Abstract

The photorefractive effect is theoretically studied at the interface between a thin photoconducting layer and an oxidic electro-optic crystal. A grating charge distribution in the photoconducting layer creates an electric field that penetrates the electro-optic crystal, giving a refractive-index modulation near the interface. The photorefractive gratings of different crystal geometries are discussed.

© 1998 Optical Society of America

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References

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  1. J. S. Schildkraut and D. J. Williams, “Homogeneous and multilayer photorefractive-polymer systems,” in Proceedings of the Third Conference on Non-linear Optics, Part 2, R. A. Fisher and J. F. Reintjes, eds., Proc. SPIE 1626, 2 (1992).
    [CrossRef]
  2. J. E. Viallet, G. Picoli, and P. Gravey, in “New concept of multilayer photorefractive device,” Proceedings of the Symposium on Photoinduced Space Charge Effects in Semiconductors, D. D. Nolte, N. M. H. Naegel, and K. W. Goosen, eds. (Materials Research Society, Pittsburgh, Pa., 1992), Vol. 261, p. 191.
  3. G. C. Valley and J. F. Lam, in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 75.
    [CrossRef]
  4. D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, and A. M. Glass, “Resonant photorefractive effect in semi-insulating multiple quantum wells,” J. Opt. Soc. Am. B 7, 2217 (1990).
    [CrossRef]
  5. R. A. Street, Hydrogenated Amorphous Silicon (Cambridge U. Press, Cambridge, 1990).
  6. J. Y. Chang, M. H. Garrett, P. Tayebati, H. P. Jenssen, and C. Warde, “Light-induced dark decay and sublinear intensity dependence of the response time in cobalt-doped barium titanate,” J. Opt. Soc. Am. B 12, 248 (1995).
    [CrossRef]
  7. M. Grenot, J. Pergale, J. Donjon, and G. Marie, “New electro-optic light valve device for image storage and processing,” Appl. Phys. Lett. 21, 83 (1972).
    [CrossRef]
  8. Landolt Börnstein, Ferroelectrics and Related Substances, New Series III/16a (Springer-Verlag, Berlin, 1981), p. 67.
  9. See P. Günter and J. P. Huignard, in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 24.
  10. N. Uchida, “Calculation of the efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am. 3, 63 (1973).
  11. Q. Wang, R. M. Brubaker, D. D. Nolte, and M. R. Melloch, “Photorefractive quantum wells: transverse Franz–Keldysh geometry” J. Opt. Soc. Am. B 9, 1626 (1992).
    [CrossRef]
  12. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 9, p. 356.
  13. M. Aguilar, M. Carascosa, F. Agullo-Lopez, and L. F. Magana, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840 (1995).
    [CrossRef]
  14. G. A. Brost, R. A. Motes, and J. R. Rotge, “Intensity dependent absorption and photorefractive effects in barium titanate.” J. Opt. Soc. Am. B 5, 1879 (1988).
    [CrossRef]

1995 (2)

J. Y. Chang, M. H. Garrett, P. Tayebati, H. P. Jenssen, and C. Warde, “Light-induced dark decay and sublinear intensity dependence of the response time in cobalt-doped barium titanate,” J. Opt. Soc. Am. B 12, 248 (1995).
[CrossRef]

M. Aguilar, M. Carascosa, F. Agullo-Lopez, and L. F. Magana, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840 (1995).
[CrossRef]

1992 (2)

Q. Wang, R. M. Brubaker, D. D. Nolte, and M. R. Melloch, “Photorefractive quantum wells: transverse Franz–Keldysh geometry” J. Opt. Soc. Am. B 9, 1626 (1992).
[CrossRef]

J. S. Schildkraut and D. J. Williams, “Homogeneous and multilayer photorefractive-polymer systems,” in Proceedings of the Third Conference on Non-linear Optics, Part 2, R. A. Fisher and J. F. Reintjes, eds., Proc. SPIE 1626, 2 (1992).
[CrossRef]

1990 (1)

1988 (1)

1973 (1)

N. Uchida, “Calculation of the efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am. 3, 63 (1973).

1972 (1)

M. Grenot, J. Pergale, J. Donjon, and G. Marie, “New electro-optic light valve device for image storage and processing,” Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Aguilar, M.

M. Aguilar, M. Carascosa, F. Agullo-Lopez, and L. F. Magana, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840 (1995).
[CrossRef]

Agullo-Lopez, F.

M. Aguilar, M. Carascosa, F. Agullo-Lopez, and L. F. Magana, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840 (1995).
[CrossRef]

Brost, G. A.

Brubaker, R. M.

Carascosa, M.

M. Aguilar, M. Carascosa, F. Agullo-Lopez, and L. F. Magana, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840 (1995).
[CrossRef]

Chang, J. Y.

Donjon, J.

M. Grenot, J. Pergale, J. Donjon, and G. Marie, “New electro-optic light valve device for image storage and processing,” Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Doran, G. E.

Garrett, M. H.

Glass, A. M.

Grenot, M.

M. Grenot, J. Pergale, J. Donjon, and G. Marie, “New electro-optic light valve device for image storage and processing,” Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Jenssen, H. P.

Knox, W. H.

Magana, L. F.

M. Aguilar, M. Carascosa, F. Agullo-Lopez, and L. F. Magana, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840 (1995).
[CrossRef]

Marie, G.

M. Grenot, J. Pergale, J. Donjon, and G. Marie, “New electro-optic light valve device for image storage and processing,” Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Melloch, M. R.

Motes, R. A.

Nolte, D. D.

Olson, D. H.

Pergale, J.

M. Grenot, J. Pergale, J. Donjon, and G. Marie, “New electro-optic light valve device for image storage and processing,” Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Rotge, J. R.

Schildkraut, J. S.

J. S. Schildkraut and D. J. Williams, “Homogeneous and multilayer photorefractive-polymer systems,” in Proceedings of the Third Conference on Non-linear Optics, Part 2, R. A. Fisher and J. F. Reintjes, eds., Proc. SPIE 1626, 2 (1992).
[CrossRef]

Tayebati, P.

Uchida, N.

N. Uchida, “Calculation of the efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am. 3, 63 (1973).

Wang, Q.

Warde, C.

Williams, D. J.

J. S. Schildkraut and D. J. Williams, “Homogeneous and multilayer photorefractive-polymer systems,” in Proceedings of the Third Conference on Non-linear Optics, Part 2, R. A. Fisher and J. F. Reintjes, eds., Proc. SPIE 1626, 2 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

M. Grenot, J. Pergale, J. Donjon, and G. Marie, “New electro-optic light valve device for image storage and processing,” Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

J. Appl. Phys. (1)

M. Aguilar, M. Carascosa, F. Agullo-Lopez, and L. F. Magana, “Holographic recording in photorefractive thin films: edge effects,” J. Appl. Phys. 78, 4840 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

N. Uchida, “Calculation of the efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am. 3, 63 (1973).

J. Opt. Soc. Am. B (4)

Proc. SPIE (1)

J. S. Schildkraut and D. J. Williams, “Homogeneous and multilayer photorefractive-polymer systems,” in Proceedings of the Third Conference on Non-linear Optics, Part 2, R. A. Fisher and J. F. Reintjes, eds., Proc. SPIE 1626, 2 (1992).
[CrossRef]

Other (6)

J. E. Viallet, G. Picoli, and P. Gravey, in “New concept of multilayer photorefractive device,” Proceedings of the Symposium on Photoinduced Space Charge Effects in Semiconductors, D. D. Nolte, N. M. H. Naegel, and K. W. Goosen, eds. (Materials Research Society, Pittsburgh, Pa., 1992), Vol. 261, p. 191.

G. C. Valley and J. F. Lam, in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 75.
[CrossRef]

R. A. Street, Hydrogenated Amorphous Silicon (Cambridge U. Press, Cambridge, 1990).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 9, p. 356.

Landolt Börnstein, Ferroelectrics and Related Substances, New Series III/16a (Springer-Verlag, Berlin, 1981), p. 67.

See P. Günter and J. P. Huignard, in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 24.

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Figures (4)

Fig. 1
Fig. 1

(a) Photorefractive interface structure, showing two coherent laser beams interfering to write a grating pattern in a photoconducting layer on the surface of an electro-optic crystal. (b) Schematic diagram of the electric-field lines produced by the photoexcited charge distribution in the photoconducting layer penetrating the electro-optic crystal.

Fig. 2
Fig. 2

Calculated maximum values of the x and z components of the electric field plotted on a logarithmic scale as a function of depth in an example structure. The material parameters are detailed in the text.

Fig. 3
Fig. 3

Calculated diffraction efficiency for a c-axis-oriented (solid curve) and a-axis-oriented (dashed curve) device as function of (a) the external reading angle and (b) the electro-optic layer thickness. The filled and open circles give the bulk Bragg diffraction efficiency in the c-axis and the a-axis orientations, respectively. Material parameters are given in the text.

Fig. 4
Fig. 4

Calculated diffraction efficiency for a c-axis-oriented (solid curve) and a-axis-oriented (dashed curve) device as function of (a) the grating spacing and (b) the photoconducting layer thickness. Material parameters are given in the text.

Equations (25)

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τdi=0σd+σph
Isat=σdhνμταe,
i,xx 2ϕi(x, z)x2+i,zz 2ϕi(x, z)z2=-ρi(x)0,
ϕi(x, z)=[Ai+Bi exp(αiz)+Ci exp(-αiz)]sin(Kx),
Ex(x, z)-ρ0K0 1(3,xx3,zz)1/2
×tanh(α2d)exp(-α3z)cos(Kx),
Ez(x, z)ρ0K0 13,zz tanh(α2d)exp(-α3z)sin(Kx).
Ex(x)=-ρbK0 13,xx cos(Kx),
1nx2+rxxxEx+rxxzEzx2+1ny2+ryyxEx+ryyzEzy2+1nz2+rzzxEx+rzzzEzz2
+2(rxyxEx+rxyzEz)xy+2(ryzxEx+ryzzEz)yz
+2(rzxxEx+rzxzEz)zx=1,
1no2+r13Ez(x2+y2)+1ne2+r33Ezz2
+2r51Exxz=1,
tan(2β)=2r51Ex1no2-1ne2
1ne2+r33Exx2+1no2+r13Ex(y2+z2)
+2r51Ezxz=1.
x2no2+y2ne2+z2no2+2r51(Exxy+Ezyz)=1.
1neff,p2=cos(θ)2nx2+sin(θ)2nz2.
1neff,s2=1ny2.
Δneff,p=-12 neff3[r13 cos2(θ)+r33 sin2(θ)]Ez(x, z)+neff3 sin(θ)cos(θ)r51Ex(x, z).
Δneff,s=-12 neff,s3r13Ez(x, z).
tan(2ζ)=2r51(Ex2+Ez2)1/2(1/no2)-(1/ne2).
ϕ=2πλ Δnds,
η1=r13 cos2(θ)+r33 sin2(θ)c2+2r51 sin(θ)cos(θ)(ac)1/22ξ,
ξ=4π2neff3λ2 cos2(θ)×1-2 cos[Kd3 tan(θ)]exp(-α3d3)+exp(-2α3d3)α32+K2 tan2(θ)×ρ0 tanh(α2d2)K02,

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