Abstract

Holograms are recorded with focused beams in an iron-doped lithium niobate crystal. The diffraction efficiency shows a maximum after several seconds of recording, unlike in the case of writing with two homogeneous plane waves in the same crystal. This behavior can be attributed to a compensation field caused by incomplete illumination of the crystal. The field finally stops the bulk photovoltaic effect, which is the main driving force of the process. Based on this assumptions, we derive an analytical expression for the evolution of the diffraction efficiency which correctly fits the experimental data.

© 2009 Optical Society of America

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  1. P. Günter and J.-P. Huignard, Eds., "Photorefractive materials and their applications 1-3," Springer series in optical sciences, (Springer, Berlin, 2005, 2006, 2007).
  2. K. Buse, "Light-induced charge transport processes in photorefractive crystals I: Models and experimental methods," Appl. Phys. B 64, 273-291 (1997).
    [CrossRef]
  3. N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438-440 (1976).
  4. K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, "Low-spatial-frequency refractive-index changes in irondoped lithium niobate crystals upon illumination with a focused continuous-wave laser beam," J. Opt. Soc. Am. B 17, 586-592 (2000).
    [CrossRef]
  5. A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520-1532 (1995).
    [CrossRef] [PubMed]
  6. K. Peithmann, A. Wiebrock, and K. Buse, "Photorefractive properties of highly doped lithium niobate crystals in the visible and near-infrared," Appl. Phys. B 68, 777-784 (1999).
    [CrossRef]
  7. H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
    [CrossRef]
  8. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  9. S. Tao, B. Wang, G. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).
  10. K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
    [CrossRef]
  11. H. A. Eggert, B. Hecking, and K. Buse, "Electrical Fixing in Near-Stoichiometric Lithium Niobate Crystals," Opt. Lett. 29, 2476-2478 (2004).
    [CrossRef] [PubMed]
  12. M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
    [CrossRef]

2004

S. Tao, B. Wang, G. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).

H. A. Eggert, B. Hecking, and K. Buse, "Electrical Fixing in Near-Stoichiometric Lithium Niobate Crystals," Opt. Lett. 29, 2476-2478 (2004).
[CrossRef] [PubMed]

2002

M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

2000

1999

K. Peithmann, A. Wiebrock, and K. Buse, "Photorefractive properties of highly doped lithium niobate crystals in the visible and near-infrared," Appl. Phys. B 68, 777-784 (1999).
[CrossRef]

1997

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

K. Buse, "Light-induced charge transport processes in photorefractive crystals I: Models and experimental methods," Appl. Phys. B 64, 273-291 (1997).
[CrossRef]

1995

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520-1532 (1995).
[CrossRef] [PubMed]

1977

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

1976

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438-440 (1976).

1969

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

Anderson, D. Z.

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520-1532 (1995).
[CrossRef] [PubMed]

Breer, S.

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

Burr, G.

S. Tao, B. Wang, G. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).

Buse, K.

H. A. Eggert, B. Hecking, and K. Buse, "Electrical Fixing in Near-Stoichiometric Lithium Niobate Crystals," Opt. Lett. 29, 2476-2478 (2004).
[CrossRef] [PubMed]

K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, "Low-spatial-frequency refractive-index changes in irondoped lithium niobate crystals upon illumination with a focused continuous-wave laser beam," J. Opt. Soc. Am. B 17, 586-592 (2000).
[CrossRef]

K. Peithmann, A. Wiebrock, and K. Buse, "Photorefractive properties of highly doped lithium niobate crystals in the visible and near-infrared," Appl. Phys. B 68, 777-784 (1999).
[CrossRef]

K. Buse, "Light-induced charge transport processes in photorefractive crystals I: Models and experimental methods," Appl. Phys. B 64, 273-291 (1997).
[CrossRef]

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

Chen, J.

S. Tao, B. Wang, G. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).

Dischler, B.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Eggert, H. A.

Engelmann, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Gao, M.

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

Gonser, U.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Hecking, B.

Jazbinsek, M.

M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

Kapphan, S.

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

Keune, W.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

Kratzig, E.

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

Krätzig, E.

K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, "Low-spatial-frequency refractive-index changes in irondoped lithium niobate crystals upon illumination with a focused continuous-wave laser beam," J. Opt. Soc. Am. B 17, 586-592 (2000).
[CrossRef]

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438-440 (1976).

Kurz, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Peithmann, K.

K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, "Low-spatial-frequency refractive-index changes in irondoped lithium niobate crystals upon illumination with a focused continuous-wave laser beam," J. Opt. Soc. Am. B 17, 586-592 (2000).
[CrossRef]

K. Peithmann, A. Wiebrock, and K. Buse, "Photorefractive properties of highly doped lithium niobate crystals in the visible and near-infrared," Appl. Phys. B 68, 777-784 (1999).
[CrossRef]

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

Räuber, A.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Tao, S.

S. Tao, B. Wang, G. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).

Wang, B.

S. Tao, B. Wang, G. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).

Wiebrock, A.

K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, "Low-spatial-frequency refractive-index changes in irondoped lithium niobate crystals upon illumination with a focused continuous-wave laser beam," J. Opt. Soc. Am. B 17, 586-592 (2000).
[CrossRef]

K. Peithmann, A. Wiebrock, and K. Buse, "Photorefractive properties of highly doped lithium niobate crystals in the visible and near-infrared," Appl. Phys. B 68, 777-784 (1999).
[CrossRef]

Zgonik, M.

M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520-1532 (1995).
[CrossRef] [PubMed]

Appl. Phys.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, "Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods," Appl. Phys. 12, 355-368 (1977).
[CrossRef]

Appl. Phys. B

K. Buse, "Light-induced charge transport processes in photorefractive crystals I: Models and experimental methods," Appl. Phys. B 64, 273-291 (1997).
[CrossRef]

M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

K. Peithmann, A. Wiebrock, and K. Buse, "Photorefractive properties of highly doped lithium niobate crystals in the visible and near-infrared," Appl. Phys. B 68, 777-784 (1999).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

J. Mod. Opt.

S. Tao, B. Wang, G. Burr, and J. Chen, "Diffraction efficiency of volume gratings with finite size: corrected analytical solution," J. Mod. Opt. 51, 1115-1122 (2004).

J. Opt. Soc. Am. B

Opt. Lett.

Phys Rev. B

K. Buse, S. Breer, K. Peithmann, S. Kapphan, M. Gao, and E. Kratzig, "Origin of thermal fixing in photorefractive lithium niobate crystals," Phys Rev. B 56, 1225-1235 (1997).
[CrossRef]

Phys. Rev. A

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field," Phys. Rev. A 51, 1520-1532 (1995).
[CrossRef] [PubMed]

Sov. Tech. Phys. Lett.

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438-440 (1976).

Other

P. Günter and J.-P. Huignard, Eds., "Photorefractive materials and their applications 1-3," Springer series in optical sciences, (Springer, Berlin, 2005, 2006, 2007).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup as it is used to write holograms with two focused beams. The angle between the two recording beams is 2γ.

Fig. 2.
Fig. 2.

The diffraction efficiency as it evolves with time. Two focused beams are used to write the hologram. A fit of the analytical formula (10) is plotted as a solid line.

Fig. 3.
Fig. 3.

Diffraction efficiency versus time while a hologram is recorded with two focused beams. One beam illuminates the crystal for different durations before starting the recording process. The pre-illumination times are: oe-17-03-1321-i001 45s, oe-17-03-1321-i002 90s, oe-17-03-1321-i003 180s, oe-17-03-1321-i004 300s, oe-17-03-1321-i005 600s.

Fig. 4.
Fig. 4.

Slope of asin(√η) for different pre-illumination times. The error at t p = 90s is estimated from six different curves obtained under nominally identical conditions. The solid, gray line is an exponential fit.

Fig. 5.
Fig. 5.

Scheme of holographic recording with focused light. The focused light is restricted to a small area illustrated by the white spot in the center. The box shows a cross section of the light intensity. Thus charges accumulate at the borders of the illuminated area. The corresponding compensation field E comp finally compensates the bulk photovoltaic field E phv

Equations (14)

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

j = β I + α I E , z j = t ρ , z E = ρ ε ε 0 .
t z E = 1 ε ε 0 z j .
t E = t E | z = L crys / 2 1 ε ε 0 j = t E | z = L crys / 2 1 ε ε 0 ( β I + α I E ) .
t E SC ( 0 ) = ( 1 L illu L crys ) α I illu ε ε 0 ( β α + E SC ( 0 ) ) .
τ = ε ε 0 α I illu ( 1 L illu L crys )
E SC ( 0 ) = β α ( 1 e t / τ ) .
τ = ε ε 0 α I illu .
τ t E SC ( 1 ) + E SC ( 1 ) = m ( E SC ( 0 ) + E phv , c + E phv , u ) .
E SC ( 1 ) = m E phv , c ( t / τ ) e t / τ m E phv , u ( 1 e t / τ ) .
η = sin 2 ( const × E SC ( 1 ) ) = sin 2 { A 1 [ ( t / τ ) exp ( t / τ ) + b ( 1 exp ( t / τ ) ) ] }
E SC ( 0 ) = E phv , c ( 1 e t p / τ p e t / τ )
E SC ( 1 ) = m E phv , c ( t / τ ) e t p / τ p e t / τ m phv , u ( 1 e t / τ ) .
t E SC ( 1 ) | t = 0 = m E phv , c / τ e t p / τ p m E phv , u / τ .
asin η = const × t E SC ( 1 ) | t = 0 = A 2 [ exp ( t / τ ) + b ] .

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