Abstract

Spectral and temporal characteristics of light-induced absorption for BaTiO3 crystals undoped and doped with various amounts of Ce were investigated and compared. Dark decay of light-induced absorption with two time constants corresponding to two shallow levels was observed in all crystals investigated. Light-induced absorption spectra were then resolved into two components, slow and fast, according to the dark-decay time constants. The resolved spectra reveal that in all the undoped and Ce-doped crystals the two shallow levels have the same defect origins, independently of doping. The thermal activation energies of the two shallow levels were deduced to be 0.7 and 0.5 eV in all crystals, and the 0.7-eV shallow level is attributed to Fe4+/5+. Some other important parameters for the two shallow levels were also determined.

© 1998 Optical Society of America

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References

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  1. M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 195–236.
    [Crossref]
  2. E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
    [Crossref]
  3. R. A. Rupp, A. Maillard, and J. Walter, “Light-induced scattering in photorefractive crystals,” Appl. Phys. A: Solids Surf. 49, 259 (1989).
    [Crossref]
  4. A. Motes and J. J. Kim, “Intensity-dependent absorption coefficient in photorefractive BaTiO3 crystals,” J. Opt. Soc. Am. B 4, 1397 (1987).
    [Crossref]
  5. G. A. Brost, R. A. Motes, and J. R. Rotgé, “Intensity-dependent absorption and photorefractive effects in barium titanate,” J. Opt. Soc. Am. B 5, 1879 (1988).
    [Crossref]
  6. D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 195 (1990).
    [Crossref]
  7. G. A. Brost and R. A. Motes, “Origin of the sublinear photorefractive response time in BaTiO3,” Opt. Lett. 15, 1194 (1990).
    [Crossref] [PubMed]
  8. L. Holtmann, M. Unland, E. Krätzig, and G. Godefroy, “Conductivity and light-induced absorption in BaTiO3,” Appl. Phys. A: Solids Surf. 51, 13 (1990).
    [Crossref]
  9. P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effects for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
    [Crossref]
  10. U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
    [Crossref]
  11. R. N. Schwartz and B. A. Wechesler, “Electron-paramagnetic-resonance study of transition-metal-doped BaTiO3. Effect of material processing on Fermi-level position,” Phys. Rev. B 48, 7057 (1993).
    [Crossref]
  12. H. Kröse, R. Scharfschwerdt, O. F. Schimer, and H. Hesse, “Light-induced charge transport via three charge states of rhodium,” Appl. Phys. B: Photophys. Laser Chem. 61, 1 (1995).
    [Crossref]
  13. Y. Lian, S. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjunction in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
    [Crossref] [PubMed]
  14. Y. Zhu, X. Wu, and C. Yang, “Spectroscopic and self-pumped phase conjugation of visible-sensitive cerium-doped barium titanate,” in Photorefracture Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 69 (1996).
    [Crossref]
  15. G. D. Bacher, M. P. Chiao, G. J. Dunning, M. B. Klein, C. C. Klein, C. C. Nelson, and B. A. Wechesler, “Ultralong dark decay measurements in BaTiO3,” Opt. Lett. 21, 18 (1996).
    [Crossref] [PubMed]
  16. A. Motes, G. Brost, and J. Rotgé, “Temporal behavior of the intensity-dependent absorption in photorefractive BaTiO3,” Opt. Lett. 13, 509 (1988).
    [Crossref] [PubMed]
  17. G. A. Brost and R. A. Motes, “Photoinduced absorption in photorefractive BaTiO3,” Opt. Lett. 15, 538 (1990).
    [Crossref] [PubMed]
  18. J. Zhang, S. Dou, H. Gao, Y. Zhu, and P. Ye, “Decay of light-induced absorption in barium titanate,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 32 (1996).
    [Crossref]
  19. K. Buse and T. Bierwirth, “Dynamics of light-induced absorption in BaTiO3 and application for intensity stabilization,” J. Opt. Soc. Am. B 12, 629 (1995).
    [Crossref]
  20. H. W. Song, S. X. Dou, M. J. Chi, H. Gao, Y. Zhu, and P. X. Ye, “Studies of shallow levels in undoped and Rh-doped BaTiO3,” J. Opt. Soc. Am. B 15, 1329 (1998).
    [Crossref]

1998 (1)

1996 (2)

G. D. Bacher, M. P. Chiao, G. J. Dunning, M. B. Klein, C. C. Klein, C. C. Nelson, and B. A. Wechesler, “Ultralong dark decay measurements in BaTiO3,” Opt. Lett. 21, 18 (1996).
[Crossref] [PubMed]

U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
[Crossref]

1995 (2)

H. Kröse, R. Scharfschwerdt, O. F. Schimer, and H. Hesse, “Light-induced charge transport via three charge states of rhodium,” Appl. Phys. B: Photophys. Laser Chem. 61, 1 (1995).
[Crossref]

K. Buse and T. Bierwirth, “Dynamics of light-induced absorption in BaTiO3 and application for intensity stabilization,” J. Opt. Soc. Am. B 12, 629 (1995).
[Crossref]

1994 (1)

1993 (1)

R. N. Schwartz and B. A. Wechesler, “Electron-paramagnetic-resonance study of transition-metal-doped BaTiO3. Effect of material processing on Fermi-level position,” Phys. Rev. B 48, 7057 (1993).
[Crossref]

1991 (1)

1990 (4)

G. A. Brost and R. A. Motes, “Photoinduced absorption in photorefractive BaTiO3,” Opt. Lett. 15, 538 (1990).
[Crossref] [PubMed]

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 195 (1990).
[Crossref]

G. A. Brost and R. A. Motes, “Origin of the sublinear photorefractive response time in BaTiO3,” Opt. Lett. 15, 1194 (1990).
[Crossref] [PubMed]

L. Holtmann, M. Unland, E. Krätzig, and G. Godefroy, “Conductivity and light-induced absorption in BaTiO3,” Appl. Phys. A: Solids Surf. 51, 13 (1990).
[Crossref]

1989 (1)

R. A. Rupp, A. Maillard, and J. Walter, “Light-induced scattering in photorefractive crystals,” Appl. Phys. A: Solids Surf. 49, 259 (1989).
[Crossref]

1988 (2)

1987 (1)

1980 (1)

E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
[Crossref]

Bacher, G. D.

Bierwirth, T.

Brost, G.

Brost, G. A.

Buse, K.

U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
[Crossref]

K. Buse and T. Bierwirth, “Dynamics of light-induced absorption in BaTiO3 and application for intensity stabilization,” J. Opt. Soc. Am. B 12, 629 (1995).
[Crossref]

Chi, M. J.

Chiao, M. P.

Doormann, V.

E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
[Crossref]

Dou, S.

Y. Lian, S. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjunction in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

J. Zhang, S. Dou, H. Gao, Y. Zhu, and P. Ye, “Decay of light-induced absorption in barium titanate,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 32 (1996).
[Crossref]

Dou, S. X.

Dunning, G. J.

Feinberg, J.

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 195 (1990).
[Crossref]

Gao, H.

Godefroy, G.

L. Holtmann, M. Unland, E. Krätzig, and G. Godefroy, “Conductivity and light-induced absorption in BaTiO3,” Appl. Phys. A: Solids Surf. 51, 13 (1990).
[Crossref]

Hesse, H.

U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
[Crossref]

H. Kröse, R. Scharfschwerdt, O. F. Schimer, and H. Hesse, “Light-induced charge transport via three charge states of rhodium,” Appl. Phys. B: Photophys. Laser Chem. 61, 1 (1995).
[Crossref]

Holtmann, L.

L. Holtmann, M. Unland, E. Krätzig, and G. Godefroy, “Conductivity and light-induced absorption in BaTiO3,” Appl. Phys. A: Solids Surf. 51, 13 (1990).
[Crossref]

Kämper, S.

U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
[Crossref]

Kim, J. J.

Klein, C. C.

Klein, M. B.

G. D. Bacher, M. P. Chiao, G. J. Dunning, M. B. Klein, C. C. Klein, C. C. Nelson, and B. A. Wechesler, “Ultralong dark decay measurements in BaTiO3,” Opt. Lett. 21, 18 (1996).
[Crossref] [PubMed]

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 195–236.
[Crossref]

Krätzig, E.

U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
[Crossref]

L. Holtmann, M. Unland, E. Krätzig, and G. Godefroy, “Conductivity and light-induced absorption in BaTiO3,” Appl. Phys. A: Solids Surf. 51, 13 (1990).
[Crossref]

E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
[Crossref]

Kröse, H.

H. Kröse, R. Scharfschwerdt, O. F. Schimer, and H. Hesse, “Light-induced charge transport via three charge states of rhodium,” Appl. Phys. B: Photophys. Laser Chem. 61, 1 (1995).
[Crossref]

Lian, Y.

Mahgerefteh, D.

P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effects for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
[Crossref]

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 195 (1990).
[Crossref]

Maillard, A.

R. A. Rupp, A. Maillard, and J. Walter, “Light-induced scattering in photorefractive crystals,” Appl. Phys. A: Solids Surf. 49, 259 (1989).
[Crossref]

Motes, A.

Motes, R. A.

Nelson, C. C.

Orlowski, R.

E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
[Crossref]

Rosenkranz, M.

E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
[Crossref]

Rotgé, J.

Rotgé, J. R.

Rupp, R. A.

R. A. Rupp, A. Maillard, and J. Walter, “Light-induced scattering in photorefractive crystals,” Appl. Phys. A: Solids Surf. 49, 259 (1989).
[Crossref]

Scharfschwerdt, R.

H. Kröse, R. Scharfschwerdt, O. F. Schimer, and H. Hesse, “Light-induced charge transport via three charge states of rhodium,” Appl. Phys. B: Photophys. Laser Chem. 61, 1 (1995).
[Crossref]

Schimer, O. F.

H. Kröse, R. Scharfschwerdt, O. F. Schimer, and H. Hesse, “Light-induced charge transport via three charge states of rhodium,” Appl. Phys. B: Photophys. Laser Chem. 61, 1 (1995).
[Crossref]

Schwartz, R. N.

R. N. Schwartz and B. A. Wechesler, “Electron-paramagnetic-resonance study of transition-metal-doped BaTiO3. Effect of material processing on Fermi-level position,” Phys. Rev. B 48, 7057 (1993).
[Crossref]

Song, H. W.

Stevendaal, U. V.

U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
[Crossref]

Tayebati, P.

Unland, M.

L. Holtmann, M. Unland, E. Krätzig, and G. Godefroy, “Conductivity and light-induced absorption in BaTiO3,” Appl. Phys. A: Solids Surf. 51, 13 (1990).
[Crossref]

Walter, J.

R. A. Rupp, A. Maillard, and J. Walter, “Light-induced scattering in photorefractive crystals,” Appl. Phys. A: Solids Surf. 49, 259 (1989).
[Crossref]

Wechesler, B. A.

G. D. Bacher, M. P. Chiao, G. J. Dunning, M. B. Klein, C. C. Klein, C. C. Nelson, and B. A. Wechesler, “Ultralong dark decay measurements in BaTiO3,” Opt. Lett. 21, 18 (1996).
[Crossref] [PubMed]

R. N. Schwartz and B. A. Wechesler, “Electron-paramagnetic-resonance study of transition-metal-doped BaTiO3. Effect of material processing on Fermi-level position,” Phys. Rev. B 48, 7057 (1993).
[Crossref]

Welz, F.

E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
[Crossref]

Wu, X.

Y. Lian, S. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjunction in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Y. Zhu, X. Wu, and C. Yang, “Spectroscopic and self-pumped phase conjugation of visible-sensitive cerium-doped barium titanate,” in Photorefracture Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 69 (1996).
[Crossref]

Yang, C.

Y. Lian, S. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjunction in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Y. Zhu, X. Wu, and C. Yang, “Spectroscopic and self-pumped phase conjugation of visible-sensitive cerium-doped barium titanate,” in Photorefracture Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 69 (1996).
[Crossref]

Ye, P.

Y. Lian, S. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjunction in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

J. Zhang, S. Dou, H. Gao, Y. Zhu, and P. Ye, “Decay of light-induced absorption in barium titanate,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 32 (1996).
[Crossref]

Ye, P. X.

Zhang, J.

J. Zhang, S. Dou, H. Gao, Y. Zhu, and P. Ye, “Decay of light-induced absorption in barium titanate,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 32 (1996).
[Crossref]

Zhu, Y.

H. W. Song, S. X. Dou, M. J. Chi, H. Gao, Y. Zhu, and P. X. Ye, “Studies of shallow levels in undoped and Rh-doped BaTiO3,” J. Opt. Soc. Am. B 15, 1329 (1998).
[Crossref]

Y. Lian, S. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjunction in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Y. Zhu, X. Wu, and C. Yang, “Spectroscopic and self-pumped phase conjugation of visible-sensitive cerium-doped barium titanate,” in Photorefracture Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 69 (1996).
[Crossref]

J. Zhang, S. Dou, H. Gao, Y. Zhu, and P. Ye, “Decay of light-induced absorption in barium titanate,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 32 (1996).
[Crossref]

Appl. Phys. A: Solids Surf. (2)

R. A. Rupp, A. Maillard, and J. Walter, “Light-induced scattering in photorefractive crystals,” Appl. Phys. A: Solids Surf. 49, 259 (1989).
[Crossref]

L. Holtmann, M. Unland, E. Krätzig, and G. Godefroy, “Conductivity and light-induced absorption in BaTiO3,” Appl. Phys. A: Solids Surf. 51, 13 (1990).
[Crossref]

Appl. Phys. B: Photophys. Laser Chem. (2)

U. V. Stevendaal, K. Buse, S. Kämper, H. Hesse, and E. Krätzig, “Light-induced charge transport processes in photorefractive barium titanate doped with rhodium and iron,” Appl. Phys. B: Photophys. Laser Chem. 63, 315 (1996).
[Crossref]

H. Kröse, R. Scharfschwerdt, O. F. Schimer, and H. Hesse, “Light-induced charge transport via three charge states of rhodium,” Appl. Phys. B: Photophys. Laser Chem. 61, 1 (1995).
[Crossref]

J. Opt. Soc. Am. B (5)

Opt. Lett. (5)

Phys. Rev. B (1)

R. N. Schwartz and B. A. Wechesler, “Electron-paramagnetic-resonance study of transition-metal-doped BaTiO3. Effect of material processing on Fermi-level position,” Phys. Rev. B 48, 7057 (1993).
[Crossref]

Phys. Rev. Lett. (1)

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 195 (1990).
[Crossref]

Solid State Commun. (1)

E. Krätzig, F. Welz, R. Orlowski, V. Doormann, and M. Rosenkranz, “Holographic storage properties of BaTiO3,” Solid State Commun. 34, 817 (1980).
[Crossref]

Other (3)

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 195–236.
[Crossref]

Y. Zhu, X. Wu, and C. Yang, “Spectroscopic and self-pumped phase conjugation of visible-sensitive cerium-doped barium titanate,” in Photorefracture Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 69 (1996).
[Crossref]

J. Zhang, S. Dou, H. Gao, Y. Zhu, and P. Ye, “Decay of light-induced absorption in barium titanate,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE2896, 32 (1996).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the two-shallow-level (one deep and two shallow levels) charge-transport model for p-type BaTiO3. CB, conduction band; VB, valence band.

Fig. 2
Fig. 2

Steady-state light-induced absorption spectra for BaTiO3 undoped and doped with various amounts of Ce. Pump light intensity, I=500 mW/cm2. The wavelength of pump light λp is 514.5 nm. hν is the photon energy of the probe light. Inset, experimental arrangement for the measurement of light-induced absorption. The c axis of the crystal comes out of the paper.

Fig. 3
Fig. 3

Typical dark-decay dynamics of normalized light-induced absorption at different probe wavelengths in 50-ppm Ce-doped BaTiO3. The pump light (I=500 mW/cm2, λp=514.5 nm) was blocked at t=0.

Fig. 4
Fig. 4

Resolved light-induced absorption spectra according to the dark-decay time constant for all the crystals: (a) the slow component α1, (b) the fast component α2. hν is the photon energy of the probe light.

Fig. 5
Fig. 5

Arrhenius plots19 of the logarithm of dark-decay time constants τ1 and τ2 for undoped (triangle) and for 50-ppm Ce-doped (circle) BaTiO3 (I=500 mW/cm2, λp=514.5 nm).

Fig. 6
Fig. 6

Inverse buildup time constant 1/τ of light-induced (λp=514.5 nm) absorption versus pump intensity in 50-ppm Ce-doped BaTiO3.

Fig. 7
Fig. 7

Slow component α1 and fast component α2 of light-induced (λp=514.5 nm) absorption versus pump intensity I in 50-ppm Ce-doped BaTiO3. The probe wavelength is 633 nm. Squares and circles, experimental results; curves, theoretical fits.

Fig. 8
Fig. 8

Relative magnitude of the fast component of light-induced (λp=514.5 nm) absorption, α2/(α1+α2), versus pump intensity I, obtained from Fig. 7.

Tables (3)

Tables Icon

Table 1 Parameters of the BaTiO3 Crystals Used in Our Experiments

Tables Icon

Table 2 Parameters Determined from Fitting of the Dynamics of Light-Induced Absorption in Fig. 2

Tables Icon

Table 3 Charge-Transport Model Parameters for the Two Shallow Levels |1〉 and |2〉 of 50-ppm Ce-Doped BaTiO3

Equations (8)

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

αli
=d-1 ln[Iprobe(pumplightoff)/Iprobe(pumplighton)],
αli=α1[exp(-t/τ1)]+α2[exp(-t/τ2)]
τk-1=βk/(1+ρk),k=1, 2,
βk(T)=βk0 exp(-Eak/kBT),k=1, 2,
αli=α1[1-exp(-t/τ1)]+α2[1-exp(-t/τ2)],
τk=(qkskI+βk+hrk)-1,k=1, 2,
αksknk(1+βkeμ/rkσ)-1,k=1, 2,

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