Abstract

Photovoltaic laser beam degradation in lithium niobate (LiNbO3) has been investigated through a finite-differences beam propagation method for nonlinear media. The simulations use a two-center model (Fe2+Fe3+, NbLi4+NbLi5+) that has been recently proved to be necessary to successfully describe the photorefractive effect in nominally pure LiNbO3. Refractive index profiles and intensity and phase beam profiles have been calculated for a wide intensity range and several material distances. A good agreement is obtained on comparing simulations and experimental data. This includes self-defocusing for moderate intensities and the complex beam profile structures appearing for high intensities, providing a complete description of this nonlinear optical phenomenon.

© 2014 Optical Society of America

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  1. L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Status Solidi A 201, 253–283 (2004).
    [CrossRef]
  2. A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
    [CrossRef]
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  4. M. Carrascosa, J. Villarroel, J. Carnicero, A. García-Cabañes, and J. M. Cabrera, “Understanding light intensity thresholds for catastrophic optical damage in LiNbO3,” Opt. Express 16, 115–120 (2008).
    [CrossRef]
  5. R. L. Holman and J. P. Cressman, “Optical damage resistance of lithium niobate waveguides,” Opt. Eng. 21, 216025 (1982).
    [CrossRef]
  6. J. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
    [CrossRef]
  7. S. Sevostyanov and O. Kostritskii, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 527–533 (1997).
    [CrossRef]
  8. A. Alcázar de V., J. Rams, J. M. Cabrera, and F. Agulló-López, “Light-induced damage mechanisms in a-phase proton-exchanged LiNbO3 waveguides,” Appl. Phys. B 68, 989–993 (1999).
    [CrossRef]
  9. F. Devaux, J. Safioui, M. Chauvet, and R. Passier, “Two-photoactive-center model applied to photorefractive self-focusing in biased LiNbO3,” Phys. Rev. A 81, 013825 (2010).
    [CrossRef]
  10. J. Villarroel, O. Caballero-Calero, B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Photorefractive non-linear beam propagation in lithium niobate waveguides above the optical damage threshold,” Opt. Mater. 33, 103–106 (2010).
    [CrossRef]
  11. M. Jubera, J. Villarroel, A. García-Cabañes, M. Carrascosa, J. Olivares, and F. Lüdtke, “Characterization and inhibition of photorefractive optical damage of swift–heavy ion irradiation waveguides in LiNbO3,” J. Opt. Soc. Am. B 29, 3000–3005 (2012).
    [CrossRef]
  12. M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
    [CrossRef]
  13. F. Jermann and J. Otten, “Light-induced charge transport in LiNbO3: Fe at high light intensities,” J. Opt. Soc. Am. B 10, 2085–2092 (1993).
    [CrossRef]
  14. J. Villarroel, J. Carnicero, F. Luedtke, M. Carrascosa, A. García-Cabañes, J. M. Cabrera, A. Alcazar, and B. Ramiro, “Analysis of photorefractive optical damage in lithium niobate: application to planar waveguides,” Opt. Express 18, 20852–20861 (2010).
    [CrossRef]
  15. 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, 818–821 (1994).
    [CrossRef]
  16. K. Buse, “Light-induced charge transport processes in photorefractive crystals II: materials,” Appl. Phys. B 64, 391–407 (1997).
    [CrossRef]
  17. 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, 351–358 (2004).
    [CrossRef]
  18. N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
    [CrossRef]
  19. N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
    [CrossRef]
  20. G. de la Paliza, O. Caballero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, “Superlinear photovoltaic currents in proton exchanged LiNbO3 waveguides,” Appl. Phys. B 76, 555–559 (2003).
    [CrossRef]
  21. M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3: Fe crystals at high light intensities,” J. Phys. D. 30, 144–149 (1997).
    [CrossRef]
  22. 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]
  23. G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003), Chap. 5.
  24. J. M. Cabrera, P. Townsend, and E. Glavas, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22, 611–616 (1989).
    [CrossRef]

2012 (1)

2010 (3)

J. Villarroel, J. Carnicero, F. Luedtke, M. Carrascosa, A. García-Cabañes, J. M. Cabrera, A. Alcazar, and B. Ramiro, “Analysis of photorefractive optical damage in lithium niobate: application to planar waveguides,” Opt. Express 18, 20852–20861 (2010).
[CrossRef]

F. Devaux, J. Safioui, M. Chauvet, and R. Passier, “Two-photoactive-center model applied to photorefractive self-focusing in biased LiNbO3,” Phys. Rev. A 81, 013825 (2010).
[CrossRef]

J. Villarroel, O. Caballero-Calero, B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Photorefractive non-linear beam propagation in lithium niobate waveguides above the optical damage threshold,” Opt. Mater. 33, 103–106 (2010).
[CrossRef]

2008 (1)

2004 (2)

L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Status Solidi A 201, 253–283 (2004).
[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, 351–358 (2004).
[CrossRef]

2003 (1)

G. de la Paliza, O. Caballero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, “Superlinear photovoltaic currents in proton exchanged LiNbO3 waveguides,” Appl. Phys. B 76, 555–559 (2003).
[CrossRef]

2000 (2)

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. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
[CrossRef]

1999 (1)

A. Alcázar de V., J. Rams, J. M. Cabrera, and F. Agulló-López, “Light-induced damage mechanisms in a-phase proton-exchanged LiNbO3 waveguides,” Appl. Phys. B 68, 989–993 (1999).
[CrossRef]

1997 (3)

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

S. Sevostyanov and O. Kostritskii, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 527–533 (1997).
[CrossRef]

M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3: Fe crystals at high light intensities,” J. Phys. D. 30, 144–149 (1997).
[CrossRef]

1995 (1)

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

1994 (2)

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, 818–821 (1994).
[CrossRef]

N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
[CrossRef]

1993 (1)

1992 (1)

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

1989 (1)

J. M. Cabrera, P. Townsend, and E. Glavas, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22, 611–616 (1989).
[CrossRef]

1982 (1)

R. L. Holman and J. P. Cressman, “Optical damage resistance of lithium niobate waveguides,” Opt. Eng. 21, 216025 (1982).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Agulló-López, F.

J. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
[CrossRef]

A. Alcázar de V., J. Rams, J. M. Cabrera, and F. Agulló-López, “Light-induced damage mechanisms in a-phase proton-exchanged LiNbO3 waveguides,” Appl. Phys. B 68, 989–993 (1999).
[CrossRef]

Alcazar, A.

Alcázar, A.

J. Villarroel, O. Caballero-Calero, B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Photorefractive non-linear beam propagation in lithium niobate waveguides above the optical damage threshold,” Opt. Mater. 33, 103–106 (2010).
[CrossRef]

Alcázar de V., A.

A. Alcázar de V., J. Rams, J. M. Cabrera, and F. Agulló-López, “Light-induced damage mechanisms in a-phase proton-exchanged LiNbO3 waveguides,” Appl. Phys. B 68, 989–993 (1999).
[CrossRef]

Alcázar-de-Velasco, A.

J. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
[CrossRef]

Anderson, D. Z.

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, 818–821 (1994).
[CrossRef]

Arizmendi, L.

L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Status Solidi A 201, 253–283 (2004).
[CrossRef]

Asano, H.

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Ballman, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

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]

Born, E.

N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
[CrossRef]

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Boysen, H.

N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
[CrossRef]

Buse, K.

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]

M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3: Fe crystals at high light intensities,” J. Phys. D. 30, 144–149 (1997).
[CrossRef]

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

Caballero, O.

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, 351–358 (2004).
[CrossRef]

G. de la Paliza, O. Caballero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, “Superlinear photovoltaic currents in proton exchanged LiNbO3 waveguides,” Appl. Phys. B 76, 555–559 (2003).
[CrossRef]

Caballero-Calero, O.

J. Villarroel, O. Caballero-Calero, B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Photorefractive non-linear beam propagation in lithium niobate waveguides above the optical damage threshold,” Opt. Mater. 33, 103–106 (2010).
[CrossRef]

Cabrera, J.

J. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
[CrossRef]

Cabrera, J. M.

J. Villarroel, J. Carnicero, F. Luedtke, M. Carrascosa, A. García-Cabañes, J. M. Cabrera, A. Alcazar, and B. Ramiro, “Analysis of photorefractive optical damage in lithium niobate: application to planar waveguides,” Opt. Express 18, 20852–20861 (2010).
[CrossRef]

M. Carrascosa, J. Villarroel, J. Carnicero, A. García-Cabañes, and J. M. Cabrera, “Understanding light intensity thresholds for catastrophic optical damage in LiNbO3,” Opt. Express 16, 115–120 (2008).
[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, 351–358 (2004).
[CrossRef]

G. de la Paliza, O. Caballero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, “Superlinear photovoltaic currents in proton exchanged LiNbO3 waveguides,” Appl. Phys. B 76, 555–559 (2003).
[CrossRef]

A. Alcázar de V., J. Rams, J. M. Cabrera, and F. Agulló-López, “Light-induced damage mechanisms in a-phase proton-exchanged LiNbO3 waveguides,” Appl. Phys. B 68, 989–993 (1999).
[CrossRef]

J. M. Cabrera, P. Townsend, and E. Glavas, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22, 611–616 (1989).
[CrossRef]

Carnicero, J.

Carrascosa, M.

M. Jubera, J. Villarroel, A. García-Cabañes, M. Carrascosa, J. Olivares, and F. Lüdtke, “Characterization and inhibition of photorefractive optical damage of swift–heavy ion irradiation waveguides in LiNbO3,” J. Opt. Soc. Am. B 29, 3000–3005 (2012).
[CrossRef]

J. Villarroel, O. Caballero-Calero, B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Photorefractive non-linear beam propagation in lithium niobate waveguides above the optical damage threshold,” Opt. Mater. 33, 103–106 (2010).
[CrossRef]

J. Villarroel, J. Carnicero, F. Luedtke, M. Carrascosa, A. García-Cabañes, J. M. Cabrera, A. Alcazar, and B. Ramiro, “Analysis of photorefractive optical damage in lithium niobate: application to planar waveguides,” Opt. Express 18, 20852–20861 (2010).
[CrossRef]

M. Carrascosa, J. Villarroel, J. Carnicero, A. García-Cabañes, and J. M. Cabrera, “Understanding light intensity thresholds for catastrophic optical damage in LiNbO3,” Opt. Express 16, 115–120 (2008).
[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, 351–358 (2004).
[CrossRef]

G. de la Paliza, O. Caballero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, “Superlinear photovoltaic currents in proton exchanged LiNbO3 waveguides,” Appl. Phys. B 76, 555–559 (2003).
[CrossRef]

J. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
[CrossRef]

Chauvet, M.

F. Devaux, J. Safioui, M. Chauvet, and R. Passier, “Two-photoactive-center model applied to photorefractive self-focusing in biased LiNbO3,” Phys. Rev. A 81, 013825 (2010).
[CrossRef]

Cressman, J. P.

R. L. Holman and J. P. Cressman, “Optical damage resistance of lithium niobate waveguides,” Opt. Eng. 21, 216025 (1982).
[CrossRef]

de la Paliza, G.

G. de la Paliza, O. Caballero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, “Superlinear photovoltaic currents in proton exchanged LiNbO3 waveguides,” Appl. Phys. B 76, 555–559 (2003).
[CrossRef]

Devaux, F.

F. Devaux, J. Safioui, M. Chauvet, and R. Passier, “Two-photoactive-center model applied to photorefractive self-focusing in biased LiNbO3,” Phys. Rev. A 81, 013825 (2010).
[CrossRef]

Dziedzik, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Frey, F.

N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
[CrossRef]

García-Cabañes, A.

Glavas, E.

J. M. Cabrera, P. Townsend, and E. Glavas, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22, 611–616 (1989).
[CrossRef]

Hayasi, T.

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[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]

Holman, R. L.

R. L. Holman and J. P. Cressman, “Optical damage resistance of lithium niobate waveguides,” Opt. Eng. 21, 216025 (1982).
[CrossRef]

Houe, M.

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Imlau, M.

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]

Iyi, N.

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

Izumi, F.

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

Jermann, F.

Jubera, M.

Kimura, S.

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

Kitamura, K.

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

Kostritskii, O.

S. Sevostyanov and O. Kostritskii, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 527–533 (1997).
[CrossRef]

Kratzig, E.

M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3: Fe crystals at high light intensities,” J. Phys. D. 30, 144–149 (1997).
[CrossRef]

Lifante, G.

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003), Chap. 5.

Lüdtke, F.

Luedtke, F.

Metzger, T.

N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
[CrossRef]

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Olivares, J.

Otten, J.

Passier, R.

F. Devaux, J. Safioui, M. Chauvet, and R. Passier, “Two-photoactive-center model applied to photorefractive self-focusing in biased LiNbO3,” Phys. Rev. A 81, 013825 (2010).
[CrossRef]

Ramiro, B.

J. Villarroel, O. Caballero-Calero, B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Photorefractive non-linear beam propagation in lithium niobate waveguides above the optical damage threshold,” Opt. Mater. 33, 103–106 (2010).
[CrossRef]

J. Villarroel, J. Carnicero, F. Luedtke, M. Carrascosa, A. García-Cabañes, J. M. Cabrera, A. Alcazar, and B. Ramiro, “Analysis of photorefractive optical damage in lithium niobate: application to planar waveguides,” Opt. Express 18, 20852–20861 (2010).
[CrossRef]

Rams, J.

J. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
[CrossRef]

A. Alcázar de V., J. Rams, J. M. Cabrera, and F. Agulló-López, “Light-induced damage mechanisms in a-phase proton-exchanged LiNbO3 waveguides,” Appl. Phys. B 68, 989–993 (1999).
[CrossRef]

Rubinina, N.

T. Volk, M. Wolecke, and N. Rubinina, “Optical damage resistance in lithium niobate,” in Photorefractive Materials and Their Applications II, P. Günter and J. P. Huignard, eds. (Springer, 2007), pp. 165–203.

Saffman, M.

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, 818–821 (1994).
[CrossRef]

Safioui, J.

F. Devaux, J. Safioui, M. Chauvet, and R. Passier, “Two-photoactive-center model applied to photorefractive self-focusing in biased LiNbO3,” Phys. Rev. A 81, 013825 (2010).
[CrossRef]

Sevostyanov, S.

S. Sevostyanov and O. Kostritskii, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 527–533 (1997).
[CrossRef]

Simon, M.

M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3: Fe crystals at high light intensities,” J. Phys. D. 30, 144–149 (1997).
[CrossRef]

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Townsend, P.

J. M. Cabrera, P. Townsend, and E. Glavas, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22, 611–616 (1989).
[CrossRef]

Townsend, P. D.

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Villarroel, J.

Volk, T.

T. Volk, M. Wolecke, and N. Rubinina, “Optical damage resistance in lithium niobate,” in Photorefractive Materials and Their Applications II, P. Günter and J. P. Huignard, eds. (Springer, 2007), pp. 165–203.

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]

M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3: Fe crystals at high light intensities,” J. Phys. D. 30, 144–149 (1997).
[CrossRef]

Woike, T.

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]

Wolecke, M.

T. Volk, M. Wolecke, and N. Rubinina, “Optical damage resistance in lithium niobate,” in Photorefractive Materials and Their Applications II, P. Günter and J. P. Huignard, eds. (Springer, 2007), pp. 165–203.

Yamamoto, K.

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

Zotov, N.

N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
[CrossRef]

Zozulya, A. A.

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, 818–821 (1994).
[CrossRef]

Appl. Phys. B (5)

S. Sevostyanov and O. Kostritskii, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 527–533 (1997).
[CrossRef]

A. Alcázar de V., J. Rams, J. M. Cabrera, and F. Agulló-López, “Light-induced damage mechanisms in a-phase proton-exchanged LiNbO3 waveguides,” Appl. Phys. B 68, 989–993 (1999).
[CrossRef]

K. Buse, “Light-induced charge transport processes in photorefractive crystals II: materials,” Appl. Phys. B 64, 391–407 (1997).
[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, 351–358 (2004).
[CrossRef]

G. de la Paliza, O. Caballero, A. García-Cabañes, M. Carrascosa, and J. M. Cabrera, “Superlinear photovoltaic currents in proton exchanged LiNbO3 waveguides,” Appl. Phys. B 76, 555–559 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzik, R. G. Smith, A. A. Ballman, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

J. Appl. Phys. (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]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. Solids (1)

N. Zotov, H. Boysen, F. Frey, T. Metzger, and E. Born, “Cation substitution models of congruent LiNbO3 investigated by X-ray and neutron powder diffraction,” J. Phys. Chem. Solids 55, 145–152 (1994).
[CrossRef]

J. Phys. D (2)

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

J. M. Cabrera, P. Townsend, and E. Glavas, “A comparison of optical damage in different types of LiNbO3 waveguides,” J. Phys. D 22, 611–616 (1989).
[CrossRef]

J. Phys. D. (1)

M. Simon, S. Wevering, K. Buse, and E. Kratzig, “The bulk photovoltaic effect of photorefractive LiNbO3: Fe crystals at high light intensities,” J. Phys. D. 30, 144–149 (1997).
[CrossRef]

J. Solid State Chem. (1)

N. Iyi, K. Kitamura, F. Izumi, K. Yamamoto, T. Hayasi, H. Asano, and S. Kimura, “Comparative study of defects structures in lithium niobate with different compositions,” J. Solid State Chem. 101, 340–352 (1992).
[CrossRef]

Opt. Commun. (1)

J. Rams, A. Alcázar-de-Velasco, M. Carrascosa, J. Cabrera, and F. Agulló-López, “Optical damage inhibition and thresholding effects in lithium niobate above room temperature,” Opt. Commun. 178, 211–216 (2000).
[CrossRef]

Opt. Eng. (1)

R. L. Holman and J. P. Cressman, “Optical damage resistance of lithium niobate waveguides,” Opt. Eng. 21, 216025 (1982).
[CrossRef]

Opt. Express (2)

Opt. Mater. (1)

J. Villarroel, O. Caballero-Calero, B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Photorefractive non-linear beam propagation in lithium niobate waveguides above the optical damage threshold,” Opt. Mater. 33, 103–106 (2010).
[CrossRef]

Phys. Rev. A (1)

F. Devaux, J. Safioui, M. Chauvet, and R. Passier, “Two-photoactive-center model applied to photorefractive self-focusing in biased LiNbO3,” Phys. Rev. A 81, 013825 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

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, 818–821 (1994).
[CrossRef]

Phys. Status Solidi A (1)

L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Status Solidi A 201, 253–283 (2004).
[CrossRef]

Other (2)

T. Volk, M. Wolecke, and N. Rubinina, “Optical damage resistance in lithium niobate,” in Photorefractive Materials and Their Applications II, P. Günter and J. P. Huignard, eds. (Springer, 2007), pp. 165–203.

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003), Chap. 5.

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Figures (10)

Fig. 1.
Fig. 1.

Logarithmic plot of the simulated saturating refractive index change Δnsat versus the beam intensity inside the waveguide. Three different regions (I, II, III) can be distinguished.

Fig. 2.
Fig. 2.

Saturating refractive index profiles along the X axis for several beam intensities indicated in the figure. The input Gaussian beam profile is also plotted with an arbitrary scale.

Fig. 3.
Fig. 3.

Far field of a Gaussian beam after propagation in the waveguide along a length of 1 mm at different intensities.

Fig. 4.
Fig. 4.

Scheme of the geometry of the waveguide used in the BPM-NLM.

Fig. 5.
Fig. 5.

Simulations of the beam intensity and the refractive index change profiles along a length of 10 mm in a planar waveguide for light intensities of 20, 300, and 1350W/cm2.

Fig. 6.
Fig. 6.

Simulated light intensity, refractive index, and phase profiles after the input beam has propagated 3 mm along the material for in-coupled light intensities of 20 and 1350W/cm2. In the intensity and phase profiles, the propagation through linear media is also shown with dashed lines for comparison.

Fig. 7.
Fig. 7.

Phase profiles of the input beam calculated after a propagation of 30 mm at the light intensities of 20W/cm2 (dashed), and 1350W/cm2 (dotted). The propagation through linear media is shown with a continuous line for comparison.

Fig. 8.
Fig. 8.

FWHM of the beam intensity profile as a function of the input beam intensity. Continuous and dashed lines correspond to BPM-NLM simulation at the initial temperature of the sample, 305 K, and at 310 K, respectively, and circles correspond to experimental data.

Fig. 9.
Fig. 9.

Comparison between the recorded intensity profile of the light beam and the corresponding BPM-NLM simulation for the following input beam intensities in W/cm2: 20, 300, 700, and 1350. The light propagates 3 mm inside the guide, 3 mm through the prism outcoupler, and 80 mm in the air. (a) Simulation of the beam propagation through the overall distance. (b) and (c) Calculated and measured density plots of the cross section of the beam.

Fig. 10.
Fig. 10.

Simulated (dashed lines) and measured (continuous lines) beam profiles corresponding to the spots of Fig 9. The intensity of the incident beam inside the waveguide is indicated in the figure.

Tables (1)

Tables Icon

Table 1. Material Parameters Used for the Simulations

Equations (9)

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j=eI(L1S1N1+L2S2N2)eμeneE,
Esat=L1S1N1+L2S2N2μeneI,
Δnsat=12n3r33Esat,
Δφ(x)=2πnλLΔnsat(x),
E(kx)=E0exp(x2w02+iΔφ(x)+ikxx)dx,
2E+k0n(x,y,z,)E=0,
2ik0n0uy=(2ux2+2uz2)u+k02(n2n02)u.
E(i+1)=f(E(i),n(i),n(i+1)).
E(i+1)=f(E(i),n(i)+Δn(E(i)),n(i+1)+Δn(E(i+1))),

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