Abstract

We report on the formation and subsequent dark evolution of induced absorption and photorefractive gratings produced by a high-intensity 15-ns pulse in an as-grown sample of BaTiO3 crystal. We show that the experimentally observed multiple time constants for decay of the induced absorption and buildup of the grating in the dark can be explained and successfully simulated by a numerical model of photorefraction incorporating two secondary (hole-trapping) centers in addition to the deep level. The model also takes into account combined electron and hole photoconductivity and high-intensity illumination. We present a full description of the method of numerical solution of the zeroth (homogeneous illumination) and the first-order parameters (inhomogeneous illumination) in this model regime for either steady-state or transient pulse trains and dark-evolution conditions.

[Optical Society of America ]

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References

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  1. N. V. Kukhtarev , V. M. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. 1. Steady-state , Ferroelectrics FEROA8 22 , 949 ( 1979
    [CrossRef]
  2. R. A. Motes and J. J. Kim , Intensity-dependent absorption coefficient in photorefractive BaTiO 3 crystals , J. Opt. Soc. Am. B JOBPDE 4 , 1379 ( 1987
    [CrossRef]
  3. R. Orlowski and E. Kratzig , Holographic method for the determination of photoinduced electron and hole transport in electro-optic crystals , Solid State Commun. SSCOA4 27 , 1351 ( 1978
    [CrossRef]
  4. M. B. Klein and G. C. Valley , Beam coupling in BaTiO 3 at 442 nm , J. Appl. Phys. JAPIAU 57 , 4901 ( 1985
    [CrossRef]
  5. S. Ducharme and J. Feinberg , Speed of the photorefractive effect in a BaTiO 3 single crystal , J. Appl. Phys. JAPIAU 56 , 839 ( 1984
    [CrossRef]
  6. R. A. Motes and J. J. Kim , Beam coupling in photorefractive BaTiO 3 crystals , Opt. Lett. OPLEDP 12 , 199 ( 1987
    [CrossRef] [PubMed]
  7. G. A. Brost , R. A. Motes , and J. R. Rotge , Intensity-dependent absorption and photorefractive effect in barium titanate , J. Opt. Soc. Am. B JOBPDE 5 , 1879 ( 1988
    [CrossRef]
  8. P. Tayebati , Effect of shallow traps on electron hole com-petition in semi-insulating photorefractive materials , J. Opt. Soc. Am. B JOBPDE 8 , 1053 ( 1991
    [CrossRef]
  9. N. Barry , L. Duffault , R. Troth , R. Ramos-Garcia , and M. J. Damzen , Comparison between continuous-wave and pulsed photorefraction in BaTiO 3 , J. Opt. Soc. Am. B JOBPDE 11 , 1758 ( 1994
    [CrossRef]
  10. G. A. Brost and R. A. Motes , Origin of the sublinear photorefractive response time in BaTiO 3 , Opt. Lett. OPLEDP 15 , 1194 ( 1990
    [CrossRef] [PubMed]
  11. M. J. Damzen and N. Barry , Intensity-dependent hole electron competition and photorefractive saturation in BaTiO 3 when using intense laser pulses , J. Opt. Soc. Am. B JOBPDE 10 , 600 ( 1993
    [CrossRef]
  12. F. P. Strohkendl , Light induced dark decays of photorefractive gratings and their observation in Bi 12 SO 20 , J. Appl. Phys. JAPIAU 65 , 3773 ( 1989
    [CrossRef]
  13. P. Tayebati , The effect of shallow traps on the dark storage of photorefractive gratings in Bi 12 SO 20 , J. Appl. Phys. JAPIAU 70 , 4082 ( 1991
    [CrossRef]
  14. P. Tayebati and D. Mahgerefteh , Theory of the photorefractive effect for Bi 12 SiO 20 and BaTiO 3 with shallow traps , J. Opt. Soc. Am. B JOBPDE 8 , 1053 ( 1991
    [CrossRef]
  15. A. L. Smirl , K. Bohnert , G. C. Valey , R. A. Mullen , and T. F. Boggess , Formation, decay, and erasure of photorefractive gratings written in barium titanate by picosecond pulses , J. Opt. Soc. Am. B JOBPDE 6 , 606 ( 1989
    [CrossRef]
  16. K. Buse , J. Frejlich , G. Kuper , and E. Kra tzig , Dark build-up of holograms in BaTiO 3 after recording , Appl. Phys. A APSFDB 57 , 437 ( 1993
    [CrossRef]
  17. R. C. Troth , R. Ramos-Garcia , and M. J. Damzen , Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO 3 crystal , Opt. Commun. OPCOB8 116 , 435 ( 1995
    [CrossRef]
  18. A. Motes , G. A. Brost , J. R. Rotge , and J. J. Kim , Temporal behavior of the intensity-dependent absorption in photorefractive BaTiO 3 , Opt. Lett. OPLEDP 13 , 509 ( 1988
    [CrossRef] [PubMed]
  19. K. Buse and E. Kra tzig , Light-induced absorption in BaTiO 3 and KNbO 3 generated with high intensity laser pulses , Opt. Mater. OMATET 1 , 165 ( 1992
    [CrossRef]
  20. R. Cudney , R. M. Pierce , G. D. Bacher , and J. Feinberg , Absorption gratings in photorefractive crystals with multiple levels , J. Opt. Soc. Am. B JOBPDE 8 , 1326 ( 1991
    [CrossRef]
  21. K. Buse , Thermal gratings and pyroelectrically produced charge distributions in BaTiO 3 and KNbO 3 , J. Opt. Soc. Am. B JOBPDE 10 , 1266 ( 1993
    [CrossRef]
  22. F. Jariego and F. Agullo -Lo pez , Holographic writing and erasure in unipolar photorefractive materials with multiple active centers: theoretical analysis , Appl. Opt. APOPAI 30 , 4615 ( 1991
    [CrossRef] [PubMed]
  23. G. C. Valley and M. B. Klein , Optimal properties of photorefractive materials for optical data processing , Opt. Eng. OPEGAR 22 , 704 ( 1983
    [CrossRef]
  24. S. H. Wemple , M. Didomenico , and I. Camlibel , Dielectric and optical properties of melt-grown BaTiO 3 , J. Phys. Chem. Solids JPCSAW 29 , 1797 ( 1968
    [CrossRef]
  25. S. Ducharme , J. Feinberg , and R. R. Neurgaonkar , Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate , IEEE J. Quantum Electron. IEJQA7 QE-23 , 2116 ( 1987
    [CrossRef]
  26. I. Camlibel , M. Didomenico , and S. H. Wemple , Dielectric properties of single-domain melt-grown BaTiO 3 , J. Phys. Chem. Solids JPCSAW 31 , 1417 ( 1970
    [CrossRef]

Cudney, R

Markov, V. M

N. V. Kukhtarev , V. M. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. 1. Steady-state , Ferroelectrics FEROA8 22 , 949 ( 1979
[CrossRef]

Troth, R. C

R. C. Troth , R. Ramos-Garcia , and M. J. Damzen , Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO 3 crystal , Opt. Commun. OPCOB8 116 , 435 ( 1995
[CrossRef]

Valey, G. C

Other

R. Orlowski and E. Kratzig , Holographic method for the determination of photoinduced electron and hole transport in electro-optic crystals , Solid State Commun. SSCOA4 27 , 1351 ( 1978
[CrossRef]

M. B. Klein and G. C. Valley , Beam coupling in BaTiO 3 at 442 nm , J. Appl. Phys. JAPIAU 57 , 4901 ( 1985
[CrossRef]

S. Ducharme and J. Feinberg , Speed of the photorefractive effect in a BaTiO 3 single crystal , J. Appl. Phys. JAPIAU 56 , 839 ( 1984
[CrossRef]

N. V. Kukhtarev , V. M. Markov , S. G. Odulov , M. S. Soskin , and V. L. Vinetskii , Holographic storage in electrooptic crystals. 1. Steady-state , Ferroelectrics FEROA8 22 , 949 ( 1979
[CrossRef]

F. P. Strohkendl , Light induced dark decays of photorefractive gratings and their observation in Bi 12 SO 20 , J. Appl. Phys. JAPIAU 65 , 3773 ( 1989
[CrossRef]

P. Tayebati , The effect of shallow traps on the dark storage of photorefractive gratings in Bi 12 SO 20 , J. Appl. Phys. JAPIAU 70 , 4082 ( 1991
[CrossRef]

K. Buse , J. Frejlich , G. Kuper , and E. Kra tzig , Dark build-up of holograms in BaTiO 3 after recording , Appl. Phys. A APSFDB 57 , 437 ( 1993
[CrossRef]

R. C. Troth , R. Ramos-Garcia , and M. J. Damzen , Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO 3 crystal , Opt. Commun. OPCOB8 116 , 435 ( 1995
[CrossRef]

K. Buse and E. Kra tzig , Light-induced absorption in BaTiO 3 and KNbO 3 generated with high intensity laser pulses , Opt. Mater. OMATET 1 , 165 ( 1992
[CrossRef]

G. C. Valley and M. B. Klein , Optimal properties of photorefractive materials for optical data processing , Opt. Eng. OPEGAR 22 , 704 ( 1983
[CrossRef]

S. H. Wemple , M. Didomenico , and I. Camlibel , Dielectric and optical properties of melt-grown BaTiO 3 , J. Phys. Chem. Solids JPCSAW 29 , 1797 ( 1968
[CrossRef]

S. Ducharme , J. Feinberg , and R. R. Neurgaonkar , Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate , IEEE J. Quantum Electron. IEJQA7 QE-23 , 2116 ( 1987
[CrossRef]

I. Camlibel , M. Didomenico , and S. H. Wemple , Dielectric properties of single-domain melt-grown BaTiO 3 , J. Phys. Chem. Solids JPCSAW 31 , 1417 ( 1970
[CrossRef]

R. A. Motes and J. J. Kim , Intensity-dependent absorption coefficient in photorefractive BaTiO 3 crystals , J. Opt. Soc. Am. B JOBPDE 4 , 1379 ( 1987
[CrossRef]

G. A. Brost , R. A. Motes , and J. R. Rotge , Intensity-dependent absorption and photorefractive effect in barium titanate , J. Opt. Soc. Am. B JOBPDE 5 , 1879 ( 1988
[CrossRef]

A. L. Smirl , K. Bohnert , G. C. Valey , R. A. Mullen , and T. F. Boggess , Formation, decay, and erasure of photorefractive gratings written in barium titanate by picosecond pulses , J. Opt. Soc. Am. B JOBPDE 6 , 606 ( 1989
[CrossRef]

P. Tayebati and D. Mahgerefteh , Theory of the photorefractive effect for Bi 12 SiO 20 and BaTiO 3 with shallow traps , J. Opt. Soc. Am. B JOBPDE 8 , 1053 ( 1991
[CrossRef]

P. Tayebati , Effect of shallow traps on electron hole com-petition in semi-insulating photorefractive materials , J. Opt. Soc. Am. B JOBPDE 8 , 1053 ( 1991
[CrossRef]

R. Cudney , R. M. Pierce , G. D. Bacher , and J. Feinberg , Absorption gratings in photorefractive crystals with multiple levels , J. Opt. Soc. Am. B JOBPDE 8 , 1326 ( 1991
[CrossRef]

M. J. Damzen and N. Barry , Intensity-dependent hole electron competition and photorefractive saturation in BaTiO 3 when using intense laser pulses , J. Opt. Soc. Am. B JOBPDE 10 , 600 ( 1993
[CrossRef]

K. Buse , Thermal gratings and pyroelectrically produced charge distributions in BaTiO 3 and KNbO 3 , J. Opt. Soc. Am. B JOBPDE 10 , 1266 ( 1993
[CrossRef]

N. Barry , L. Duffault , R. Troth , R. Ramos-Garcia , and M. J. Damzen , Comparison between continuous-wave and pulsed photorefraction in BaTiO 3 , J. Opt. Soc. Am. B JOBPDE 11 , 1758 ( 1994
[CrossRef]

R. A. Motes and J. J. Kim , Beam coupling in photorefractive BaTiO 3 crystals , Opt. Lett. OPLEDP 12 , 199 ( 1987
[CrossRef] [PubMed]

G. A. Brost and R. A. Motes , Origin of the sublinear photorefractive response time in BaTiO 3 , Opt. Lett. OPLEDP 15 , 1194 ( 1990
[CrossRef] [PubMed]

A. Motes , G. A. Brost , J. R. Rotge , and J. J. Kim , Temporal behavior of the intensity-dependent absorption in photorefractive BaTiO 3 , Opt. Lett. OPLEDP 13 , 509 ( 1988
[CrossRef] [PubMed]

F. Jariego and F. Agullo -Lo pez , Holographic writing and erasure in unipolar photorefractive materials with multiple active centers: theoretical analysis , Appl. Opt. APOPAI 30 , 4615 ( 1991
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for (a) induced absorption and (b) grating recording by short-pulsed illumination. When the pump–writing beams are switched off the dark evolution is studied. PMT, photomultiplier tube; BS’s, beam splitters.

Fig. 2
Fig. 2

Typical dark decay of the induced absorption at I=13 MW/cm2. The dashed curve is a theory fit as described in text. Two time constants (τ1=40 ms and τ22 s) are clearly observed.

Fig. 3
Fig. 3

Typical dark buildup of photorefractive gratings written with a pair of short pulses of 15 ns and writing intensity I0=5 MW/cm2. Inset, grating buildup during the first 500 ms.

Fig. 4
Fig. 4

Dark buildup of the space-charge field for several intensities. Inset, damped oscillation.

Fig. 5
Fig. 5

Energy-diagram model with two hole shallow traps and electron–hole competition. p and n are the hole and the electron number densities in the valence and the conduction bands, respectively.

Fig. 6
Fig. 6

Dark buildup of the space-charge field after grating writing with a one-shallow-trap model with a large number of retrappings.

Fig. 7
Fig. 7

Dark buildup of the space-charge field with single-pulse recording and two hole shallow traps.

Tables (2)

Tables Icon

Table 1 Crystal Parameters Used in the Numerical Simulations

Tables Icon

Table 2 Parameters for Shallow Traps

Equations (63)

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nt-1e je=(seI+βe)N-γenN+,
pt+1ejh=(shI+βh)N+-γhpN+(sfI+βf)Nf+-γfpNf+(ssI+βs)Ns+-γspNs,
je=eμenE+kBTμen+κeseNI,
jh=eμhpE-kBTμhp+κhshN+I,
t (n-p-N+-Nf+-Ns+)
=1e (jh+je),
E=-eε0εr (n+NA-p-N+-Nf+-Ns+),
Nf+t=-(sfI+βf)Nf+γfpNf,
Ns+t=-(ssI+βs)Ns++γspNs,
N+N+=ND,
Nf+Nf+=NTf,
Ns+Ns+=NTs.
I=I0(1+m cos kgz),
q(t)=q0(t)+q1(t)exp(ikgz),
Nf0+t=-β*Nf0+,
β*(t)=βf1+NR(t),
NR(t)=γs[NTf-Nf0+(t)]γh[ND-NA+Nf0+(t)].
α(I0)hcλ (shNA+sfNf0++ssNs0+),
sfNf0+2.4×1017 cm-1 J-1,
ssNs0+1.9×1017 cm-1 J-1.
n0p0=(seI0+βe)(shI0+βh)γeγhψ2;
n0=ψ2/p0,
N0+=NA+n0-p0-N0f+-N0s+,
N0=ND-NA-n0+p0+N0f++N0s+.
a5p05+a4p04+a3p03+a2p02+a1p0+a0=0,
a5=γhγfγs,
a4=γhγfγs(ND-NA+NTf+NTs)+γfγs(shI0+βh)+γhγs(sfI0+βf)+γhγf(ssI0+βs),
a3=-γhγfγsψ2+γhγs[(sfI0+βf)(ND-NA)+(sfI0+βf)NTs]+γhγf[(ssI0+βs)(ND-NA)+(ssI0+βs)NTf]+γfγs[-(shI0+βh)NA+(shI0+βh)NTf+(shI0+βh)NTs]+γh(sfI0+βf)(ssI0+βs)+γf(shI0+βh)×(ssI0+βs)+γs(shI0+βh)(sfI0+βf),
a2=(shI0+βh)(sfI0+βf)(ssI0+βs)-γhγf(ssI0+βs)ψ2-γhγs(sfI0+βf)ψ2-γfγs(shI0+βh)ψ2+γh(ND-NA)(sfI0+βf)(ssI0+βs)-γsNA(shI0+βh)(ssI0+βs)-γsNA(shI0+βh)×(sfI0+βf)+γfNTf(shI0+βh)×(ssI0+βs)+γsNTs(shI0+βh)(sfI0+βf),
a1=-NA(shI0+βh)(sfI0+βf)(ssI0+βs)-γh(sfI0+βf)(ssI0+βs)ψ2-γf(shI0+βh)×(ssI0+βs)ψ2-γs(shI0+βh)(sfI0+βf)ψ2,
a0=-(shI0+βh)(sfI0+βf)(ssI0+βs)ψ2.
Ax=y,
x=n1p1N1+Nf1+Ns1+,
y=semI0(ND-NA-n0+p0+Nf0++Ns0+)shmI0(NA+n0-p0-Nf0+-Ns0+)0sfmI0Nf0+ssmI0Ns0+.
A11=ΓDe+ΓRe+ΓDie-γe(Nf0++Ns0+)-ΓDih-ΓDie-ΓDih-ΓDe00,
A12=-ΓDieΓDh+ΓRh+ΓDih+γh(Nf0++Ns0+)ΓDie+ΓDih+ΓDh-γf(NTf-Nf0+)-γs(NTs-Ns0+),
A13=ΓIe-ΓDie-ΓIh+ΓDihΓDie+ΓDih00,A14=-ΓDieΓDihΓDie+ΓDihΓIf0,
A15=-ΓDieΓDihΓDie+ΓDih0ΓIs,
ΓDie=eμen0/(εrε0)(dielectricrelaxationrate),
ΓIe=seI0+βe+γen0(sumofproductionand
ionrecombinationrates),
ΓRe=γe(NA+n0-p0)(electronrecombinationrate),
ΓDe=kg2kBTμe/e(diffusionrate).
ΓDih=eμhn0/(εrε0),
ΓIh=shI0+βh+γhp0,
ΓRh=γh(ND-NA-n0+p0),
ΓDh=kg2kBTμh/e,
ΓIf=sfI0+βf+γfp0,
ΓIs=ssI0+βs+γsp0.
E1=-ekεrε0 (n1-p1-N1+-Nf1+-Ns1+).
I0(t)=I0 exp[-2(t/τp)2],
I0(t)=n=0npI0 exp[-2(t/τp)2]δ(t-n/f )
dn0dt=[seI0(t)+βe]N0-γen0N0+,
dp0dt=[shI0(t)+βh]N0+-γhp0N0+[sfI0(t)+βf]Nf0+-γfp0(NTf-Nf0+)+[ssI0(t)+βs]Ns0+-γsp0(NTs-Ns0+),
dNf0+dt=-[sfI0(t)+βf]Nf0++γfp0(NTf-Nf0+),
dNs0+dt=-[ssI0(t)+βs]Ns0++γsp0(NTs-Ns0+),
N0+=NA+n0-p0-Nf0+-Ns0+,
N0=ND-NA-n0+p0+Nf0++Ns0+.
dn1dt=-[ΓDe+ΓRe+ΓDie-γe(Nf0++Ns0+)]n1+(ΓDie)p1+(ΓDie-ΓIe)N1++(ΓDie)Nf1++(ΓDie)Ns1++mI0seN0,
dp1dt=(ΓDih)n1-[ΓDh+ΓRh+ΓDih+γh(Nf0++Ns0+)+γfNTf+γsNTs]p1+(ΓIh-ΓDih)N1++(ΓIs-ΓDih)Nf1++(ΓIp-ΓDih)Ns1++mI0(shN0++ssNf0++ssNs0+),
dN1+dt=-[ΓRe-γe(Nf0++Ns0+)]n1-[ΓRh-γh(Nf0++Ns0+)]p1-(ΓIe+ΓIh)N1++mI0(seN0-shN0+),
dNf1+dt=[γf(NTf-Nf0+)]p1-(ΓIf)Nf1+-mI0sfNf0+,
dNs1+dt=[γs(NTs-Ns0+)]p1-(ΓIs)Ns1+-mI0ssNs0+

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