Abstract

Nonlinear absorption is studied in presence of small polaron formation in lithium niobate using the z-scan technique and ultrashort laser pulses with pulse durations of 70 – 1,000 fs. A model for the analysis of the transmission loss as a function of pulse duration is introduced that considers (i) the individual contributions of two-photon and small polaron absorption, (ii) the small polaron formation time and (iii) an offset time between the optical excitation of free carriers by two-photon absorption and the appearance of small polarons. It is shown that the model allows for the analysis of the experimentally determined z-scan data with high precision over the entire range of pulse durations using a two-photon absorption coefficient of β = (5.6 ± 0.8) mm/GW. A significant contribution by small polaron absorption to the nonlinear absorption is uncovered for pulse durations exceeding the characteristic small polaron formation time of ≈ 100fs. It can be concluded that the small polaron formation time is as short as (70 – 110) fs and the appearance of small polaron formation is delayed with respect to two-photon absorption by an offset of about 80 fs.

© 2015 Optical Society of America

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  1. M. Fejer, G. Magel, D. H. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [Crossref]
  2. O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
    [Crossref]
  3. O. F. Schirmer and D. von der Linde, “Two–Photon and X–Ray–Induced Nb4+ and O− Small Polarons in LiNbO3,” Appl. Phys. Lett. 33, 35 (1978).
    [Crossref]
  4. D. Emin, Polarons (Cambridge University Press, Cambridge, 2013).
  5. C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).
  6. Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Stat. Sol. C 2, 232 (2005).
    [Crossref]
  7. 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]
  8. 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]
  9. 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]
  10. H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
    [Crossref]
  11. M. Imlau, H. Badorreck, and C. Merschjann, “Optical nonlinearities of small polarons in lithium niobate,” Appl. Phys. Rev. 2, 040606 (2015).
    [Crossref]
  12. D. Maxein and K. Buse, “Interaction of Femtosecond Laser Pulses with Lithium Niobate Crystals: Transmission Changes and Refractive Index Modulations,” J. Holography Speckle 5, 1–5 (2009).
    [Crossref]
  13. A. Seilmeier and W. Kaiser, “Generation of tunable picosecond light pulses covering the frequency range between 2700 and 32,000 cm−1,” Appl. Phys. A 23, 113 (1980).
    [Crossref]
  14. R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
    [Crossref]
  15. H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659 (1997).
    [Crossref]
  16. R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
    [Crossref]
  17. O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
    [Crossref] [PubMed]
  18. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
    [Crossref]
  19. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of Bound-electronic and Free-carrier Nonlinearities In ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
    [Crossref]
  20. S. Redfield and W. J. Burke, “Optical Absorption Edge of LiNbO3,” J. Appl. Phys.45 (1974).
    [Crossref]
  21. H. Badorreck, School of Physics, Osnabrueck University, Barbarastr. 7, 49076 Osnabrueck, Germany, A. Shumelyuk, S. Nolte, M. Imlau, and S. Odoulov are preparing a manuscript to be called “Selfdiffraction from moving gratings recorded in LiNbO3 with ultra-short laser pulses of different colors.”
  22. A. Othonos, “Probing ultrafast carrier and phonon dynamics in semiconductors,” J. Appl. Phys. 83, 1789–1830 (1998).
    [Crossref]
  23. M. Garcia-Lechuga, J. Siegel, J. Hernandez-Rueda, and J. Solis, “Imaging the ultrafast Kerr effect, free carrier generation, relaxation and ablation dynamics of Lithium Niobate irradiated with femtosecond laser pulses,” J. Appl. Phys. 116, 113502 (2014).
    [Crossref]
  24. O. F. Schirmer, O. Thiemann, and M. Wöhlecke, “Defects in LiNbO3 — I. Experimental Aspects,” J. Phys. Chem. Solids 52, 185 (1991).
    [Crossref]
  25. O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys. Condens. Matter 18, R667 (2006).
    [Crossref]
  26. O. F. Schirmer, M. Imlau, C. Merschjann, and B. Schoke, “Electron small polarons and bipolarons in LiNbO3,” J. Phys. Condens. Matter 21, 123201 (2009).
    [Crossref]
  27. B. Faust, H. Müller, and O. F. Schirmer, “Free small polarons in LiNbO3,” Ferroelectrics 153, 297 (1994).
    [Crossref]
  28. Y. Li, W. G. Schmidt, and S. Sanna, “Intrinsic LiNbO3 point defects from hybrid density functional calculations,” Phys. Rev. B 89, 094111 (2014).
    [Crossref]
  29. Y. Li, S. Sanna, and W. G. Schmidt, “Modeling intrinsic defects in LiNbO3 within the Slater-Janak transition state model,” The Journal of Chemical Physics 140, 234113 (2014).
    [Crossref]
  30. K. Ogusu and K. Shinkawa, “Optical nonlinearities in silicon for pulse durations of the order of nanoseconds at 1.06 μm,” Opt. Express 16, 14780–14791 (2008).
    [Crossref] [PubMed]
  31. P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
    [Crossref]
  32. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
    [Crossref] [PubMed]
  33. O. F. Schirmer, M. Imlau, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B 83, 165106 (2011).
    [Crossref]

2015 (1)

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

2014 (3)

M. Garcia-Lechuga, J. Siegel, J. Hernandez-Rueda, and J. Solis, “Imaging the ultrafast Kerr effect, free carrier generation, relaxation and ablation dynamics of Lithium Niobate irradiated with femtosecond laser pulses,” J. Appl. Phys. 116, 113502 (2014).
[Crossref]

Y. Li, W. G. Schmidt, and S. Sanna, “Intrinsic LiNbO3 point defects from hybrid density functional calculations,” Phys. Rev. B 89, 094111 (2014).
[Crossref]

Y. Li, S. Sanna, and W. G. Schmidt, “Modeling intrinsic defects in LiNbO3 within the Slater-Janak transition state model,” The Journal of Chemical Physics 140, 234113 (2014).
[Crossref]

2013 (1)

O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
[Crossref]

2011 (1)

O. F. Schirmer, M. Imlau, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B 83, 165106 (2011).
[Crossref]

2009 (4)

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

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

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]

D. Maxein and K. Buse, “Interaction of Femtosecond Laser Pulses with Lithium Niobate Crystals: Transmission Changes and Refractive Index Modulations,” J. Holography Speckle 5, 1–5 (2009).
[Crossref]

2008 (1)

2006 (2)

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys. Condens. Matter 18, R667 (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 (3)

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]

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

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
[Crossref] [PubMed]

2004 (1)

R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
[Crossref]

1999 (1)

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

1998 (1)

A. Othonos, “Probing ultrafast carrier and phonon dynamics in semiconductors,” J. Appl. Phys. 83, 1789–1830 (1998).
[Crossref]

1997 (2)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
[Crossref]

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659 (1997).
[Crossref]

1996 (1)

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
[Crossref]

1994 (1)

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

1992 (2)

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of Bound-electronic and Free-carrier Nonlinearities In ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[Crossref]

M. Fejer, G. Magel, D. H. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

1991 (1)

O. F. Schirmer, O. Thiemann, and M. Wöhlecke, “Defects in LiNbO3 — I. Experimental Aspects,” J. Phys. Chem. Solids 52, 185 (1991).
[Crossref]

1990 (2)

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

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

1980 (1)

A. Seilmeier and W. Kaiser, “Generation of tunable picosecond light pulses covering the frequency range between 2700 and 32,000 cm−1,” Appl. Phys. A 23, 113 (1980).
[Crossref]

1978 (1)

O. F. Schirmer and D. von der Linde, “Two–Photon and X–Ray–Induced Nb4+ and O− Small Polarons in LiNbO3,” Appl. Phys. Lett. 33, 35 (1978).
[Crossref]

Ashihara, 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]

Badorreck, H.

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

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
[Crossref] [PubMed]

Burke, W. J.

S. Redfield and W. J. Burke, “Optical Absorption Edge of LiNbO3,” J. Appl. Phys.45 (1974).
[Crossref]

Buse, K.

D. Maxein and K. Buse, “Interaction of Femtosecond Laser Pulses with Lithium Niobate Crystals: Transmission Changes and Refractive Index Modulations,” J. Holography Speckle 5, 1–5 (2009).
[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]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
[Crossref] [PubMed]

Byer, R.

M. Fejer, G. Magel, D. H. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

Chapple, P. B.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
[Crossref]

Conradi, D.

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

Corradi, G.

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

Denks, V.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

DeSalvo, R.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
[Crossref]

Emin, D.

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

Faust, B.

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

Fejer, M.

M. Fejer, G. Magel, D. H. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

Ganeev, R.

R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
[Crossref]

Garcia-Lechuga, M.

M. Garcia-Lechuga, J. Siegel, J. Hernandez-Rueda, and J. Solis, “Imaging the ultrafast Kerr effect, free carrier generation, relaxation and ablation dynamics of Lithium Niobate irradiated with femtosecond laser pulses,” J. Appl. Phys. 116, 113502 (2014).
[Crossref]

Grigorjeva, L.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

Hagan, D.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
[Crossref]

Hagan, D. J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of Bound-electronic and Free-carrier Nonlinearities In ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[Crossref]

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

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Hatano, H. H.

O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
[Crossref]

Hermann, J. A.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
[Crossref]

Hernandez-Rueda, J.

M. Garcia-Lechuga, J. Siegel, J. Hernandez-Rueda, and J. Solis, “Imaging the ultrafast Kerr effect, free carrier generation, relaxation and ablation dynamics of Lithium Niobate irradiated with femtosecond laser pulses,” J. Appl. Phys. 116, 113502 (2014).
[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]

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]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
[Crossref] [PubMed]

Imlau, M.

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, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B 83, 165106 (2011).
[Crossref]

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

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

Ji, W.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659 (1997).
[Crossref]

Jundt, D. H.

M. Fejer, G. Magel, D. H. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

Kaiser, W.

A. Seilmeier and W. Kaiser, “Generation of tunable picosecond light pulses covering the frequency range between 2700 and 32,000 cm−1,” Appl. Phys. A 23, 113 (1980).
[Crossref]

Kitamura, K.

O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
[Crossref]

Kotomin, E.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

Kulagin, I.

R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
[Crossref]

Li, H.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659 (1997).
[Crossref]

Li, Y.

Y. Li, W. G. Schmidt, and S. Sanna, “Intrinsic LiNbO3 point defects from hybrid density functional calculations,” Phys. Rev. B 89, 094111 (2014).
[Crossref]

Y. Li, S. Sanna, and W. G. Schmidt, “Modeling intrinsic defects in LiNbO3 within the Slater-Janak transition state model,” The Journal of Chemical Physics 140, 234113 (2014).
[Crossref]

Louchev, O. A.

O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
[Crossref]

Magel, G.

M. Fejer, G. Magel, D. H. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

Maxein, D.

D. Maxein and K. Buse, “Interaction of Femtosecond Laser Pulses with Lithium Niobate Crystals: Transmission Changes and Refractive Index Modulations,” J. Holography Speckle 5, 1–5 (2009).
[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]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
[Crossref] [PubMed]

Mcduff, R. G.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
[Crossref]

Mckay, T. J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
[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, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B 83, 165106 (2011).
[Crossref]

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

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

Millers, D.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

Müller, H.

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

Nagirnyi, V.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

Ogusu, K.

Othonos, A.

A. Othonos, “Probing ultrafast carrier and phonon dynamics in semiconductors,” J. Appl. Phys. 83, 1789–1830 (1998).
[Crossref]

Polgar, K.

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

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]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
[Crossref] [PubMed]

Qiu, Y.

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

Redfield, S.

S. Redfield and W. J. Burke, “Optical Absorption Edge of LiNbO3,” J. Appl. Phys.45 (1974).
[Crossref]

Ryasnyansky, A.

R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
[Crossref]

Said, A.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
[Crossref]

Said, A. A.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of Bound-electronic and Free-carrier Nonlinearities In ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Saito, N.

O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
[Crossref]

Sanna, S.

Y. Li, W. G. Schmidt, and S. Sanna, “Intrinsic LiNbO3 point defects from hybrid density functional calculations,” Phys. Rev. B 89, 094111 (2014).
[Crossref]

Y. Li, S. Sanna, and W. G. Schmidt, “Modeling intrinsic defects in LiNbO3 within the Slater-Janak transition state model,” The Journal of Chemical Physics 140, 234113 (2014).
[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, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B 83, 165106 (2011).
[Crossref]

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

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

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

O. F. Schirmer, O. Thiemann, and M. Wöhlecke, “Defects in LiNbO3 — I. Experimental Aspects,” J. Phys. Chem. Solids 52, 185 (1991).
[Crossref]

O. F. Schirmer and D. von der Linde, “Two–Photon and X–Ray–Induced Nb4+ and O− Small Polarons in LiNbO3,” Appl. Phys. Lett. 33, 35 (1978).
[Crossref]

Schmidt, W. G.

Y. Li, W. G. Schmidt, and S. Sanna, “Intrinsic LiNbO3 point defects from hybrid density functional calculations,” Phys. Rev. B 89, 094111 (2014).
[Crossref]

Y. Li, S. Sanna, and W. G. Schmidt, “Modeling intrinsic defects in LiNbO3 within the Slater-Janak transition state model,” The Journal of Chemical Physics 140, 234113 (2014).
[Crossref]

Schoke, B.

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

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

Seilmeier, A.

A. Seilmeier and W. Kaiser, “Generation of tunable picosecond light pulses covering the frequency range between 2700 and 32,000 cm−1,” Appl. Phys. A 23, 113 (1980).
[Crossref]

Sheik-Bahae, M.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
[Crossref]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of Bound-electronic and Free-carrier Nonlinearities In ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[Crossref]

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

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Sheldon, P.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

Shinkawa, K.

Siegel, J.

M. Garcia-Lechuga, J. Siegel, J. Hernandez-Rueda, and J. Solis, “Imaging the ultrafast Kerr effect, free carrier generation, relaxation and ablation dynamics of Lithium Niobate irradiated with femtosecond laser pulses,” J. Appl. Phys. 116, 113502 (2014).
[Crossref]

Solis, J.

M. Garcia-Lechuga, J. Siegel, J. Hernandez-Rueda, and J. Solis, “Imaging the ultrafast Kerr effect, free carrier generation, relaxation and ablation dynamics of Lithium Niobate irradiated with femtosecond laser pulses,” J. Appl. Phys. 116, 113502 (2014).
[Crossref]

Staromlynska, J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
[Crossref]

Sturman, B.

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Femtosecond time-resolved absorption process in lithium niobate crystals,” Opt. Lett. 30, 1366 (2005).
[Crossref] [PubMed]

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]

Thiemann, O.

O. F. Schirmer, O. Thiemann, and M. Wöhlecke, “Defects in LiNbO3 — I. Experimental Aspects,” J. Phys. Chem. Solids 52, 185 (1991).
[Crossref]

Tugushev, R.

R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
[Crossref]

Ucer, K.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

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. Stat. Sol. C 2, 232 (2005).
[Crossref]

Usmanov, T.

R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
[Crossref]

Van Stryland, E.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
[Crossref]

Van Stryland, E. W.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of Bound-electronic and Free-carrier Nonlinearities In ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

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

von der Linde, D.

O. F. Schirmer and D. von der Linde, “Two–Photon and X–Ray–Induced Nb4+ and O− Small Polarons in LiNbO3,” Appl. Phys. Lett. 33, 35 (1978).
[Crossref]

Wada, S.

O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
[Crossref]

Wang, J.

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of Bound-electronic and Free-carrier Nonlinearities In ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

Williams, R.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[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. Stat. Sol. C 2, 232 (2005).
[Crossref]

Wöhlecke, M.

O. F. Schirmer, O. Thiemann, and M. Wöhlecke, “Defects in LiNbO3 — I. Experimental Aspects,” J. Phys. Chem. Solids 52, 185 (1991).
[Crossref]

Woike, T.

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]

Yochum, H.

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

Young, J.

Zhang, X.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659 (1997).
[Crossref]

Zhou, F.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659 (1997).
[Crossref]

Appl. Phys. A (1)

A. Seilmeier and W. Kaiser, “Generation of tunable picosecond light pulses covering the frequency range between 2700 and 32,000 cm−1,” Appl. Phys. A 23, 113 (1980).
[Crossref]

Appl. Phys. B (2)

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659 (1997).
[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]

Appl. Phys. Lett. (1)

O. F. Schirmer and D. von der Linde, “Two–Photon and X–Ray–Induced Nb4+ and O− Small Polarons in LiNbO3,” Appl. Phys. Lett. 33, 35 (1978).
[Crossref]

Appl. Phys. Rev. (1)

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

Ferroelectrics (1)

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

IEEE J. Quantum Electron. (3)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using A Single Beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[Crossref]

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996).
[Crossref]

M. Fejer, G. Magel, D. H. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

J. Appl. Phys. (4)

O. A. Louchev, H. H. Hatano, N. Saito, S. Wada, and K. Kitamura, “Laser-induced breakdown and damage generation by nonlinear frequency conversion in ferroelectric crystals: Experiment and theory,” J. Appl. Phys. 114, 203101 (2013).
[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]

A. Othonos, “Probing ultrafast carrier and phonon dynamics in semiconductors,” J. Appl. Phys. 83, 1789–1830 (1998).
[Crossref]

M. Garcia-Lechuga, J. Siegel, J. Hernandez-Rueda, and J. Solis, “Imaging the ultrafast Kerr effect, free carrier generation, relaxation and ablation dynamics of Lithium Niobate irradiated with femtosecond laser pulses,” J. Appl. Phys. 116, 113502 (2014).
[Crossref]

J. Holography Speckle (1)

D. Maxein and K. Buse, “Interaction of Femtosecond Laser Pulses with Lithium Niobate Crystals: Transmission Changes and Refractive Index Modulations,” J. Holography Speckle 5, 1–5 (2009).
[Crossref]

J. Nonlinear Opt. Phys. Mater. (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. Mcduff, “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. Mater. 06, 251–293 (1997).
[Crossref]

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

J. Phys. Chem. Sol. (1)

C. Merschjann, B. Schoke, D. Conradi, M. Imlau, G. Corradi, and K. Polgar, “Absorption cross sections and number densities of electron and hole polarons in congruently melting LiNbO3,” J. Phys. Chem. Sol. 21, 015906 (2009).

J. Phys. Chem. Solids (1)

O. F. Schirmer, O. Thiemann, and M. Wöhlecke, “Defects in LiNbO3 — I. Experimental Aspects,” J. Phys. Chem. Solids 52, 185 (1991).
[Crossref]

J. Phys. Condens. Matter (2)

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

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

Opt. Commun. (1)

R. Ganeev, I. Kulagin, A. Ryasnyansky, R. Tugushev, and T. Usmanov, “Characterization of nonlinear optical parameters of KDP, LiNbO3 and BBO crystals,” Opt. Commun. 229, 403–412 (2004).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

O. F. Schirmer, M. Imlau, and C. Merschjann, “Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation,” Phys. Rev. B 83, 165106 (2011).
[Crossref]

Y. Li, W. G. Schmidt, and S. Sanna, “Intrinsic LiNbO3 point defects from hybrid density functional calculations,” Phys. Rev. B 89, 094111 (2014).
[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. Rev. Lett. (1)

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

Phys. Stat. Sol. C (1)

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

Rad. Eff. Def. Sol. (1)

H. Yochum, K. Ucer, R. Williams, P. Sheldon, V. Nagirnyi, V. Denks, L. Grigorjeva, D. Millers, and E. Kotomin, “Short-pulse excitation and spectroscopy of KNbO3, LiNbO3 and KTiOPO4,” Rad. Eff. Def. Sol. 150, 271–276 (1999).
[Crossref]

The Journal of Chemical Physics (1)

Y. Li, S. Sanna, and W. G. Schmidt, “Modeling intrinsic defects in LiNbO3 within the Slater-Janak transition state model,” The Journal of Chemical Physics 140, 234113 (2014).
[Crossref]

Other (3)

S. Redfield and W. J. Burke, “Optical Absorption Edge of LiNbO3,” J. Appl. Phys.45 (1974).
[Crossref]

H. Badorreck, School of Physics, Osnabrueck University, Barbarastr. 7, 49076 Osnabrueck, Germany, A. Shumelyuk, S. Nolte, M. Imlau, and S. Odoulov are preparing a manuscript to be called “Selfdiffraction from moving gratings recorded in LiNbO3 with ultra-short laser pulses of different colors.”

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

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Figures (5)

Fig. 1
Fig. 1

Potential diagram of the band-to-band excitation by one-photon (α) and two-photon (β) absorption with photon energies of Eph = 2.5 eV, electron-phonon cooling process with time constant τS, relaxation to the ground state (τR) and subsequent formation of small polarons (τFC–P) in lithium niobate. Absorption cross section σ and number density of polarons NP determine the absorption triggered by optically induced transport of small polarons [11].

Fig. 2
Fig. 2

Numerical solution of Eq. (2) as a function of pulse duration (100 fs – 1,000 fs) and the following model parameters: α = 0 m−1, β = 5 mm/GW, τS = 100 fs, τFC–P = 100 fs, τR = 100 fs, σ = 100 · 10−22 m2, and peak intensity I = 8.6 PW/m2 at z = 0. E.g., this results in a maximum polaron number density of NP = 1.7 · 1017 mm−3 at the center of the pulse with maximum intensity for τ = 1, 000 fs. For comparison the red dotted graph representing Eq. (1) is also shown. The inset highlights the change in the shape of the transmission traces exemplarily for a pulse duration of 1,000 fs and a fitted graph using the original z-scan theory Eq. (1) with an TPA-coefficient increased by a factor of 2.2 in comparison to the main figure.

Fig. 3
Fig. 3

Sketch of the optical setup composed by a prism stretcher/compressor (PSC) (P1; P2 on a linear stage LS), a spatial frequency filter (SFF) (CM: concave mirrors with f = 500 mm, PH: pinhole with diameter of 100 μm) and a common configuration for z-scan technique: L1: lens (f = 150 mm), LN: lithium niobate crystal, MLS: motorized linear stage, L2–L4: lenses (f = 50 mm), D1–D3: Si-PIN detectors (photosensitive area ≫ beam spot), A: aperture with diameter of 4 mm. Incident pulses obey a maximum pulse energy of 150 μJ at 2.5 eV (center wavelength: 488 nm) and are adjusted in intensity by a neutral density filter. The repetition rate of 250 Hz is reduced to 12.5 Hz using a Chopper wheel. The pulse duration can be varied with PSC from 70 fs – 1,000 fs.

Fig. 4
Fig. 4

(Upper parts): Experimentally determined transmission as a function of scanning coordinate z for four pulse durations: (a) (70±10) fs, (b) (220±10) fs, (c)(430±10) fs and (d) (840±30) fs, all for a constant pulse energy of (270±30) nJ and at a center wavelength of λ = 488 nm. The results of our numerical fitting procedure according to Eqs. (2) to (4) are shown as green lines with the following model parameters: a two-photon absorption coefficient of β = (5.6 ± 0.8) mm/GW, a small polaron absorption cross section of σ = (210 ± 70) × 10−22 m2, and characteristic times for electron-phonon relaxation of τS = 80 fs, for interband relaxation of τR = 100 fs and for small polaron formation of τFC–P = 100 fs. For comparison, fitting of Eq. (1) to the experimental data is shown as red dashed line. The error of a single measuring point is indicated by the errorbars for selected points. (Lower parts): squared error of the fits with respect to the experimental data as a function of z. It is noteworthy, that the amount of polaronic absorption, e.g. in (d) is about 45% at z = 0; the fit with Eq. (1) would result in an overestimate for β of about 15 mm/GW.

Fig. 5
Fig. 5

Mean squared error between fit and experimental data for both, the numerical solution of our model approach according to Eqs. (2) to (4) (green), and the original z-scan theory using Eq. (1) (red). The dashed lines represent best fits with constant minimum value of the mean squared error MSEmin = (1.5±0.1)×10−4 (green) and a fit with Eq. (5) to the data points (red) with saturation amplitude MSE(t = ∞) = (4 ± 0.1) × 10−4, characteristic time constant τexp = (137 ± 8) fs, temporal offset of τ = (86 ± 5) fs, and minimum value of mean squared error MSEmin = (1.5 ± 0.1) × 10−4.

Equations (5)

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T ( z ) = 1 q ( z ) π ln ( 1 + q ( z ) exp ( s 2 ) ) d s
I ( L , r , t ) L = [ α + β I ( L , r , t ) + σ N P ( L , r , t ) ] I ( L , r , t ) .
N P ( L , r , t ) t = N FC ( L , r , t τ S ) τ FC P
N FC ( L , r , t ) t = α I ( L , r , t ) h ν + β I 2 ( L , r , t ) 2 h ν N FC ( L , r , t τ S ) τ R N FC ( L , r , t τ S ) τ FC P
MSE ( t ) = MSE ( t = ) × [ 1 exp ( ( t t offset ) τ exp ) ] + MSE min

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