Abstract

The evolution of the space-charge field under illumination with weak very short pulses is discussed. Under a weak irradiation limit the space-charge field after recombination of the carrier becomes the same regardless of whether it is a cw, a single-pulsed, or a repetitive-pulsed excitation. On irradiation with very short pulses the space-charge field tends to increase and then decrease when the space-charge field is large owing to the nonlinear effect of the recombination term in the rate equation. With this fluctuation being neglected, the evolution of the space-charge field by mode-locked pulses becomes identical to that by cw illumination having the same averaged intensity, which was confirmed experimentally with a BaTiO3 crystal and a cw and a picosecond mode-locked Nd:YAG laser.

© 1997 Optical Society of America

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    [CrossRef]
  7. H. Okamura and K. Kuroda, “Two-dimensional measurement of the temporal correlation function ofpicosecond light pulses recorded in a photorefractive crystal,” J. Opt. Soc. Am. B 14, 860–868 (1997).
    [CrossRef]
  8. 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); “Holographic storage in electrooptic crystals. II. Beam coupling-lightamplification,” Ferroelectrics 22, 961–964 (1979).
    [CrossRef]
  9. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole-electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
    [CrossRef]
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    [CrossRef]
  11. A. L. Smirl, G. C. Valley R. A. Mullen, K. Bohnert, C. D. Mire, and T. F. Boggess, “Picosecond photorefractive effect in BaTiO3,” Opt. Lett. 12, 501–503 (1987).
    [CrossRef] [PubMed]
  12. G. C. Valley and A. L. Smirl, “Theory of transient energy transfer in gallium arsenide,” IEEE J. Quantum Electron. QE-24, 304–310 (1988).
    [CrossRef]
  13. G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
    [CrossRef]
  14. A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive processin LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [CrossRef]
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    [CrossRef]
  16. P. Günter and J.-P. Huignard, eds., PhotorefractiveMaterials and Their Applications I (Springer-Verlag, Berlin, 1988), p. 53.
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    [CrossRef]
  18. M. B. Klein, Photorefractive Materials andTheir Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 220, 224.
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    [CrossRef]
  20. I. Camlibel, M. DiDomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417–1419 (1970).
    [CrossRef]

1997 (1)

1993 (2)

Y. Mazurenko, V. S. Udaltsov, A. V. Veniaminov, E. Döpel, and P. Kühmstedt, “Recording and reconstruction of femtosecond light pulses using volumeholograms,” Opt. Commun. 96, 202–207 (1993).
[CrossRef]

H. Okamura, T. Shimura, M. Itoh, K. Kuroda, and I. Ogura, “Measurement of photorefractive coupling constant of BaTiO3 using varying interactionlength method,” Opt. Commun. 99, 230–236 (1993).
[CrossRef]

1991 (1)

1990 (2)

1989 (1)

1988 (1)

G. C. Valley and A. L. Smirl, “Theory of transient energy transfer in gallium arsenide,” IEEE J. Quantum Electron. QE-24, 304–310 (1988).
[CrossRef]

1987 (1)

1986 (1)

1983 (1)

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

1981 (2)

1979 (2)

C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979).
[CrossRef]

J. P. Boyeaux and F. M. Michel-Calendini, “Small polaron interpretation of BaTiO3 transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

1974 (1)

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive processin LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

1970 (1)

I. Camlibel, M. DiDomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417–1419 (1970).
[CrossRef]

Achioli, L. H.

Boggess, T. F.

Bohnert, K.

Boyeaux, J. P.

J. P. Boyeaux and F. M. Michel-Calendini, “Small polaron interpretation of BaTiO3 transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

Camlibel, I.

I. Camlibel, M. DiDomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417–1419 (1970).
[CrossRef]

Chang, T. Y.

Chen, B. S.

Chen, C.-T.

C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979).
[CrossRef]

Cronin-Golomb, M.

DiDomenico, M.

I. Camlibel, M. DiDomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417–1419 (1970).
[CrossRef]

Dominic, V.

Döpel, E.

Y. Mazurenko, V. S. Udaltsov, A. V. Veniaminov, E. Döpel, and P. Kühmstedt, “Recording and reconstruction of femtosecond light pulses using volumeholograms,” Opt. Commun. 96, 202–207 (1993).
[CrossRef]

Feinberg, J.

Fujimoto, J. G.

Glass, A. M.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive processin LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Grousson, R.

Hellwarth, R. W.

Hermann, J. P.

Herriau, J. P.

Huignard, J. P.

Ippen, E. P.

Itoh, M.

H. Okamura, T. Shimura, M. Itoh, K. Kuroda, and I. Ogura, “Measurement of photorefractive coupling constant of BaTiO3 using varying interactionlength method,” Opt. Commun. 99, 230–236 (1993).
[CrossRef]

Jonathan, J. M. C.

Jourbert, C.

Kim, D. M.

C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979).
[CrossRef]

Kong, H.

Kühmstedt, P.

Y. Mazurenko, V. S. Udaltsov, A. V. Veniaminov, E. Döpel, and P. Kühmstedt, “Recording and reconstruction of femtosecond light pulses using volumeholograms,” Opt. Commun. 96, 202–207 (1993).
[CrossRef]

Kuroda, K.

H. Okamura and K. Kuroda, “Two-dimensional measurement of the temporal correlation function ofpicosecond light pulses recorded in a photorefractive crystal,” J. Opt. Soc. Am. B 14, 860–868 (1997).
[CrossRef]

H. Okamura, T. Shimura, M. Itoh, K. Kuroda, and I. Ogura, “Measurement of photorefractive coupling constant of BaTiO3 using varying interactionlength method,” Opt. Commun. 99, 230–236 (1993).
[CrossRef]

Lam, L. K.

Mazurenko, Y.

Y. Mazurenko, V. S. Udaltsov, A. V. Veniaminov, E. Döpel, and P. Kühmstedt, “Recording and reconstruction of femtosecond light pulses using volumeholograms,” Opt. Commun. 96, 202–207 (1993).
[CrossRef]

Michel-Calendini, F. M.

J. P. Boyeaux and F. M. Michel-Calendini, “Small polaron interpretation of BaTiO3 transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

Mire, C. D.

Mullen, R. A.

Negran, T. J.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive processin LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Ogura, I.

H. Okamura, T. Shimura, M. Itoh, K. Kuroda, and I. Ogura, “Measurement of photorefractive coupling constant of BaTiO3 using varying interactionlength method,” Opt. Commun. 99, 230–236 (1993).
[CrossRef]

Okamura, H.

H. Okamura and K. Kuroda, “Two-dimensional measurement of the temporal correlation function ofpicosecond light pulses recorded in a photorefractive crystal,” J. Opt. Soc. Am. B 14, 860–868 (1997).
[CrossRef]

H. Okamura, T. Shimura, M. Itoh, K. Kuroda, and I. Ogura, “Measurement of photorefractive coupling constant of BaTiO3 using varying interactionlength method,” Opt. Commun. 99, 230–236 (1993).
[CrossRef]

Roblin, M. L.

Shimura, T.

H. Okamura, T. Shimura, M. Itoh, K. Kuroda, and I. Ogura, “Measurement of photorefractive coupling constant of BaTiO3 using varying interactionlength method,” Opt. Commun. 99, 230–236 (1993).
[CrossRef]

Smirl, A. L.

G. C. Valley and A. L. Smirl, “Theory of transient energy transfer in gallium arsenide,” IEEE J. Quantum Electron. QE-24, 304–310 (1988).
[CrossRef]

A. L. Smirl, G. C. Valley R. A. Mullen, K. Bohnert, C. D. Mire, and T. F. Boggess, “Picosecond photorefractive effect in BaTiO3,” Opt. Lett. 12, 501–503 (1987).
[CrossRef] [PubMed]

Strohkendl, F. P.

Udaltsov, V. S.

Y. Mazurenko, V. S. Udaltsov, A. V. Veniaminov, E. Döpel, and P. Kühmstedt, “Recording and reconstruction of femtosecond light pulses using volumeholograms,” Opt. Commun. 96, 202–207 (1993).
[CrossRef]

Ulman, M.

Valley, G. C.

T. F. Boggess, J. O. White, and G. C. Valley, “Two-photon absorption and anisotropic transient energy transfer in BaTiO3 with 1-psec excitation,” J. Opt. Soc. Am. B 7, 2255–2258 (1990).
[CrossRef]

G. C. Valley and A. L. Smirl, “Theory of transient energy transfer in gallium arsenide,” IEEE J. Quantum Electron. QE-24, 304–310 (1988).
[CrossRef]

A. L. Smirl, G. C. Valley R. A. Mullen, K. Bohnert, C. D. Mire, and T. F. Boggess, “Picosecond photorefractive effect in BaTiO3,” Opt. Lett. 12, 501–503 (1987).
[CrossRef] [PubMed]

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

Veniaminov, A. V.

Y. Mazurenko, V. S. Udaltsov, A. V. Veniaminov, E. Döpel, and P. Kühmstedt, “Recording and reconstruction of femtosecond light pulses using volumeholograms,” Opt. Commun. 96, 202–207 (1993).
[CrossRef]

von der Linde, D.

C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979).
[CrossRef]

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive processin LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Wemple, S. H.

I. Camlibel, M. DiDomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417–1419 (1970).
[CrossRef]

White, J. O.

Yao, X. S.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

C.-T. Chen, D. M. Kim, and D. von der Linde, “Efficient hologram recording in LiNbO3:Fe using optical pulses,” Appl. Phys. Lett. 34, 321–324 (1979).
[CrossRef]

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive processin LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. C. Valley and A. L. Smirl, “Theory of transient energy transfer in gallium arsenide,” IEEE J. Quantum Electron. QE-24, 304–310 (1988).
[CrossRef]

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

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

J. Phys. C (1)

J. P. Boyeaux and F. M. Michel-Calendini, “Small polaron interpretation of BaTiO3 transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

J. Phys. Chem. Solids (1)

I. Camlibel, M. DiDomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417–1419 (1970).
[CrossRef]

Opt. Commun. (2)

Y. Mazurenko, V. S. Udaltsov, A. V. Veniaminov, E. Döpel, and P. Kühmstedt, “Recording and reconstruction of femtosecond light pulses using volumeholograms,” Opt. Commun. 96, 202–207 (1993).
[CrossRef]

H. Okamura, T. Shimura, M. Itoh, K. Kuroda, and I. Ogura, “Measurement of photorefractive coupling constant of BaTiO3 using varying interactionlength method,” Opt. Commun. 99, 230–236 (1993).
[CrossRef]

Opt. Lett. (4)

Other (3)

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); “Holographic storage in electrooptic crystals. II. Beam coupling-lightamplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

M. B. Klein, Photorefractive Materials andTheir Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 220, 224.

P. Günter and J.-P. Huignard, eds., PhotorefractiveMaterials and Their Applications I (Springer-Verlag, Berlin, 1988), p. 53.

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Figures (3)

Fig. 1
Fig. 1

Experimental results of the grating formation in a photorefractive BaTiO3 crystal for (a) cw and (b) mode-locked Nd:YAG lasers (wavelength 532 nm). The total energy of the transmitted probe beam is plotted as a function of time. The probe beam is blocked periodically by a mechanical chopper to observe the diffraction as well as the two-wave mixing amplification. The pulse length of the mode-locked pulse is 3.5 ps, and the repetition rate is 82 MHz. Other experimental conditions are the same for cw and pulses: The average intensity of the pump beam is 12.7 mW/cm2, and the ratio of the intensities of the probe to the pump beam is 1:11. The diameter of the probe beam is 0.3 mm. The incident beams were ordinarily polarized to minimize the effect of beam fanning. The grating period is 4.9 µm.

Fig. 2
Fig. 2

Result of the numerical simulation of the evolution of the space-charge field by five successive delta functionlike pulses as a function of time normalized by the carrier recombination time τR. The pulse interval is 15τR. The initial space-charge field is zero, and the initial carrier density is 10-7NA, where NA is the acceptor density. The modulation of the incident pulse is 0.1.

Fig. 3
Fig. 3

Result of the numerical simulation of the evolution of the space-charge field E1(t) at saturation by a delta functionlike illumination. The deviation from the initial value E1(0) is plotted as a function of time normalized by the carrier recombination time τR. The initial space-charge field is equal to the saturated space-charge field of 97.1 V/cm. The modulation of the incident pulse is 0.1, and the initial carrier density is 10-7NA, where NA is the acceptor density. The space-charge field increases after irradiation and then returns to its initial value.

Equations (24)

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

nt+·je=(sI+β)(N-Ni)-γnNi,
j=eμnE-kBTμn,
t(n-Ni)=-·je,
·E=(e/0)(n+NA-Ni),
2E1(t)t2+iτE+1τD+1τR+γn0(t)+n0(t)n0(τp)τdi(τp)
×E1t+iτE+1τDγn0(t)E1(t)=0,(tτp),
n0(t)=n0(τp)exp[-(t-τp)/τR]1+[n0(τp)/NA]{1-exp[-(t-τp)/τR]},
(t>τp).
ΔE1E1()-E1(τp)=1τD+iτE+1τR-1×E1tt=τp-1τD+iτEγτRE1(τp)n0(τp),
τpn0(t)dt=τRNA ln[1+n0(τp)/NA]τRn0(τp).
E1tt=τp=-1τdi(τp)E1(τp)+(E0-iED) n1(τp)n0(τp),
ΔE1=1τdi(τp)1τD+iτE+1τR-1×-1+1τD+iτE 0eμNAE1(τp)+i(ED+iE0) n1(τp)n0(τp).
n0(τp)=s(N-NA)0τpI0(t)dt,
n1(τp)=s(N-NA)0τpI1(t)dt+is0KE1e0τpI0(t)dt.
ΔE1=-aE1(τp)0τpI0(t)dt+ib0τpI1(t)dt,
a=s NNAKs2Ke21+K(K+iV)/Ks21+K(K+iV)/Ke2,
b=s NNAKs2Ke2kBTeK+iV1+K(K+iV)/Ke2,
E1(t)/t=-aI0(t)E1(t)+ibI1(t),
Ii(t)1τint0τintIi(t)dt=1τint0τpIi(t)dt.
E1(t=)=im ba=im kBTeK+iV1+K(K+iV)/Ks2,
E1=im kBTeK+iV1+(NA/N)K(K+iV)/Ks2.
ΔE1=E1()-E1(τp)=1τD+iτE+1τR-1E1tt=τp+γ+1n0(τp)τdi(τp)n0(τp)E1(τp),+γ+1n0(τp)τdi(τp)τpE1(t) n0(t)tdt-1τD+iτEγτpn0(t)E1(t)dt,
τpE1(t) n0tdtE1(τp)[n0(t)]τp=-E1(τp)n0(τp),
τpE1(t)n0(t)dtE1(τp)τpn0(t)dt=τpn0(τp)E1(τp).

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