Abstract

Femtosecond-pulse-induced (Epump = 2.5 eV) picosecond infrared absorption is studied in the spectral region between 0.30 eV and 1.05 eV in LiNbO3:Mg. We find a non-instantaneous mid-infrared absorption peak in the time domain up to 1 ps and a broad-band, long-lived absorption (maximum at 0.85 eV, width ≈ 0.5 eV), for t > 1 ps. The modelling succeeds by considering small NbNb4+ electron polaron formation along the sequence: (i) two-photon injection of hot electron-hole pairs at Nb-O-octahedra, (ii) dissociation and electron cooling by electron-phonon-scattering, and (iii) electron self-localization by strong electron-phonon-coupling.

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

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References

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  1. Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
    [Crossref]
  2. J. Hirohashi, V. Pasiskevicius, S. Wang, and F. Laurell, “Picosecond blue-light-induced infrared absorption in single-domain and periodically poled ferroelectrics,” J. Appl. Phys. 101, 033105 (2007).
    [Crossref]
  3. S. Favre, T. Sidler, and R.-P. Salathe, “High-power long-pulse second harmonic generation and optical damage with free-running Nd: YAG laser,” IEEE J. Quantum Electron. 39, 733–740 (2003).
    [Crossref]
  4. R. M. Wood, Laser-Induced Damage of Optical Materials (Series in Optics and Optoelectronics) (CRC Press, 2003).
    [Crossref]
  5. G. Li and X. Xu, “Thermally induced dephasing of high power second harmonic generation in MgO:LiNbO3 waveguides,” Chin. Opt. Lett. 9, 121901 (2011).
    [Crossref]
  6. O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys. Conden. Matter 18, R667–R704 (2006).
    [Crossref]
  7. O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Conden. Matter 21, 123201 (2009).
    [Crossref]
  8. D. Emin, “Optical properties of large and small polarons and bipolarons,” Phys. Rev. B 48, 13691–13702 (1993).
    [Crossref]
  9. Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: Measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
    [Crossref]
  10. T. Holstein, “Studies of polaron motion,” Annals Phys. 8, 343–389 (1959).
    [Crossref]
  11. D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
    [Crossref]
  12. O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006).
    [Crossref]
  13. D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847 (1984).
    [Crossref]
  14. D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
    [Crossref]
  15. S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron Dynamics in Lithium Niobate upon Femtosecond Pulse Irradiation: Influence of Magnesium Doping and Stoichiometry Control,” J. Appl. Phys. 105, 083102 (2009).
    [Crossref]
  16. S. Enomoto and S. Ashihara, “Comparative study on light-induced absorption between MgO:LiNbO3 and MgO:LiTaO3,” J. Appl. Phys. 110, 063111 (2011).
    [Crossref]
  17. G. M. Greetham, P. Burgos, Q. Cao, I. P. Clark, P. S. Codd, R. C. Farrow, M. W. George, M. Kogimtzis, P. Matousek, A. W. Parker, M. R. Pollard, D. A. Robinson, Z. Xin, and M. Towrie, “Ultra: A unique instrument for time-resolved spectroscopy,” Appl. Spectrosc. 64, 1311–1319 (2010).
    [Crossref] [PubMed]
  18. F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
    [Crossref]
  19. O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
    [Crossref]
  20. D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
    [Crossref]
  21. X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
    [Crossref]
  22. T. Roth and R. Laenen, “Absorption of free carriers in diamond determined from the visible to the mid-infrared by femtosecond two-photon absorption spectroscopy,” Opt. Commun. 189, 289–296 (2001).
    [Crossref]
  23. R. Williams and K. Song, “The self-trapped exciton,” J. Phys. Chem. Solids 51, 679–716 (1990).
    [Crossref]
  24. M. D. Fontana and P. Bourson, “Microstructure and defects probed by raman spectroscopy in lithium niobate crystals and devices,” Appl. Phys. Rev. 2, 040602 (2015).
    [Crossref]
  25. G. Blasse, “Fluorescence of niobium-activated antimonates and an empirical criterion for the occurrence of luminescence,” J. Chem. Phys. 48, 3108–3114 (1968).
    [Crossref]
  26. C. Fischer, M. Wöhlecke, T. Volk, and N. Rubinina, “Influence of the damage resistant impurities Zn and Mg on the UV-excited luminescence in LiNbO3,” Phys. Status Solidi (a) 137, 247–255 (1993).
    [Crossref]
  27. D. Emin, “Dynamics of the optically induced properties of a small-polaronic glass,” J. Non-Cryst. Solids 35–36, 969–973 (1980).
    [Crossref]
  28. D. Emin, Polarons (Cambridge University Press, 2013).
  29. H. Badorreck, S. Nolte, F. Freytag, P. Bäune, V. Dieckmann, and M. Imlau, “Scanning nonlinear absorption in lithium niobate over the time regime of small polaron formation,” Opt. Mater. Express 5, 2729 (2015).
    [Crossref]
  30. M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
    [Crossref]
  31. B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics. 153, 297–302 (1994).
    [Crossref]
  32. G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
    [Crossref]

2015 (3)

M. D. Fontana and P. Bourson, “Microstructure and defects probed by raman spectroscopy in lithium niobate crystals and devices,” Appl. Phys. Rev. 2, 040602 (2015).
[Crossref]

H. Badorreck, S. Nolte, F. Freytag, P. Bäune, V. Dieckmann, and M. Imlau, “Scanning nonlinear absorption in lithium niobate over the time regime of small polaron formation,” Opt. Mater. Express 5, 2729 (2015).
[Crossref]

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

2012 (1)

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

2011 (2)

G. Li and X. Xu, “Thermally induced dephasing of high power second harmonic generation in MgO:LiNbO3 waveguides,” Chin. Opt. Lett. 9, 121901 (2011).
[Crossref]

S. Enomoto and S. Ashihara, “Comparative study on light-induced absorption between MgO:LiNbO3 and MgO:LiTaO3,” J. Appl. Phys. 110, 063111 (2011).
[Crossref]

2010 (1)

2009 (2)

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron Dynamics in Lithium Niobate upon Femtosecond Pulse Irradiation: Influence of Magnesium Doping and Stoichiometry Control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Conden. Matter 21, 123201 (2009).
[Crossref]

2008 (2)

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

2007 (1)

J. Hirohashi, V. Pasiskevicius, S. Wang, and F. Laurell, “Picosecond blue-light-induced infrared absorption in single-domain and periodically poled ferroelectrics,” J. Appl. Phys. 101, 033105 (2007).
[Crossref]

2006 (2)

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys. Conden. Matter 18, R667–R704 (2006).
[Crossref]

O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006).
[Crossref]

2005 (2)

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: Measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[Crossref]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

2004 (1)

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

2003 (1)

S. Favre, T. Sidler, and R.-P. Salathe, “High-power long-pulse second harmonic generation and optical damage with free-running Nd: YAG laser,” IEEE J. Quantum Electron. 39, 733–740 (2003).
[Crossref]

2001 (2)

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

T. Roth and R. Laenen, “Absorption of free carriers in diamond determined from the visible to the mid-infrared by femtosecond two-photon absorption spectroscopy,” Opt. Commun. 189, 289–296 (2001).
[Crossref]

2000 (1)

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

1996 (1)

X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
[Crossref]

1994 (1)

B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics. 153, 297–302 (1994).
[Crossref]

1993 (2)

C. Fischer, M. Wöhlecke, T. Volk, and N. Rubinina, “Influence of the damage resistant impurities Zn and Mg on the UV-excited luminescence in LiNbO3,” Phys. Status Solidi (a) 137, 247–255 (1993).
[Crossref]

D. Emin, “Optical properties of large and small polarons and bipolarons,” Phys. Rev. B 48, 13691–13702 (1993).
[Crossref]

1990 (1)

R. Williams and K. Song, “The self-trapped exciton,” J. Phys. Chem. Solids 51, 679–716 (1990).
[Crossref]

1984 (1)

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847 (1984).
[Crossref]

1980 (1)

D. Emin, “Dynamics of the optically induced properties of a small-polaronic glass,” J. Non-Cryst. Solids 35–36, 969–973 (1980).
[Crossref]

1968 (1)

G. Blasse, “Fluorescence of niobium-activated antimonates and an empirical criterion for the occurrence of luminescence,” J. Chem. Phys. 48, 3108–3114 (1968).
[Crossref]

1959 (1)

T. Holstein, “Studies of polaron motion,” Annals Phys. 8, 343–389 (1959).
[Crossref]

Alexandrovski, A.

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

Ashihara, S.

S. Enomoto and S. Ashihara, “Comparative study on light-induced absorption between MgO:LiNbO3 and MgO:LiTaO3,” J. Appl. Phys. 110, 063111 (2011).
[Crossref]

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron Dynamics in Lithium Niobate upon Femtosecond Pulse Irradiation: Influence of Magnesium Doping and Stoichiometry Control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

Badorreck, H.

Bäune, P.

Berben, D.

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

Beyer, O.

O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006).
[Crossref]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

Blasse, G.

G. Blasse, “Fluorescence of niobium-activated antimonates and an empirical criterion for the occurrence of luminescence,” J. Chem. Phys. 48, 3108–3114 (1968).
[Crossref]

Bourson, P.

M. D. Fontana and P. Bourson, “Microstructure and defects probed by raman spectroscopy in lithium niobate crystals and devices,” Appl. Phys. Rev. 2, 040602 (2015).
[Crossref]

Bryan, D. A.

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847 (1984).
[Crossref]

Bückers, J.

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

Burgos, P.

Buse, K.

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006).
[Crossref]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

Cao, Q.

Clark, I. P.

Codd, P. S.

Conradi, D.

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

Corradi, G.

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

Dieckmann, V.

Emin, D.

D. Emin, “Optical properties of large and small polarons and bipolarons,” Phys. Rev. B 48, 13691–13702 (1993).
[Crossref]

D. Emin, “Dynamics of the optically induced properties of a small-polaronic glass,” J. Non-Cryst. Solids 35–36, 969–973 (1980).
[Crossref]

D. Emin, Polarons (Cambridge University Press, 2013).

Enomoto, S.

S. Enomoto and S. Ashihara, “Comparative study on light-induced absorption between MgO:LiNbO3 and MgO:LiTaO3,” J. Appl. Phys. 110, 063111 (2011).
[Crossref]

Farrow, R. C.

Faust, B.

B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics. 153, 297–302 (1994).
[Crossref]

Favre, S.

S. Favre, T. Sidler, and R.-P. Salathe, “High-power long-pulse second harmonic generation and optical damage with free-running Nd: YAG laser,” IEEE J. Quantum Electron. 39, 733–740 (2003).
[Crossref]

Fejer, M. M.

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

Fischer, C.

C. Fischer, M. Wöhlecke, T. Volk, and N. Rubinina, “Influence of the damage resistant impurities Zn and Mg on the UV-excited luminescence in LiNbO3,” Phys. Status Solidi (a) 137, 247–255 (1993).
[Crossref]

Fontana, M. D.

M. D. Fontana and P. Bourson, “Microstructure and defects probed by raman spectroscopy in lithium niobate crystals and devices,” Appl. Phys. Rev. 2, 040602 (2015).
[Crossref]

Foulon, G.

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

Freytag, F.

Furukawa, Y.

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

George, M. W.

Gerson, R.

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847 (1984).
[Crossref]

Greetham, G. M.

Haertle, D.

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

Herth, P.

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

Hirohashi, J.

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron Dynamics in Lithium Niobate upon Femtosecond Pulse Irradiation: Influence of Magnesium Doping and Stoichiometry Control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

J. Hirohashi, V. Pasiskevicius, S. Wang, and F. Laurell, “Picosecond blue-light-induced infrared absorption in single-domain and periodically poled ferroelectrics,” J. Appl. Phys. 101, 033105 (2007).
[Crossref]

Holstein, T.

T. Holstein, “Studies of polaron motion,” Annals Phys. 8, 343–389 (1959).
[Crossref]

Hsieh, H. T.

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

Imlau, M.

H. Badorreck, S. Nolte, F. Freytag, P. Bäune, V. Dieckmann, and M. Imlau, “Scanning nonlinear absorption in lithium niobate over the time regime of small polaron formation,” Opt. Mater. Express 5, 2729 (2015).
[Crossref]

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Conden. Matter 21, 123201 (2009).
[Crossref]

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

Kitaeva, G.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Kitamura, K.

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

Kogimtzis, M.

Kong, Y.

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

Kratz, S.

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

Kuznetsov, K.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Laenen, R.

T. Roth and R. Laenen, “Absorption of free carriers in diamond determined from the visible to the mid-infrared by femtosecond two-photon absorption spectroscopy,” Opt. Commun. 189, 289–296 (2001).
[Crossref]

Laurell, F.

J. Hirohashi, V. Pasiskevicius, S. Wang, and F. Laurell, “Picosecond blue-light-induced infrared absorption in single-domain and periodically poled ferroelectrics,” J. Appl. Phys. 101, 033105 (2007).
[Crossref]

Li, G.

Li, H.

X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
[Crossref]

Matousek, P.

Maxein, D.

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006).
[Crossref]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

Merschjann, C.

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Conden. Matter 21, 123201 (2009).
[Crossref]

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

Morozova, V.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Müller, H.

B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics. 153, 297–302 (1994).
[Crossref]

Naumova, I.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Nolte, S.

Parker, A. W.

Pasiskevicius, V.

J. Hirohashi, V. Pasiskevicius, S. Wang, and F. Laurell, “Picosecond blue-light-induced infrared absorption in single-domain and periodically poled ferroelectrics,” J. Appl. Phys. 101, 033105 (2007).
[Crossref]

Penin, A.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Polgár, K.

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

Pollard, M. R.

Psaltis, D.

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

Qiu, Y.

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: Measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[Crossref]

Reckenthaeler, P.

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

Robinson, D. A.

Roth, T.

T. Roth and R. Laenen, “Absorption of free carriers in diamond determined from the visible to the mid-infrared by femtosecond two-photon absorption spectroscopy,” Opt. Commun. 189, 289–296 (2001).
[Crossref]

Route, R. K.

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

Rubinina, N.

C. Fischer, M. Wöhlecke, T. Volk, and N. Rubinina, “Influence of the damage resistant impurities Zn and Mg on the UV-excited luminescence in LiNbO3,” Phys. Status Solidi (a) 137, 247–255 (1993).
[Crossref]

Salathe, R.-P.

S. Favre, T. Sidler, and R.-P. Salathe, “High-power long-pulse second harmonic generation and optical damage with free-running Nd: YAG laser,” IEEE J. Quantum Electron. 39, 733–740 (2003).
[Crossref]

Sasamoto, S.

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron Dynamics in Lithium Niobate upon Femtosecond Pulse Irradiation: Influence of Magnesium Doping and Stoichiometry Control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

Schirmer, O. F.

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Conden. Matter 21, 123201 (2009).
[Crossref]

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys. Conden. Matter 18, R667–R704 (2006).
[Crossref]

B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics. 153, 297–302 (1994).
[Crossref]

Schoke, B.

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Conden. Matter 21, 123201 (2009).
[Crossref]

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

Shepelev, A.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Sidler, T.

S. Favre, T. Sidler, and R.-P. Salathe, “High-power long-pulse second harmonic generation and optical damage with free-running Nd: YAG laser,” IEEE J. Quantum Electron. 39, 733–740 (2003).
[Crossref]

Song, K.

R. Williams and K. Song, “The self-trapped exciton,” J. Phys. Chem. Solids 51, 679–716 (1990).
[Crossref]

Sturman, B.

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

Tomaschke, H. E.

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847 (1984).
[Crossref]

Towrie, M.

Ucer, K. B.

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: Measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[Crossref]

Viskovatich, A.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Volk, T.

C. Fischer, M. Wöhlecke, T. Volk, and N. Rubinina, “Influence of the damage resistant impurities Zn and Mg on the UV-excited luminescence in LiNbO3,” Phys. Status Solidi (a) 137, 247–255 (1993).
[Crossref]

Wang, S.

J. Hirohashi, V. Pasiskevicius, S. Wang, and F. Laurell, “Picosecond blue-light-induced infrared absorption in single-domain and periodically poled ferroelectrics,” J. Appl. Phys. 101, 033105 (2007).
[Crossref]

Wang, X.

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
[Crossref]

Wevering, S.

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

Williams, R.

R. Williams and K. Song, “The self-trapped exciton,” J. Phys. Chem. Solids 51, 679–716 (1990).
[Crossref]

Williams, R. T.

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: Measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[Crossref]

Wöhlecke, M.

C. Fischer, M. Wöhlecke, T. Volk, and N. Rubinina, “Influence of the damage resistant impurities Zn and Mg on the UV-excited luminescence in LiNbO3,” Phys. Status Solidi (a) 137, 247–255 (1993).
[Crossref]

Woike, T.

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006).
[Crossref]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

Wood, R. M.

R. M. Wood, Laser-Induced Damage of Optical Materials (Series in Optics and Optoelectronics) (CRC Press, 2003).
[Crossref]

Xin, F.

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

Xin, Z.

Xu, G.

X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
[Crossref]

Xu, J.

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

Xu, X.

Yang, X.

X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
[Crossref]

Zhai, Z.

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

Zhang, G.

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

Zhigunov, D.

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Zhu, J.

X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
[Crossref]

Annals Phys. (1)

T. Holstein, “Studies of polaron motion,” Annals Phys. 8, 343–389 (1959).
[Crossref]

Appl. Phys. B (3)

O. Beyer, D. Maxein, T. Woike, and K. Buse, “Generation of small bound polarons in lithium niobate crystals on the subpicosecond time scale,” Appl. Phys. B 83, 527–530 (2006).
[Crossref]

D. Maxein, S. Kratz, P. Reckenthaeler, J. Bückers, D. Haertle, T. Woike, and K. Buse, “Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses,” Appl. Phys. B 92, 543–547 (2008).
[Crossref]

G. Kitaeva, K. Kuznetsov, V. Morozova, I. Naumova, A. Penin, A. Shepelev, A. Viskovatich, and D. Zhigunov, “Reduction-induced polarons and optical response of Mg-doped LiNbO3 crystals,” Appl. Phys. B 78, 759–764 (2004).
[Crossref]

Appl. Phys. Lett. (2)

D. A. Bryan, R. Gerson, and H. E. Tomaschke, “Increased optical damage resistance in lithium niobate,” Appl. Phys. Lett. 44, 847 (1984).
[Crossref]

Y. Furukawa, K. Kitamura, A. Alexandrovski, R. K. Route, M. M. Fejer, and G. Foulon, “Green-induced infrared absorption in MgO doped LiNbO3,” Appl. Phys. Lett. 78, 1970–1972 (2001).
[Crossref]

Appl. Phys. Rev. (2)

M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
[Crossref]

M. D. Fontana and P. Bourson, “Microstructure and defects probed by raman spectroscopy in lithium niobate crystals and devices,” Appl. Phys. Rev. 2, 040602 (2015).
[Crossref]

Appl. Spectrosc. (1)

Chin. Opt. Lett. (1)

Cryst. Res. Technol. (1)

X. Yang, G. Xu, H. Li, J. Zhu, and X. Wang, “Optical absorption edge of Mg + Zn: LiNbO3,” Cryst. Res. Technol. 31, 521–527 (1996).
[Crossref]

Ferroelectrics. (1)

B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics. 153, 297–302 (1994).
[Crossref]

IEEE J. Quantum Electron. (1)

S. Favre, T. Sidler, and R.-P. Salathe, “High-power long-pulse second harmonic generation and optical damage with free-running Nd: YAG laser,” IEEE J. Quantum Electron. 39, 733–740 (2003).
[Crossref]

J. Appl. Phys. (4)

J. Hirohashi, V. Pasiskevicius, S. Wang, and F. Laurell, “Picosecond blue-light-induced infrared absorption in single-domain and periodically poled ferroelectrics,” J. Appl. Phys. 101, 033105 (2007).
[Crossref]

S. Sasamoto, J. Hirohashi, and S. Ashihara, “Polaron Dynamics in Lithium Niobate upon Femtosecond Pulse Irradiation: Influence of Magnesium Doping and Stoichiometry Control,” J. Appl. Phys. 105, 083102 (2009).
[Crossref]

S. Enomoto and S. Ashihara, “Comparative study on light-induced absorption between MgO:LiNbO3 and MgO:LiTaO3,” J. Appl. Phys. 110, 063111 (2011).
[Crossref]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium–niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[Crossref]

J. Chem. Phys. (1)

G. Blasse, “Fluorescence of niobium-activated antimonates and an empirical criterion for the occurrence of luminescence,” J. Chem. Phys. 48, 3108–3114 (1968).
[Crossref]

J. Non-Cryst. Solids (1)

D. Emin, “Dynamics of the optically induced properties of a small-polaronic glass,” J. Non-Cryst. Solids 35–36, 969–973 (1980).
[Crossref]

J. Phys. Chem. Solids (1)

R. Williams and K. Song, “The self-trapped exciton,” J. Phys. Chem. Solids 51, 679–716 (1990).
[Crossref]

J. Phys. Conden. Matter (2)

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys. Conden. Matter 18, R667–R704 (2006).
[Crossref]

O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Conden. Matter 21, 123201 (2009).
[Crossref]

Opt. Commun. (1)

T. Roth and R. Laenen, “Absorption of free carriers in diamond determined from the visible to the mid-infrared by femtosecond two-photon absorption spectroscopy,” Opt. Commun. 189, 289–296 (2001).
[Crossref]

Opt. Mater. Express (1)

Phys. Rev. B (2)

D. Emin, “Optical properties of large and small polarons and bipolarons,” Phys. Rev. B 48, 13691–13702 (1993).
[Crossref]

F. Xin, Z. Zhai, X. Wang, Y. Kong, J. Xu, and G. Zhang, “Threshold behavior of the einstein oscillator, electron-phonon interaction, band-edge absorption, and small hole polarons in linbo3:mg crystals,” Phys. Rev. B 86, 165132 (2012).
[Crossref]

Phys. Rev. E (1)

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[Crossref]

Phys. Status Solidi (a) (1)

C. Fischer, M. Wöhlecke, T. Volk, and N. Rubinina, “Influence of the damage resistant impurities Zn and Mg on the UV-excited luminescence in LiNbO3,” Phys. Status Solidi (a) 137, 247–255 (1993).
[Crossref]

Phys. Status Solidi C (1)

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: Measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[Crossref]

Phys. Status Solidi RRL (1)

D. Conradi, C. Merschjann, B. Schoke, M. Imlau, G. Corradi, and K. Polgár, “Influence of Mg doping on the behaviour of polaronic light-induced absorption in LiNbO3,” Phys. Status Solidi RRL 2, 284–286 (2008).
[Crossref]

Other (2)

R. M. Wood, Laser-Induced Damage of Optical Materials (Series in Optics and Optoelectronics) (CRC Press, 2003).
[Crossref]

D. Emin, Polarons (Cambridge University Press, 2013).

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Figures (4)

Fig. 1
Fig. 1 Transient absorption in the ps range for a 2.5 eV pump pulse ( I pump 0 = ( 1.4 ± 0.2 ) PW / m 2 ) and probe photon energies Eprobe = 0.40 eV (3000 nm), 0.60 eV (2066 nm), 0.80 eV (1550 nm). The transient absorption is defined as Δα(Eprobe, δt) = α(Eprobe, δt)pumpedα(Eprobe, δt)unpumped. The depicted values represent the average over 2000 pump-probe events and the error margin is given by the standard deviation. The gray data points are the corresponding DFG correlation signal between pump and probe pulse (schematic setup shown in the insert) and the dotted black lines correspond to the numerical fits (see chapter 3.2).
Fig. 2
Fig. 2 Recombination paths of fs-pulse generated hot electrons and holes in LN:Mg displayed (a) in a model of the atomic structure and (b) in an energy level diagram. Three recombination paths are considered: (1) the direct recombination of electrons and holes, (2) the formation of self-trapped excitons within a Nb-O-octahedron, and (3) the phonon-assisted formation of small polarons. Our modelling of Eqs. 1-3 is based on relaxation path (3), i.e., paths (1) and (2) are disregarded in our model. This assumption accords with our experimental setup and crystal choice being tailored for small free polaron detection. Furthermore, it considers the comparably low probability for paths (1) and (2).
Fig. 3
Fig. 3 Numerical fit of the transient absorption (green line) and the data set (green dots) at 0.6 eV. Fitting parameters: τc = 100 fs and τp = 150 fs. The dynamics of the individual number densities are calculated assuming full conversion of pump photons to hot electrons and are plotted as orange (Nh), blue (Nc) and yellow (Np) lines. Note that Nh does not contribute to the MIR absorption as σh = 0, but is still fully defined due to the nonlinear term in Eq. 1.
Fig. 4
Fig. 4 Absorption fingerprint of fs-pulse induced free polarons at a fixed time delay of t = 2 ps ( I pump 0 = ( 2.5 ± 0.2 ) PW / m 2 ). The continuous line fits Eq. 7 to the experimental data set. The error margin is given by the standard deviation and the error made by determining the light intensity.

Tables (1)

Tables Icon

Table 1 Polaron stabilization energy Ep and half width at half maximum W of the MIR absorption feature in comparison.

Equations (7)

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

N h ( L , t ) t = β I 2 ( L , t ) 2 ω N h ( L , t ) τ c
N c ( L , t ) t = N h ( L , t ) τ c N c ( L , t ) τ p
N p ( L , t ) t = N c ( L , t ) τ p ,
I ( t , L ) = 2 exp [ 4 log ( 2 ) ( t τ pump ) 2 ] β L π 0 ln [ 1 + β I pump 0 L exp ( s 2 ) ] ds .
α calc ( t ) = 1 d 0 d [ σ p N p ( L , t ) + σ h N h ( L , t ) + σ c N c ( L , t ) ] dL .
α exp ( Δ t ) = 2 log ( 2 ) π τ probe 2 α calc ( t ) exp [ 4 log ( 2 ) ( t Δ t τ probe ) 2 ] dt
Δ α ( ω ) 1 ω exp [ ( 2 E p ω ) 2 / ( 8 E p k B T ) ] ,

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