Abstract

Experimental results on the developing kinetics and final diffraction efficiency of fixed holograms in iron-doped lithium niobate are presented. Samples with two different oxidation states are studied. The developing kinetics of well-oxidized samples show oscillations superposed to a saturation dependence, whereas they are not present for the less oxidized sample. The final developed ratio is found to depend on the grating spacing and the oxidation state of the samples. All these features are well explained with the charge-transport theory and are found to be dependent on the photovoltaic properties of the samples, doping, and oxidation state. From the analysis of the experimental data, the photovoltaic field amplitude of the samples is obtained.

© 2000 Optical Society of America

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References

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  1. R. Müller, M. T. Santos, L. Arizmendi, and J. M. Cabrera, “A narrow-band interference filter with photorefractive LiNbO3,” J. Phys. D 27, 241–246 (1994).
    [CrossRef]
  2. S. Breer and K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
    [CrossRef]
  3. J. F. Heanue, M. C. Bashaw, A. J. Daiber, R. Snyder, and L. Hesselink, “Digital holographic storage system incorporating thermal fixing in lithium niobate,” Opt. Lett. 21, 1615–1617 (1996).
    [CrossRef] [PubMed]
  4. A. Mendez and L. Arizmendi, “Maximum diffraction efficiency of fixed holograms in lithium niobate,” Opt. Mater. 10, 55–59 (1998).
    [CrossRef]
  5. D. Kirillov and J. Feinberg, “Fixable complementary gratings in photorefractive BaTiO3,” Opt. Lett. 16, 1520–1522 (1991).
    [CrossRef] [PubMed]
  6. G. Montemezzani and P. Günter, “Thermal hologram fixing in pure and doped KNbO3 crystals,” J. Opt. Soc. Am. B 7, 2323–2328 (1990).
    [CrossRef]
  7. T. Imai, S. Yagi, and H. Yamazaki, “Thermal fixing of photorefractive holograms in KTa1−xNbxO3 and its relation to proton concentration,” J. Opt. Soc. Am. B 13, 2524–2528 (1996).
    [CrossRef]
  8. L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1988).
    [CrossRef]
  9. J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
    [CrossRef]
  10. M. Carrascosa and F. Agulló-López, “Optimization of the developing stage for fixed gratings in LiNbO3,” Opt. Commun. 126, 240–246 (1996).
    [CrossRef]
  11. A. Yariv, S. Orlov, G. Rakuljic, and V. Leyva, “Holographic fixing, readout and storage dynamics in photorefractive materials,” Opt. Lett. 20, 1334–1336 (1995).
    [CrossRef] [PubMed]
  12. A. Yariv, S. S. Orlov, and G. A. Rakuljic, “Holographic storage dynamics in lithium niobate: theory and experiment,” J. Opt. Soc. Am. B 13, 2513–2523 (1996).
    [CrossRef]
  13. S. Breer, K. Buse, and F. Rickermann, “Improved developing of thermally fixed holograms in photorefractive LiNbO3 crystals with high-intensity laser pulses,” Opt. Lett. 23, 73–75 (1998).
    [CrossRef]
  14. H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
    [CrossRef]
  15. A. García-Cabañes, L. Arizmendi, J. M. Cabrera, and F. Agulló-López, “New aspects of reduction treatments on Fe-doped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 15, 131–135 (1987).
  16. R. Müller, L. Arizmendi, M. Carrascosa, and J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
    [CrossRef]
  17. M. Carrascosa and F. Agulló-López, “Selective developing and screening of fixed photorefractive holograms,” Opt. Commun. 151, 257–262 (1998).
    [CrossRef]
  18. R. A. Rupp, R. Sommerfeldt, K. H. Ringhofer, and E. Krätzig, “Space charge field limitations in photorefractive LiNbO3: Fe crystals,” Appl. Phys. B 51, 364–370 (1990).
    [CrossRef]
  19. R. Sommerfeldt, L. Holtmann, E. Krätzig, and B. C. Grabmaier, “Influence of Mg doping and composition on the light-induced charge transport in LiNbO3,” Phys. Status Solidi A 106, 89–98 (1988).
    [CrossRef]

1998 (4)

S. Breer and K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

A. Mendez and L. Arizmendi, “Maximum diffraction efficiency of fixed holograms in lithium niobate,” Opt. Mater. 10, 55–59 (1998).
[CrossRef]

M. Carrascosa and F. Agulló-López, “Selective developing and screening of fixed photorefractive holograms,” Opt. Commun. 151, 257–262 (1998).
[CrossRef]

S. Breer, K. Buse, and F. Rickermann, “Improved developing of thermally fixed holograms in photorefractive LiNbO3 crystals with high-intensity laser pulses,” Opt. Lett. 23, 73–75 (1998).
[CrossRef]

1996 (4)

1995 (1)

1994 (1)

R. Müller, M. T. Santos, L. Arizmendi, and J. M. Cabrera, “A narrow-band interference filter with photorefractive LiNbO3,” J. Phys. D 27, 241–246 (1994).
[CrossRef]

1992 (1)

R. Müller, L. Arizmendi, M. Carrascosa, and J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

1991 (1)

1990 (2)

R. A. Rupp, R. Sommerfeldt, K. H. Ringhofer, and E. Krätzig, “Space charge field limitations in photorefractive LiNbO3: Fe crystals,” Appl. Phys. B 51, 364–370 (1990).
[CrossRef]

G. Montemezzani and P. Günter, “Thermal hologram fixing in pure and doped KNbO3 crystals,” J. Opt. Soc. Am. B 7, 2323–2328 (1990).
[CrossRef]

1988 (2)

R. Sommerfeldt, L. Holtmann, E. Krätzig, and B. C. Grabmaier, “Influence of Mg doping and composition on the light-induced charge transport in LiNbO3,” Phys. Status Solidi A 106, 89–98 (1988).
[CrossRef]

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1988).
[CrossRef]

1987 (1)

A. García-Cabañes, L. Arizmendi, J. M. Cabrera, and F. Agulló-López, “New aspects of reduction treatments on Fe-doped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 15, 131–135 (1987).

1977 (1)

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

1971 (1)

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Agulló-López, F.

M. Carrascosa and F. Agulló-López, “Selective developing and screening of fixed photorefractive holograms,” Opt. Commun. 151, 257–262 (1998).
[CrossRef]

M. Carrascosa and F. Agulló-López, “Optimization of the developing stage for fixed gratings in LiNbO3,” Opt. Commun. 126, 240–246 (1996).
[CrossRef]

A. García-Cabañes, L. Arizmendi, J. M. Cabrera, and F. Agulló-López, “New aspects of reduction treatments on Fe-doped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 15, 131–135 (1987).

Amodei, J. J.

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Arizmendi, L.

A. Mendez and L. Arizmendi, “Maximum diffraction efficiency of fixed holograms in lithium niobate,” Opt. Mater. 10, 55–59 (1998).
[CrossRef]

R. Müller, M. T. Santos, L. Arizmendi, and J. M. Cabrera, “A narrow-band interference filter with photorefractive LiNbO3,” J. Phys. D 27, 241–246 (1994).
[CrossRef]

R. Müller, L. Arizmendi, M. Carrascosa, and J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1988).
[CrossRef]

A. García-Cabañes, L. Arizmendi, J. M. Cabrera, and F. Agulló-López, “New aspects of reduction treatments on Fe-doped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 15, 131–135 (1987).

Bashaw, M. C.

Breer, S.

S. Breer and K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

S. Breer, K. Buse, and F. Rickermann, “Improved developing of thermally fixed holograms in photorefractive LiNbO3 crystals with high-intensity laser pulses,” Opt. Lett. 23, 73–75 (1998).
[CrossRef]

Buse, K.

S. Breer, K. Buse, and F. Rickermann, “Improved developing of thermally fixed holograms in photorefractive LiNbO3 crystals with high-intensity laser pulses,” Opt. Lett. 23, 73–75 (1998).
[CrossRef]

S. Breer and K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

Cabrera, J. M.

R. Müller, M. T. Santos, L. Arizmendi, and J. M. Cabrera, “A narrow-band interference filter with photorefractive LiNbO3,” J. Phys. D 27, 241–246 (1994).
[CrossRef]

R. Müller, L. Arizmendi, M. Carrascosa, and J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

A. García-Cabañes, L. Arizmendi, J. M. Cabrera, and F. Agulló-López, “New aspects of reduction treatments on Fe-doped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 15, 131–135 (1987).

Carrascosa, M.

M. Carrascosa and F. Agulló-López, “Selective developing and screening of fixed photorefractive holograms,” Opt. Commun. 151, 257–262 (1998).
[CrossRef]

M. Carrascosa and F. Agulló-López, “Optimization of the developing stage for fixed gratings in LiNbO3,” Opt. Commun. 126, 240–246 (1996).
[CrossRef]

R. Müller, L. Arizmendi, M. Carrascosa, and J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

Daiber, A. J.

Dischler, B.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Engelmann, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Feinberg, J.

García-Cabañes, A.

A. García-Cabañes, L. Arizmendi, J. M. Cabrera, and F. Agulló-López, “New aspects of reduction treatments on Fe-doped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 15, 131–135 (1987).

Gonser, U.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Grabmaier, B. C.

R. Sommerfeldt, L. Holtmann, E. Krätzig, and B. C. Grabmaier, “Influence of Mg doping and composition on the light-induced charge transport in LiNbO3,” Phys. Status Solidi A 106, 89–98 (1988).
[CrossRef]

Günter, P.

Heanue, J. F.

Hesselink, L.

Holtmann, L.

R. Sommerfeldt, L. Holtmann, E. Krätzig, and B. C. Grabmaier, “Influence of Mg doping and composition on the light-induced charge transport in LiNbO3,” Phys. Status Solidi A 106, 89–98 (1988).
[CrossRef]

Imai, T.

Keune, W.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Kirillov, D.

Krätzig, E.

R. A. Rupp, R. Sommerfeldt, K. H. Ringhofer, and E. Krätzig, “Space charge field limitations in photorefractive LiNbO3: Fe crystals,” Appl. Phys. B 51, 364–370 (1990).
[CrossRef]

R. Sommerfeldt, L. Holtmann, E. Krätzig, and B. C. Grabmaier, “Influence of Mg doping and composition on the light-induced charge transport in LiNbO3,” Phys. Status Solidi A 106, 89–98 (1988).
[CrossRef]

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Kurz, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Leyva, V.

Mendez, A.

A. Mendez and L. Arizmendi, “Maximum diffraction efficiency of fixed holograms in lithium niobate,” Opt. Mater. 10, 55–59 (1998).
[CrossRef]

Montemezzani, G.

Müller, R.

R. Müller, M. T. Santos, L. Arizmendi, and J. M. Cabrera, “A narrow-band interference filter with photorefractive LiNbO3,” J. Phys. D 27, 241–246 (1994).
[CrossRef]

R. Müller, L. Arizmendi, M. Carrascosa, and J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

Orlov, S.

Orlov, S. S.

Rakuljic, G.

Rakuljic, G. A.

Räuber, E.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Rickermann, F.

Ringhofer, K. H.

R. A. Rupp, R. Sommerfeldt, K. H. Ringhofer, and E. Krätzig, “Space charge field limitations in photorefractive LiNbO3: Fe crystals,” Appl. Phys. B 51, 364–370 (1990).
[CrossRef]

Rupp, R. A.

R. A. Rupp, R. Sommerfeldt, K. H. Ringhofer, and E. Krätzig, “Space charge field limitations in photorefractive LiNbO3: Fe crystals,” Appl. Phys. B 51, 364–370 (1990).
[CrossRef]

Santos, M. T.

R. Müller, M. T. Santos, L. Arizmendi, and J. M. Cabrera, “A narrow-band interference filter with photorefractive LiNbO3,” J. Phys. D 27, 241–246 (1994).
[CrossRef]

Snyder, R.

Sommerfeldt, R.

R. A. Rupp, R. Sommerfeldt, K. H. Ringhofer, and E. Krätzig, “Space charge field limitations in photorefractive LiNbO3: Fe crystals,” Appl. Phys. B 51, 364–370 (1990).
[CrossRef]

R. Sommerfeldt, L. Holtmann, E. Krätzig, and B. C. Grabmaier, “Influence of Mg doping and composition on the light-induced charge transport in LiNbO3,” Phys. Status Solidi A 106, 89–98 (1988).
[CrossRef]

Staebler, D. L.

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Yagi, S.

Yamazaki, H.

Yariv, A.

Appl. Phys. (1)

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and E. Räuber, “Photorefractive centers in LiNbO3. Study by optical-, mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Appl. Phys. B (2)

S. Breer and K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

R. A. Rupp, R. Sommerfeldt, K. H. Ringhofer, and E. Krätzig, “Space charge field limitations in photorefractive LiNbO3: Fe crystals,” Appl. Phys. B 51, 364–370 (1990).
[CrossRef]

Appl. Phys. Lett. (2)

R. Müller, L. Arizmendi, M. Carrascosa, and J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Cryst. Lattice Defects Amorphous Mater. (1)

A. García-Cabañes, L. Arizmendi, J. M. Cabrera, and F. Agulló-López, “New aspects of reduction treatments on Fe-doped LiNbO3,” Cryst. Lattice Defects Amorphous Mater. 15, 131–135 (1987).

J. Appl. Phys. (1)

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1988).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. D (1)

R. Müller, M. T. Santos, L. Arizmendi, and J. M. Cabrera, “A narrow-band interference filter with photorefractive LiNbO3,” J. Phys. D 27, 241–246 (1994).
[CrossRef]

Opt. Commun. (2)

M. Carrascosa and F. Agulló-López, “Optimization of the developing stage for fixed gratings in LiNbO3,” Opt. Commun. 126, 240–246 (1996).
[CrossRef]

M. Carrascosa and F. Agulló-López, “Selective developing and screening of fixed photorefractive holograms,” Opt. Commun. 151, 257–262 (1998).
[CrossRef]

Opt. Lett. (4)

Opt. Mater. (1)

A. Mendez and L. Arizmendi, “Maximum diffraction efficiency of fixed holograms in lithium niobate,” Opt. Mater. 10, 55–59 (1998).
[CrossRef]

Phys. Status Solidi A (1)

R. Sommerfeldt, L. Holtmann, E. Krätzig, and B. C. Grabmaier, “Influence of Mg doping and composition on the light-induced charge transport in LiNbO3,” Phys. Status Solidi A 106, 89–98 (1988).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Developing kinetics of fixed holograms under homogeneous illumination. (a), (b), and (c) for the oxidized sample with 0.58-, 0.97-, and 2.16-µm fringe spacing, respectively. (d), (e), and (f) for the reduced sample with 0.58-, 0.97-, and 2.16-µm fringe spacing, respectively.

Fig. 2
Fig. 2

Developing kinetics for a partially fixed hologram. Reduced sample with grating spacing of 2.16 µm.

Fig. 3
Fig. 3

Final developed rate Dr versus grating spatial frequency. Triangles, experimental data for the oxidized sample, and circles, reduced sample. Dotted curves, result of fitting data to the theoretical dependence, Eq. (12).

Fig. 4
Fig. 4

Graph comparing the experimental oscillatory kinetics of Fig. 1(a) (solid curve) and a plot of the theoretical time dependence of Eq. (8) (dotted curve) with best value of parameters to reproduce similar oscillations.

Fig. 5
Fig. 5

Plot of the theoretical developing kinetics given by expression (5) for different values of Eph. (a) Dashed curve for Eph=0, and solid curve for Eph=1 kV/cm. (b) For Eph=100 kV/cm. (Other parameters used in the calculation are Λ=2.1 µm, N=1.8×1019 cm-3, and NA=1.7×1019 cm-3.)

Fig. 6
Fig. 6

Plot of the electric field components of the developed gratings versus the spatial displacement along the grating vector direction. The curves were plotted for a grating frequency of 3.7×106 m-1 and by use of the final developed rate and phase shift obtained from the experimental data. Plot (a) corresponds to the reduced sample and plot (b) to the oxidized one. Dashed curves, ionic component; dotted curves, electronic component; and solid curves, resulting developed grating.

Tables (1)

Tables Icon

Table 1 Summary of Sample Parameters and Resulting Values

Equations (14)

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

dE˜edt+g˜eE˜e+ghEh=0,
g˜e=1Dτ1+EDEq+iEphEq,
gh=1Dτ,D=1+EDEM,
ED=KBTeK,Eq=eNT0K,EM=γNAμK,
1NT=1NA+1ND,τ=γNAσI0ND0μe,
Eph=EphNAN,
E˜T (t)=E˜e [1-exp(-g˜et)]+Ee0 exp(-g˜et)+Eh,
E˜e=-ghEhg˜e.
E˜T(t)=-ghg˜e-1Eh[1-exp(-g˜et)].
E˜T(t)=Eph2+iEphEqEq2+Eph2Eh×1-exp-tτexp-itτEphEq,
EphEq=Eph(NA/N)eNT/0K=0eEphNDK.
Dr=ETEh=Eph2Eq2+(ED2+Eph2+EqED)2[(Eq+ED)2+Eph2]21/2,
ϕ=arctanEphEq+ED.
Dr=ETEh=(Eph/Eq)21+(Eph/Eq)21/2,

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