Abstract

I investigated photorefractive grating formation in materials exhibiting the bulk photovoltaic effect on illumination with weak, very short light pulses. For a light pulse shorter than the time constants of the carrier, the existing theory of grating formation, as well as the expression for the photovoltaic current, breaks down. Nevertheless, my experiment, which is the first quantitative comparison of this kind to my knowledge, showed no meaningful difference between the pulsed and cw excitations of Fe:LiNbO3 for the same average intensity. I developed a simple model in which the bulk photovoltaic effect was implemented as a spatial shift in the initial carrier distribution, and I derived an analytical expression for the space-charge field. The resulting expression agreed with that of the quasi-cw approximation in the limit of a small spatial shift, thus supporting my experimental results.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Okamura and K. Kuroda, “Two-dimensional measurement of the temporal correlation function of picosecond light pulses recorded in a photorefractive crystal,” J. Opt. Soc. Am. B 14, 860–868 (1997).
    [CrossRef]
  2. X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7, 2347–2355 (1990).
    [CrossRef]
  3. I. V. Gusev, B. Ya. Zel’dovich, V. A. Krivoshchekov, and V. V. Shkunov, “Stimulated diffusion backscattering of nanosecond pulses under exposure accumulation conditions,” Zh. Eksp. Teor. Fiz. 99, 1082–1087 (1991).
  4. G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
    [CrossRef]
  5. H. Okamura, K. Takeuchi, T. Tanaka, and K. Kuroda, “Grating formation with very short pulses in photorefractive materials: weak excitation limit,” J. Opt. Soc. Am. B 14, 2650–2656 (1997).
    [CrossRef]
  6. A. M. Glass, D. von der Linde, and T. J. Negran, “The photovoltaic effect and the charge transport in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [CrossRef]
  7. M. Carrascosa, J. M. Cabera, and F. Agullo-Lopez, “Role of photovoltaic drift on the initial writing and erasure rates of holographic gratings: Some implications,” Opt. Commun. 69, 83–86 (1988).
    [CrossRef]
  8. L. Young, N. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
    [CrossRef]
  9. E. Krätzig and O. F. Schirmer, “Photorefractive centers in electro-optic crystals,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Springer-Verlag, Berlin (1988), pp. 141–144.
  10. D. L. Staebler and J. J. Amodei, “Thermally fixed holograms in LiNbO3,” Ferroelectrics 3, 107–113 (1972).
    [CrossRef]
  11. H. Okamura, “Theory of the photorefractive grating formation in presence of the bulk photovoltaic effect,” Jpn. J. Appl. Phys., Part 1 39, 5105–5110 (2000).
    [CrossRef]
  12. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole-electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
    [CrossRef]
  13. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  14. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
    [CrossRef]
  15. P. Günter and J.-P. Huignard, in Photorefractive Materials and Their Applications I, ed. by P. Günter and J.-P. Huignard, p. 19, Springer-Verlag, Berlin (1988).
  16. D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. 15, 153–156 (1978).
    [CrossRef]
  17. K. Kurtz and D. von der Linde, “Nonlinear optical excitation of photovoltaic LiNbO3,” Ferroelectrics 21, 621–622 (1978).
    [CrossRef]
  18. C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient pulsed photorefractive process in LiNbO3:Fe for optical storage and deflection,” IEEE J. Quantum Electron. QE-16, 126–129 (1980), and “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979).
    [CrossRef]
  19. P. Günter and J.-P. Huignard, in Photorefractive Materials and Their Applications I, ed. by P. Günter and J.-P. Huignard, p. 53, Springer-Verlag, Berlin (1988).

2000 (1)

H. Okamura, “Theory of the photorefractive grating formation in presence of the bulk photovoltaic effect,” Jpn. J. Appl. Phys., Part 1 39, 5105–5110 (2000).
[CrossRef]

1997 (2)

1991 (1)

I. V. Gusev, B. Ya. Zel’dovich, V. A. Krivoshchekov, and V. V. Shkunov, “Stimulated diffusion backscattering of nanosecond pulses under exposure accumulation conditions,” Zh. Eksp. Teor. Fiz. 99, 1082–1087 (1991).

1990 (1)

1988 (1)

M. Carrascosa, J. M. Cabera, and F. Agullo-Lopez, “Role of photovoltaic drift on the initial writing and erasure rates of holographic gratings: Some implications,” Opt. Commun. 69, 83–86 (1988).
[CrossRef]

1986 (1)

1983 (1)

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

1979 (3)

L. Young, N. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

1978 (2)

D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. 15, 153–156 (1978).
[CrossRef]

K. Kurtz and D. von der Linde, “Nonlinear optical excitation of photovoltaic LiNbO3,” Ferroelectrics 21, 621–622 (1978).
[CrossRef]

1974 (1)

A. M. Glass, D. von der Linde, and T. J. Negran, “The photovoltaic effect and the charge transport in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

1972 (1)

D. L. Staebler and J. J. Amodei, “Thermally fixed holograms in LiNbO3,” Ferroelectrics 3, 107–113 (1972).
[CrossRef]

Agullo-Lopez, F.

M. Carrascosa, J. M. Cabera, and F. Agullo-Lopez, “Role of photovoltaic drift on the initial writing and erasure rates of holographic gratings: Some implications,” Opt. Commun. 69, 83–86 (1988).
[CrossRef]

Amodei, J. J.

D. L. Staebler and J. J. Amodei, “Thermally fixed holograms in LiNbO3,” Ferroelectrics 3, 107–113 (1972).
[CrossRef]

Cabera, J. M.

M. Carrascosa, J. M. Cabera, and F. Agullo-Lopez, “Role of photovoltaic drift on the initial writing and erasure rates of holographic gratings: Some implications,” Opt. Commun. 69, 83–86 (1988).
[CrossRef]

Carrascosa, M.

M. Carrascosa, J. M. Cabera, and F. Agullo-Lopez, “Role of photovoltaic drift on the initial writing and erasure rates of holographic gratings: Some implications,” Opt. Commun. 69, 83–86 (1988).
[CrossRef]

Dominic, V.

El Guibaly, F.

L. Young, N. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[CrossRef]

Feinberg, J.

Glass, A. M.

A. M. Glass, D. von der Linde, and T. J. Negran, “The photovoltaic effect and the charge transport in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Gusev, I. V.

I. V. Gusev, B. Ya. Zel’dovich, V. A. Krivoshchekov, and V. V. Shkunov, “Stimulated diffusion backscattering of nanosecond pulses under exposure accumulation conditions,” Zh. Eksp. Teor. Fiz. 99, 1082–1087 (1991).

Hellwarth, R. W.

Jonathan, J. M. C.

Krivoshchekov, V. A.

I. V. Gusev, B. Ya. Zel’dovich, V. A. Krivoshchekov, and V. V. Shkunov, “Stimulated diffusion backscattering of nanosecond pulses under exposure accumulation conditions,” Zh. Eksp. Teor. Fiz. 99, 1082–1087 (1991).

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Kuroda, K.

Kurtz, K.

K. Kurtz and D. von der Linde, “Nonlinear optical excitation of photovoltaic LiNbO3,” Ferroelectrics 21, 621–622 (1978).
[CrossRef]

Kurz, H.

D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. 15, 153–156 (1978).
[CrossRef]

Lun, E.

L. Young, N. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Moharam, N. G.

L. Young, N. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[CrossRef]

Negran, T. J.

A. M. Glass, D. von der Linde, and T. J. Negran, “The photovoltaic effect and the charge transport in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Okamura, H.

Schirmer, O. F.

D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. 15, 153–156 (1978).
[CrossRef]

Shkunov, V. V.

I. V. Gusev, B. Ya. Zel’dovich, V. A. Krivoshchekov, and V. V. Shkunov, “Stimulated diffusion backscattering of nanosecond pulses under exposure accumulation conditions,” Zh. Eksp. Teor. Fiz. 99, 1082–1087 (1991).

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Staebler, D. L.

D. L. Staebler and J. J. Amodei, “Thermally fixed holograms in LiNbO3,” Ferroelectrics 3, 107–113 (1972).
[CrossRef]

Strohkendl, F. P.

Takeuchi, K.

Tanaka, T.

Valley, G. C.

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

von der Linde, D.

K. Kurtz and D. von der Linde, “Nonlinear optical excitation of photovoltaic LiNbO3,” Ferroelectrics 21, 621–622 (1978).
[CrossRef]

D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. 15, 153–156 (1978).
[CrossRef]

A. M. Glass, D. von der Linde, and T. J. Negran, “The photovoltaic effect and the charge transport in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Yao, X. S.

Young, L.

L. Young, N. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[CrossRef]

Zel’dovich, B. Ya.

I. V. Gusev, B. Ya. Zel’dovich, V. A. Krivoshchekov, and V. V. Shkunov, “Stimulated diffusion backscattering of nanosecond pulses under exposure accumulation conditions,” Zh. Eksp. Teor. Fiz. 99, 1082–1087 (1991).

Appl. Phys. (1)

D. von der Linde, O. F. Schirmer, and H. Kurz, “Intrinsic photorefractive effect of LiNbO3,” Appl. Phys. 15, 153–156 (1978).
[CrossRef]

Appl. Phys. Lett. (1)

A. M. Glass, D. von der Linde, and T. J. Negran, “The photovoltaic effect and the charge transport in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Ferroelectrics (4)

K. Kurtz and D. von der Linde, “Nonlinear optical excitation of photovoltaic LiNbO3,” Ferroelectrics 21, 621–622 (1978).
[CrossRef]

D. L. Staebler and J. J. Amodei, “Thermally fixed holograms in LiNbO3,” Ferroelectrics 3, 107–113 (1972).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

J. Appl. Phys. (1)

L. Young, N. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[CrossRef]

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

Jpn. J. Appl. Phys., Part 1 (1)

H. Okamura, “Theory of the photorefractive grating formation in presence of the bulk photovoltaic effect,” Jpn. J. Appl. Phys., Part 1 39, 5105–5110 (2000).
[CrossRef]

Opt. Commun. (1)

M. Carrascosa, J. M. Cabera, and F. Agullo-Lopez, “Role of photovoltaic drift on the initial writing and erasure rates of holographic gratings: Some implications,” Opt. Commun. 69, 83–86 (1988).
[CrossRef]

Opt. Lett. (1)

Zh. Eksp. Teor. Fiz. (1)

I. V. Gusev, B. Ya. Zel’dovich, V. A. Krivoshchekov, and V. V. Shkunov, “Stimulated diffusion backscattering of nanosecond pulses under exposure accumulation conditions,” Zh. Eksp. Teor. Fiz. 99, 1082–1087 (1991).

Other (4)

E. Krätzig and O. F. Schirmer, “Photorefractive centers in electro-optic crystals,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Springer-Verlag, Berlin (1988), pp. 141–144.

P. Günter and J.-P. Huignard, in Photorefractive Materials and Their Applications I, ed. by P. Günter and J.-P. Huignard, p. 19, Springer-Verlag, Berlin (1988).

C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient pulsed photorefractive process in LiNbO3:Fe for optical storage and deflection,” IEEE J. Quantum Electron. QE-16, 126–129 (1980), and “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979).
[CrossRef]

P. Günter and J.-P. Huignard, in Photorefractive Materials and Their Applications I, ed. by P. Günter and J.-P. Huignard, p. 53, Springer-Verlag, Berlin (1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Experimental setup for the measurement of the bulk photovoltaic current. The light shines on the entire surface of the sample, and the current was measured through electrical contacts attached to the sides perpendicular to the c axis. To reduce noise, a lock-in detection technique was employed. Amp., amplifier.

Fig. 2
Fig. 2

Experimental setup for the observation of the grating formation. Two light sources were switched by a resettable mirror. The optical path lengths of the pump and the probe beams were adjusted to be equal by using an optical delay inserted into the probe beam arm. The intensity of the transmitted probe beam was measured as a function of time. While the chopper blocked the probe beam, a diffraction was observed.

Fig. 3
Fig. 3

The experimental results of the grating formation in a photorefractive Fe:LiNbO3 crystal for (top) cw and (bottom) mode-locked Nd:YAG lasers (532-nm wavelength). The total energy of the transmitted probe beam is plotted as a function of time. The probe beam is periodically blocked by a mechanical chopper to allow us to observe the diffraction as well as the two-wave mixing amplification. The pulse length of the mode-locked pulses is 3.5 ps and the repetition rate is 82 MHz. The diameter of the probe beam was 0.3 mm for both cases. The average intensities of the pump and the probe beams were (top) 72 and 7.2 mW/cm2 and (bottom) 68 and 7.2 mW/cm2, respectively. The incident beams were ordinarily polarized, and the grating period was 4.9 µm.

Equations (17)

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

I¯=1d 0dI0 exp(-αz)dzfI0,
nt+·je=(sI+β)(N-Ni)-γnNi,
j=eμnE-kBTμn+κs(N-Ni)I,
t(n-Ni)=-·je,
·E=(e/0)(n+NA-Ni),
ΔE1=-aE1(τp)0τpI0(t)dt+ib0τpI1(t)dt,
a=s NNA Ks2Ke2 1+K(K+iV)/Ks21+K(K+iV)/Ke2,
Ks2=Ks2/{1-[1-exp(iϕ)]NA/N},
b=s NNA Ks2Ke2 kBTe K+iV1+K(K+iV)/Ke2 exp(iϕ),
E1(t)/t=-aI0(t)E1(t)+ibI1(t),
0τpIi(t)dt=0TIi(t)dt=TIi(t),
E1t=-acw I0E1+ibcw I1,
acw=s NNA Ks2Ke2 1+(K2+i(NA/N)PK)/Ks21+K2/Ke2,
bcw=s NNA Ks2Ke2 kBTe K+iP1+K2/Ke2,
as NNA Ks2Ke2 1+(K2/Ks2)(1+iϕNA/N)1+K2/Ke2,
bs NNA Ks2Ke2 kBTe K(1+iϕ)1+K2/Ke2.
Lph=κγNAμkBTK2=κe τDτR

Metrics