W. Ashkroft and N. D. Mermin, Solid State Physics (Saunders College, 1976).

Audebert, P.

S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. D. Santos, and A. Antonnetti, “Contrasted behaviour of an electron gas in MgO, Al2O3 and SiO2,” Europhys. Lett. 29, 401–406 (1995).
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Austin, D.

V. Gruzdev, O. Sergaeva, D. Austin, and E. Chowdhury, “Multi-band Keldysh-Vinogradov model of ultrafast laser-induced excitation and heating of electron-hole plasma in wide-band-gap crystals” (to be published).

V. Gruzdev, D. Austin, O. Sergaeva, and E. Chowdhury, “Simulations of ultrafast laser-induced excitation and heating of electron sub-system of semiconductors with the Vinogradov equation and multi-band Keldysh formula,” in XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS) (IEEE, 2017).

V. Gruzdev, D. Austin, O. Sergaeva, and E. Chowhury, “Beyond the Drude approach: a Keldysh-Vinogradov model of dynamics of ultrafast laser-induced electron excitation,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2017), paper STh4J.6.

Austin, D. R.

E. Chowdhury, K. R. P. Kafka, D. R. Austin, K. Werner, N. Talisa, B. Ma, C. I. Blaga, L. F. DiMauro, H. Li, and A. Yi, “Ultra-fast bandgap photonics in mid-IR wavelengths,” Proc. SPIE 9835, 983519 (2016).
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B. N. Yatsenko, H. Bachau, A. N. Belsky, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, and A. N. Vasil’ev, “Creation of high energy electronic excitations in inorganic insulators by intense femtosecond laser pulses,” Phys. Status Solidi C 2, 240–243 (2005).
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A. Belsky, H. Bachau, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, A. Vasil’ev, and B. Yatsenko, “Observation of high energy photoelectrons from solids at moderate laser intensity,” Appl. Phys. B 78, 989–994 (2004).
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P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76, 036502 (2013).
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B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79, 155424 (2009).
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P. C. Becker, H. L. Fragnito, C. H. BritoCruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
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A. Belsky, H. Bachau, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, A. Vasil’ev, and B. Yatsenko, “Observation of high energy photoelectrons from solids at moderate laser intensity,” Appl. Phys. B 78, 989–994 (2004).
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Belsky, A. N.

B. N. Yatsenko, H. Bachau, A. N. Belsky, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, and A. N. Vasil’ev, “Creation of high energy electronic excitations in inorganic insulators by intense femtosecond laser pulses,” Phys. Status Solidi C 2, 240–243 (2005).
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Bergé, L.

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: plasma generation versus chromatic dispersion,” Physica D 220, 14–30 (2006).
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Blaga, C. I.

E. Chowdhury, K. R. P. Kafka, D. R. Austin, K. Werner, N. Talisa, B. Ma, C. I. Blaga, L. F. DiMauro, H. Li, and A. Yi, “Ultra-fast bandgap photonics in mid-IR wavelengths,” Proc. SPIE 9835, 983519 (2016).
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Bourgeade, A.

A. Bourgeade and G. Duchateau, “Time-dependent ionization models designed for intense and short laser pulse propagation in dielectric materials,” Phys. Rev. E 85, 056403 (2012).
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BritoCruz, C. H.

P. C. Becker, H. L. Fragnito, C. H. BritoCruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
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Browne, D. A.

M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
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Bulgakova, N.

S. Winkler, I. Burakov, R. Stoian, N. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi, and I. Hertel, “Transient response of dielectric materials exposed to ultrafast laser radiation,” Appl. Phys. A 84, 413–422 (2006).
[Crossref]

Burakov, I.

S. Winkler, I. Burakov, R. Stoian, N. Bulgakova, A. Husakou, A. Mermillod-Blondin, A. Rosenfeld, D. Ashkenasi, and I. Hertel, “Transient response of dielectric materials exposed to ultrafast laser radiation,” Appl. Phys. A 84, 413–422 (2006).
[Crossref]

Cartier, E.

D. Arnold, E. Cartier, and D. J. DiMaria, “Theory of high-field electron transport and impact ionization in silicon dioxide,” Phys. Rev. B 49, 10278–10297 (1994).
[Crossref]

D. Arnold and E. Cartier, “Theory of laser-induced free-electron heating and impact ionization in wide-band-gap solids,” Phys. Rev. B 46, 15102–15115 (1992).
[Crossref]

D. Arnold, E. Cartier, and D. J. DiMaria, “Acoustic-phonon runaway and impact ionization by hot electrons in silicon dioxide,” Phys. Rev. B 45, 1477–1480 (1992).
[Crossref]

Chantrell, R.

G. Marchetti, M. Hodgson, J. McHugh, R. Chantrell, and I. D’Amico, “Spin relaxation in GaAs: importance of electron-electron interactions,” Materials 7, 2795–2814 (2014).
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Chen, H. X.

T. Q. Jia, H. X. Chen, M. Huang, F. L. Zhao, X. X. Li, S. Z. Xu, H. Y. Sun, D. H. Feng, C. B. Li, X. F. Wang, R. X. Li, Z. Z. Xu, X. K. He, and H. Kuroda, “Ultraviolet-infrared femtosecond laser-induced damage in fused silica and CaF2 crystals,” Phys. Rev. B 73, 054105 (2006).
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Chimier, B.

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Légaré, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84, 094104 (2011).
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Chowdhury, E.

E. Chowdhury, K. R. P. Kafka, D. R. Austin, K. Werner, N. Talisa, B. Ma, C. I. Blaga, L. F. DiMauro, H. Li, and A. Yi, “Ultra-fast bandgap photonics in mid-IR wavelengths,” Proc. SPIE 9835, 983519 (2016).
[Crossref]

V. Gruzdev, D. Austin, O. Sergaeva, and E. Chowdhury, “Simulations of ultrafast laser-induced excitation and heating of electron sub-system of semiconductors with the Vinogradov equation and multi-band Keldysh formula,” in XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS) (IEEE, 2017).

V. Gruzdev, O. Sergaeva, D. Austin, and E. Chowdhury, “Multi-band Keldysh-Vinogradov model of ultrafast laser-induced excitation and heating of electron-hole plasma in wide-band-gap crystals” (to be published).

Chowhury, E.

V. Gruzdev, D. Austin, O. Sergaeva, and E. Chowhury, “Beyond the Drude approach: a Keldysh-Vinogradov model of dynamics of ultrafast laser-induced electron excitation,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2017), paper STh4J.6.

Christensen, B. H.

B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79, 155424 (2009).
[Crossref]

Christofilos, D.

N. Del Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallée, “Nonequilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[Crossref]

Chuang, S. L.

B. B. Hu, E. A. de Souza, W. H. Knox, J. E. Cunningham, M. C. Nuss, A. V. Kuznetsov, and S. L. Chuang, “Identifying the distinct phases of carrier transport in semiconductors with 10  fs resolution,” Phys. Rev. Lett. 74, 1689–1692 (1995).
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Conrad, U.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251, 237–258 (2000).
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Couairon, A.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601 (2002).
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Cunningham, J. E.

B. B. Hu, E. A. de Souza, W. H. Knox, J. E. Cunningham, M. C. Nuss, A. V. Kuznetsov, and S. L. Chuang, “Identifying the distinct phases of carrier transport in semiconductors with 10  fs resolution,” Phys. Rev. Lett. 74, 1689–1692 (1995).
[Crossref]

P. C. Becker, H. L. Fragnito, C. H. BritoCruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
[Crossref]

D’Amico, I.

G. Marchetti, M. Hodgson, J. McHugh, R. Chantrell, and I. D’Amico, “Spin relaxation in GaAs: importance of electron-electron interactions,” Materials 7, 2795–2814 (2014).
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G. Marchetti, M. Hodgson, and I. D’Amico, “Spin decoherence in n-type GaAs: the effectiveness of the third-body rejection method for electron-electron scattering,” J. Appl. Phys. 116, 163702 (2014).
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D’Oliveira, P.

P. Martin, S. Guizard, P. Daguzan, G. Petite, P. D’Oliveira, P. Meynadier, and M. Perdrix, “Subpicosecond study of carrier trapping dynamics in wide-band-gap crystals,” Phys. Rev. B 55, 5799–5810 (1997).
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S. Guizard, P. D’Oliveira, P. Daguzan, P. Martin, P. Meynadier, and G. Petite, “Time-resolved studies of carriers dynamics in wide band gap materials,” Nucl. Instrum. Methods Phys. Res. Sect. B 116, 43–48 (1996).
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Dachraoui, H.

Daguzan, P.

P. Martin, S. Guizard, P. Daguzan, G. Petite, P. D’Oliveira, P. Meynadier, and M. Perdrix, “Subpicosecond study of carrier trapping dynamics in wide-band-gap crystals,” Phys. Rev. B 55, 5799–5810 (1997).
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S. Guizard, P. D’Oliveira, P. Daguzan, P. Martin, P. Meynadier, and G. Petite, “Time-resolved studies of carriers dynamics in wide band gap materials,” Nucl. Instrum. Methods Phys. Res. Sect. B 116, 43–48 (1996).
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S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. D. Santos, and A. Antonnetti, “Contrasted behaviour of an electron gas in MgO, Al2O3 and SiO2,” Europhys. Lett. 29, 401–406 (1995).
[Crossref]

de Souza, E. A.

B. B. Hu, E. A. de Souza, W. H. Knox, J. E. Cunningham, M. C. Nuss, A. V. Kuznetsov, and S. L. Chuang, “Identifying the distinct phases of carrier transport in semiconductors with 10  fs resolution,” Phys. Rev. Lett. 74, 1689–1692 (1995).
[Crossref]

Del Fatti, N.

N. Del Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallée, “Nonequilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
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J. R. Gulley, S. W. Winkler, W. M. Dennis, C. M. Liebig, and R. Stoian, “Interaction of ultrashort-laser pulses with induced undercritical plasmas in fused silica,” Phys. Rev. A 85, 013808 (2012).
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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, 138–141 (2011).
[Crossref]

DiMaria, D. J.

D. Arnold, E. Cartier, and D. J. DiMaria, “Theory of high-field electron transport and impact ionization in silicon dioxide,” Phys. Rev. B 49, 10278–10297 (1994).
[Crossref]

D. Arnold, E. Cartier, and D. J. DiMaria, “Acoustic-phonon runaway and impact ionization by hot electrons in silicon dioxide,” Phys. Rev. B 45, 1477–1480 (1992).
[Crossref]

DiMauro, L. F.

E. Chowdhury, K. R. P. Kafka, D. R. Austin, K. Werner, N. Talisa, B. Ma, C. I. Blaga, L. F. DiMauro, H. Li, and A. Yi, “Ultra-fast bandgap photonics in mid-IR wavelengths,” Proc. SPIE 9835, 983519 (2016).
[Crossref]

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, 138–141 (2011).
[Crossref]

Duchateau, G.

C. Mezel, G. Duchateau, G. Geneste, and B. Siberchicot, “A model for multiphoton absorption in dielectric materials induced by short laser pulses at moderate intensities,” J. Phys. Condens. Matter 25, 235501 (2013).
[Crossref]

A. Bourgeade and G. Duchateau, “Time-dependent ionization models designed for intense and short laser pulse propagation in dielectric materials,” Phys. Rev. E 85, 056403 (2012).
[Crossref]

El-Khamhawy, A.

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, A. El-Khamhawy, and D. von der Linde, “Multiphoton ionization in dielectrics: comparison of circular and linear polarization,” Phys. Rev. Lett. 97, 237403 (2006).
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Elsaesser, T.

L. Rota, P. Lugli, T. Elsaesser, and J. Shah, “Ultrafast thermalization of photoexcited carriers in polar semiconductors,” Phys. Rev. B 47, 4226–4237 (1993).
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Emmert, L. A.

L. A. Emmert and W. Rudolph, “Femtosecond laser-induced damage in dielectric materials,” in Laser-Induced Damage in Optical Materials (CRC Press, Taylor and Francis, 2015), Chap. 5.

Epifanov, A. S.

A. S. Epifanov, “Avalanche ionization induced in solid transparent dielectrics by strong laser pulses,” Sov. Phys. JETP 40, 897–902 (1975).

Epshtein, E. M.

E. M. Epshtein, “Scattering of electrons by phonons in a strong radiation field,” Sov. Phys. Solid State 11, 2213–2217 (1970).

Fedorov, N.

A. Mouskeftaras, S. Guizard, N. Fedorov, and S. Klimentov, “Mechanisms of femtosecond laser ablation of dielectrics revealed by double pump-probe experiment,” Appl. Phys. A 110, 709–715 (2013).
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Feit, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).
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Feng, D. H.

T. Q. Jia, H. X. Chen, M. Huang, F. L. Zhao, X. X. Li, S. Z. Xu, H. Y. Sun, D. H. Feng, C. B. Li, X. F. Wang, R. X. Li, Z. Z. Xu, X. K. He, and H. Kuroda, “Ultraviolet-infrared femtosecond laser-induced damage in fused silica and CaF2 crystals,” Phys. Rev. B 73, 054105 (2006).
[Crossref]

Fork, R. L.

P. C. Becker, H. L. Fragnito, C. H. BritoCruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
[Crossref]

Fradin, D. W.

L. H. Holway and D. W. Fradin, “Electron avalanche breakdown by laser radiation in insulating crystals,” J. Appl. Phys. 46, 279–291 (1975).
[Crossref]

Fragnito, H. L.

P. C. Becker, H. L. Fragnito, C. H. BritoCruz, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank, “Femtosecond photon echoes from band-to-band transitions in GaAs,” Phys. Rev. Lett. 61, 1647–1649 (1988).
[Crossref]

Franco, M.

L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89, 186601 (2002).
[Crossref]

Gaarde, M. B.

M. Wu, D. A. Browne, K. J. Schafer, and M. B. Gaarde, “Multilevel perspective on high-order harmonic generation in solids,” Phys. Rev. A 94, 063403 (2016).
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Gamaly, E. G.

E. G. Gamaly and A. V. Rode, “Ultrafast re-structuring of the electronic landscape of transparent dielectrics: new material states (Die-Met),” Appl. Phys. A 124, 278 (2018).
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Garcia, M. E.

B. Rethfeld, D. S. Ivanov, M. E. Garcia, and S. I. Anisimov, “Modelling ultrafast laser ablation,” J. Phys. D 50, 193001 (2017).
[Crossref]

Gaudin, J.

B. N. Yatsenko, H. Bachau, A. N. Belsky, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, and A. N. Vasil’ev, “Creation of high energy electronic excitations in inorganic insulators by intense femtosecond laser pulses,” Phys. Status Solidi C 2, 240–243 (2005).
[Crossref]

A. Belsky, H. Bachau, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, A. Vasil’ev, and B. Yatsenko, “Observation of high energy photoelectrons from solids at moderate laser intensity,” Appl. Phys. B 78, 989–994 (2004).
[Crossref]

Geindre, J. P.

S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. D. Santos, and A. Antonnetti, “Contrasted behaviour of an electron gas in MgO, Al2O3 and SiO2,” Europhys. Lett. 29, 401–406 (1995).
[Crossref]

Geneste, G.

C. Mezel, G. Duchateau, G. Geneste, and B. Siberchicot, “A model for multiphoton absorption in dielectric materials induced by short laser pulses at moderate intensities,” J. Phys. Condens. Matter 25, 235501 (2013).
[Crossref]

Geoffroy, G.

B. N. Yatsenko, H. Bachau, A. N. Belsky, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, and A. N. Vasil’ev, “Creation of high energy electronic excitations in inorganic insulators by intense femtosecond laser pulses,” Phys. Status Solidi C 2, 240–243 (2005).
[Crossref]

A. Belsky, H. Bachau, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, A. Vasil’ev, and B. Yatsenko, “Observation of high energy photoelectrons from solids at moderate laser intensity,” Appl. Phys. B 78, 989–994 (2004).
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S. Mao, F. Quéré, S. Guizard, X. Mao, R. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys. A 79, 1695–1709 (2004).
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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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B. N. Yatsenko, H. Bachau, A. N. Belsky, J. Gaudin, G. Geoffroy, S. Guizard, P. Martin, G. Petite, A. Philippov, and A. N. Vasil’ev, “Creation of high energy electronic excitations in inorganic insulators by intense femtosecond laser pulses,” Phys. Status Solidi C 2, 240–243 (2005).
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Supplementary Material (2)

NameDescription
» Visualization 1       Time evolution of energy distribution of conduction-band electrons in crystalline ZnSe generated by interband transitions from light-hole (blue), heavy-hole (red), and split-off (green) valence bands. Produced using the Vinogradov equation (Eq. (12)).
» Visualization 2       Time evolution of energy distribution of conduction-band electrons in crystalline ZnSe generated by interband transitions from light-hole (blue), heavy-hole (red), and split-off (green) valence bands. Produced using the Drude equation (Eq. (11)).

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Figures (5)

Fig. 1.
Fig. 1. Sketch of intraband electron dynamics. Three valence bands are shown to be specific: heavy-hole (HH—red), light-hole (LH—blue), and split-off (SO—green).
Fig. 2.
Fig. 2. (a) Time variations of the rates of the interband electron transitions from the HH (red), LH (blue), and SO (green) valence bands induced by a 100-fs laser pulse at wavelength 2400 nm and peak irradiance 10    TW / cm 2 . The black curve depicts the total effects produced by summing the specific contributions from each valence band. (b) Time variations of the effective band gaps for the three valence bands.
Fig. 3.
Fig. 3. Electron distributions in the ZnSe conduction band at the tail ( t = 200    fs ) of a 100-fs laser pulse at 10    TW / cm 2 peak irradiance at several values of wavelength: (a) and (e)  800    nm ; (b) and (f)  1500    nm ; (c) and (g)  2400    nm ; (d) and (h)  3600    nm . Panels (a) through (d) are for the Vinogradov model of Eq. (12). Panels (e) through (h) are for the Drude equation of Eq. (11). Separate contributions of each valence band are depicted by red for HH, blue for LH, and green for SO. The bottom of the conduction band is assumed to be at zero level.
Fig. 4.
Fig. 4. Snapshots of the instant energy distribution of conduction electrons delivered by the Vinogradov model [panels (a) through (f)] and the Drude equation [panels (g) through (l)] obtained at laser wavelength 2400 nm. Other parameters and notations are similar to Fig. 3. Contribution of each valence band is shown separately in the same way as in Fig. 3. Note the change of the vertical axis with the transition from upper to lower panels.
Fig. 5.
Fig. 5. Illustration of the physical effects that determine increasing and decreasing trends of electron distributions in the conduction band (shown by the gray curved arrows): (a) and (b) in the Keldysh–Vinogradov model, (c) in the Keldysh–Drude model. Three time instants (1, 2, and 3) at a leading edge of a laser pulse are shown for each case. Red horizontal arrows and red vertical bars in the conduction band are for instant 1, blue arrows and bars are for instant 2, and the green arrows and bars are for instant 3.

Tables (1)

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Table 1. Material Parameters of ZnSe [59] Utilized in the Simulations

Equations (25)

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N ( t , ε ) = i N i ( t , ε ) ; d N i ( t , ε ) d t = f i ( t ) W i [ F ( t ) ] ,
f i ( t ) = 1 1 N i 0 ε i 0 N i ( t , ε ) d ε ,
N i ( t = 0 ) = 0 .
Δ i eff = 2 π Δ [ 1 + γ i 2 γ i · E ( 1 1 + γ i 2 ) ] , i = HH , LH ,
γ i = ω m i R Δ e F ( t ) , i = HH , LH ,
E ( t ) = E 0 f ( t τ p ) cos ( ω t ) = F ( t ) cos ( ω t ) ,
Δ SO eff = ( Δ + Δ SO ) · ( 1 + 1 4 γ SO 2 ) = ( Δ + Δ SO ) · ( 1 + e 2 F ( t ) 2 4 m SO R Δ ω 2 ) ,
γ SO = ω m SO R ( Δ + Δ SO ) e F ( t ) .
1 m i R = 1 m CB + 1 m i .
n i ( t ) = Δ i eff ω + 1 ,
( d ε d t ) DR = e 2 F 2 ( t ) 2 m CB ω 2 ω 2 ω 2 + ν DR 2 ν DR ,
A ( ϵ , t ) = d ε d t = ( e F ( t ) ω ) e 2 Ω 0 ( ε 0 ε ) π ε 0 ε coth ( Ω 0 2 k B T phonon ) × Ψ ( ω 2 m ε ( t ) e F ( t ) ) ,
Ψ ( x ) = { 4 3 1 x 2 + 2 arcsin ( x ) 3 x + 2 3 x 2 arcosh ( 1 x ) , if    x 1 , π 3 x , if    x > 1 } .
ε i 0 ( t ) = m i R 2 m CB Δ [ ( ω Δ n i ( t ) ) 2 1 ] , i = HH , LH .
ε SO 0 ( t ) = m SO R 2 m CB ( Δ + Δ SO ) [ ω Δ + Δ SO n SO ( t ) 1 ] .
ε TL τ p ν Dr e 2 E 0 2 2 m CB ω 2 ω 2 ω 2 + ν Dr 2 .
p e E 0 ω ;
p 2 2 m CB ω .
f ( p , t ) t + e E ( t ) p f ( p , t ) = 2 π s , k | C s k | 2 V { f ( p + k , t ) [ n s k δ ( ε p ε p + k ω s k ) + ( n s k + 1 ) δ ( ε p ε p + k + ω s k ) ] f ( p , t ) [ n s k δ ( ε p ε p + k + ω s k ) + ( n s k + 1 ) δ ( ε p ε p + k ω s k ) ] } ,
F ( P , t ) = f ( P e t E ( τ ) d τ , t ) .
d W d t = e 2 m CB P P [ E * g 1 ( P , t ) + E * g 1 ( P , t ) ] = P d ε p d t g 0 ( P , t ) ,
E ( t ) = 1 2 [ E e i ω t + E * e i ω t ] ,
F ( P , t ) = n e i n ω t g n ( P , t ) .
2 e 2 E 0 2 m CB ω 2 ω if    P e E 0 ω ,
2 e E 0 P m CB ω ω if    P e E 0 ω .