Abstract

The appearance of light intensity thresholds for catastrophic optical damage in LiNbO3 is satisfactorily explained by using a photorefractive model based on the Fe2+↔Fe3+ and NbLi 4+↔NbLi 5+ defect pairs. Model simulations of the photorefractive amplification gain as a function of the light intensity present sharp threshold behavior. A similar behavior is shown by the saturating refractive index change. In agreement with experiments, predicted thresholds appear shifted towards higher intensities (up to a 104 factor) when the NbLi concentration is decreased or the temperature is increased. The model also explains very recent data on the threshold enhancement with the Fe2+/Fe3+ ratio in optical waveguides.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  11. M. Asobe, O. Tadanaga, T. Yanagawa, H. Itoh, and H. Suzuki, "Reducing photorefractive effect in periodically poled ZnO- and MgO-doped LiNbO3 wavelength converters," Appl. Phys. Lett. 78, 3163-5 (2001).
    [CrossRef]
  12. J. Rams, A. Alcazar de Velasco, M. Carrascosa, J. M. Cabrera, and F. Agulló-López, "Optical damage inhibition and thresholding effectd in lithium niobate above room temperature," Opt. Commun. 178, 211-6 (2000).
    [CrossRef]
  13. A. Ikeda, T. Oi, K. Nakayama, Y. Otsuka, and Y. Fujii, "Temperature and electric field dependences of optical damage in proton-exchanged waveguides formed on MgO-doped lithium niobate crystals," Jpn. J. Appl. Phys.  44, L1407-9 (2005).
    [CrossRef]
  14. O. Caballero-Calero, A , Alcázar, A . García-Cabañes, J. M. Cabrera, and M. Carrascosa, "Optical damage in x-cut proton exchanged LiNbO3 planar waveguides," J. Appl. Phys.  100, 93103-1-7 (2006).
    [CrossRef]
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    [CrossRef]
  16. J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3 analyses under the two-center model," Appl. Phys. B 79, 351-8 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. A. Erdmann, "The influence of shallow traps on the properties of LiNbO3 waveguides," Opt. Commun. 93, 44-8 (1992).
    [CrossRef]
  20. K. Buse, "Light-induced charge transport processes in photorefractive crystals II: materials," Appl. Phys. B 64, 391-407 (1997).
    [CrossRef]
  21. J. Carnicero, M. Carrascosa, A. Mendez, A. García-Cabañes, and J. M. Cabrera, "Optical damage control via Fe2+/Fe3+ ratio in proton exchanged LiNbO3 waveguides," Opt. Lett. 32, 2294-6 (2007).
    [CrossRef] [PubMed]
  22. A. Méndez, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, "Photorefractive charge compensation in α-phase proton-exchanged LiNbO3 waveguides," J. Opt. Soc. Am. B 17, 1412-9 (2000).
    [CrossRef]
  23. G. de la Paliza, J. Carnicero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, "Photorefractive fixing phenomena in α-phase proton-exchanged LiNbO3 waveguides," J. Opt. Soc. Am. B 22, 2229-36 (2005).
    [CrossRef]
  24. R. Göring, Z. Yuan-Ling, and S. Steinberg, "Photoconductivity and photovoltaic behaviour of LiNbO3 and LiNbO3 waveguides at high optical intensities," Appl. Phys. A 55, 97-100 (1992).
    [CrossRef]
  25. K. Gallo, M. de Micheli, and P. Baldi, "Parametric fluorescence in periodically poled LiNbO3 buried waveguides," Appl. Phys. Lett. 80, 4492-4 (2002).
    [CrossRef]
  26. S. Bian, J. Frejlich, and K. H. Ringhofer, "Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals," Phys. Rev. Lett. 78, 4035-8 (1997).
    [CrossRef]

2007

2005

A. Ikeda, T. Oi, K. Nakayama, Y. Otsuka, and Y. Fujii, "Temperature and electric field dependences of optical damage in proton-exchanged waveguides formed on MgO-doped lithium niobate crystals," Jpn. J. Appl. Phys.  44, L1407-9 (2005).
[CrossRef]

G. de la Paliza, J. Carnicero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, "Photorefractive fixing phenomena in α-phase proton-exchanged LiNbO3 waveguides," J. Opt. Soc. Am. B 22, 2229-36 (2005).
[CrossRef]

2004

J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3 analyses under the two-center model," Appl. Phys. B 79, 351-8 (2004).
[CrossRef]

2002

K. Gallo, M. de Micheli, and P. Baldi, "Parametric fluorescence in periodically poled LiNbO3 buried waveguides," Appl. Phys. Lett. 80, 4492-4 (2002).
[CrossRef]

2001

M. Asobe, O. Tadanaga, T. Yanagawa, H. Itoh, and H. Suzuki, "Reducing photorefractive effect in periodically poled ZnO- and MgO-doped LiNbO3 wavelength converters," Appl. Phys. Lett. 78, 3163-5 (2001).
[CrossRef]

2000

J. Rams, A. Alcazar de Velasco, M. Carrascosa, J. M. Cabrera, and F. Agulló-López, "Optical damage inhibition and thresholding effectd in lithium niobate above room temperature," Opt. Commun. 178, 211-6 (2000).
[CrossRef]

A. Méndez, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, "Photorefractive charge compensation in α-phase proton-exchanged LiNbO3 waveguides," J. Opt. Soc. Am. B 17, 1412-9 (2000).
[CrossRef]

1999

A. Alcazar de Velasco, J. Rams, J. M. Cabrera, and F. Agulló-Lopez, "Light-induced damage mechanisms in α-phase proton-exchanged LiNbO3 waveguides,"Appl. Phys. B 68, 989-93 (1999).
[CrossRef]

1997

M. Simon, St. Wevering, K. Buse, and E. Kratzig, "The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30,144-9 (1997).
[CrossRef]

S. Bian, J. Frejlich, and K. H. Ringhofer, "Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals," Phys. Rev. Lett. 78, 4035-8 (1997).
[CrossRef]

K. Buse, "Light-induced charge transport processes in photorefractive crystals II: materials," Appl. Phys. B 64, 391-407 (1997).
[CrossRef]

1995

Y. Kondo, and Y. Fujii, "Photorefractive effect in proton-exchanged waveguiding layers formed on lithium niobate and lithium tantalate crystals," Jpn. J. Appl. Phys. 34, L309-11 (1995).
[CrossRef]

1994

A. A. Zozulya, M. Saffman, and D. Z. Anderson, "Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries," Phys. Rev. Lett. 73, 818-21 (1994).
[CrossRef] [PubMed]

1993

1992

A. Erdmann, "The influence of shallow traps on the properties of LiNbO3 waveguides," Opt. Commun. 93, 44-8 (1992).
[CrossRef]

R. Göring, Z. Yuan-Ling, and S. Steinberg, "Photoconductivity and photovoltaic behaviour of LiNbO3 and LiNbO3 waveguides at high optical intensities," Appl. Phys. A 55, 97-100 (1992).
[CrossRef]

1991

1987

D. J. Gauthier, P. Narum, and R. W. Boyd, "Observation of deterministic chaos in a phase-conjugate mirrior," Phys. Rev. Lett. 58, 1640-3 (1987).
[CrossRef] [PubMed]

1984

D. A. Bryan, R. Gerson, and H. E. Tomaschke, "Increased optical damage resistance in lithium niobate," Appl. Phys. Lett. 44, 847-9 (1984).
[CrossRef]

1982

Appl. Phys. A

R. Göring, Z. Yuan-Ling, and S. Steinberg, "Photoconductivity and photovoltaic behaviour of LiNbO3 and LiNbO3 waveguides at high optical intensities," Appl. Phys. A 55, 97-100 (1992).
[CrossRef]

Appl. Phys. B

K. Buse, "Light-induced charge transport processes in photorefractive crystals II: materials," Appl. Phys. B 64, 391-407 (1997).
[CrossRef]

A. Alcazar de Velasco, J. Rams, J. M. Cabrera, and F. Agulló-Lopez, "Light-induced damage mechanisms in α-phase proton-exchanged LiNbO3 waveguides,"Appl. Phys. B 68, 989-93 (1999).
[CrossRef]

J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3 analyses under the two-center model," Appl. Phys. B 79, 351-8 (2004).
[CrossRef]

Appl. Phys. Lett.

M. Asobe, O. Tadanaga, T. Yanagawa, H. Itoh, and H. Suzuki, "Reducing photorefractive effect in periodically poled ZnO- and MgO-doped LiNbO3 wavelength converters," Appl. Phys. Lett. 78, 3163-5 (2001).
[CrossRef]

D. A. Bryan, R. Gerson, and H. E. Tomaschke, "Increased optical damage resistance in lithium niobate," Appl. Phys. Lett. 44, 847-9 (1984).
[CrossRef]

K. Gallo, M. de Micheli, and P. Baldi, "Parametric fluorescence in periodically poled LiNbO3 buried waveguides," Appl. Phys. Lett. 80, 4492-4 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys. D

M. Simon, St. Wevering, K. Buse, and E. Kratzig, "The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30,144-9 (1997).
[CrossRef]

Jpn. J. Appl. Phys.

Y. Kondo, and Y. Fujii, "Photorefractive effect in proton-exchanged waveguiding layers formed on lithium niobate and lithium tantalate crystals," Jpn. J. Appl. Phys. 34, L309-11 (1995).
[CrossRef]

A. Ikeda, T. Oi, K. Nakayama, Y. Otsuka, and Y. Fujii, "Temperature and electric field dependences of optical damage in proton-exchanged waveguides formed on MgO-doped lithium niobate crystals," Jpn. J. Appl. Phys.  44, L1407-9 (2005).
[CrossRef]

Opt. Commun.

J. Rams, A. Alcazar de Velasco, M. Carrascosa, J. M. Cabrera, and F. Agulló-López, "Optical damage inhibition and thresholding effectd in lithium niobate above room temperature," Opt. Commun. 178, 211-6 (2000).
[CrossRef]

A. Erdmann, "The influence of shallow traps on the properties of LiNbO3 waveguides," Opt. Commun. 93, 44-8 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

S. Bian, J. Frejlich, and K. H. Ringhofer, "Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals," Phys. Rev. Lett. 78, 4035-8 (1997).
[CrossRef]

A. A. Zozulya, M. Saffman, and D. Z. Anderson, "Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries," Phys. Rev. Lett. 73, 818-21 (1994).
[CrossRef] [PubMed]

D. J. Gauthier, P. Narum, and R. W. Boyd, "Observation of deterministic chaos in a phase-conjugate mirrior," Phys. Rev. Lett. 58, 1640-3 (1987).
[CrossRef] [PubMed]

Other

D. Kip, and M. Wesner, in Photorefractive Materials and their applications 1, P. Günter and J. P. Huignard, Eds., (Springer, New York, 2006), Chap. 10.

T. Volk, M. Wolecke, and N. Rubinina, in Photorefractive Materials and their applications 2, P. Günter and J. P. Huignard, Eds., (Springer, New York, 2007), Chap. 6.

T. Pliska, D. Fluck, and P. Gunter, in Non-linear optical effects and materials, P. Gunter Ed., (Springer, Berlin, 2000), Chap. 6.

O. Caballero-Calero, A , Alcázar, A . García-Cabañes, J. M. Cabrera, and M. Carrascosa, "Optical damage in x-cut proton exchanged LiNbO3 planar waveguides," J. Appl. Phys.  100, 93103-1-7 (2006).
[CrossRef]

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, (Claredon, Oxford, 1996).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Model simulation for the photorefractive gain coefficient Γ (continuous line) and the zero order of the photovoltaic current jpv (dashed line) as a function of the light intensity for an undoped congruent LiNbO3 sample at room temperature. (A thin dashed line has been drawn for easy recognition of the superlinear region of jpv ). Inset: simulated dependences of the saturating refractive index Δn sat and phase mismatch ϕ. (b) The continuous line of (a) has been plotted together with the same dependences for a quasi-stoichiometric sample ([NbLi]=1024 m-3) at 295 K (dashed line), and at 395 K (dotted line). Either in (a) or (b) [Fe2+]/[Fe3+]=0.05.

Fig. 2.
Fig. 2.

(a) Simulations of the gain coefficient Γ as a function of the light intensity I 0 in undoped congruent LiNbO3 for several [Fe2+]/[Fe3+] ratios. (b) Dependences of the threshold intensity (taken at Γ=10 cm-1) as a function of [NbLi] (bottom horizontal axis) and T (top horizontal axis) with [Fe2+]/[Fe3+]=0.05.

Tables (1)

Tables Icon

Table I. Parameters used for the simulations in I.S. units excepting ei in eV.

Equations (6)

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

n t = ( S 1 I + S t 1 ) N 1 + ( S 2 I + S t 2 ) N 2 S r n ( N D 1 N 1 + N D 2 N 2 ) ,
N 1 t = ( N D 1 N 1 ) t = ( S 1 I + S t 1 ) N 1 S r n ( N D 1 N 1 ) ,
N 2 t = ( N D 2 N 2 ) t = ( S 2 I + S t 2 ) N 2 S r n ( N D 2 N 2 ) ,
j = e I ( L 1 S 1 N 1 + L 2 S 2 N 2 ) + e μ n E + e D n x ,
E z = e ε ε 0 ( N 10 N 1 + N 20 N 2 ) ·
I d = I s e Γ z

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