Abstract

To optimize the diffraction efficiency of Bi12SiO2 we studied the influence on that efficiency of three physical parameters (thickness of the sample, applied dc field, and light modulation depth m). We calculated the diffraction efficiency by using the refractive-index variation along the thickness of the sample and numerically solving the beam-coupling equations (for recording and reading). We found that for given values of m and the applied field there is an optimum thickness for which the diffraction efficiency is maximum. Diffraction efficiencies of 95% were obtained for high values of the light-modulation depth (m=1) and strong electric fields (20 kV/cm).

© 2000 Optical Society of America

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References

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  1. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  2. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).
  3. J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
    [CrossRef]
  4. M. Peltier and F. Micheron, “Volume hologram recording and charge transfer process in BSO and BGO,” J. Appl. Phys. 48, 3683–3690 (1977).
    [CrossRef]
  5. J. P. Huignard and J. P. Herriau, “Real time double exposure interferometry with BSO crystals in transverse electrooptic configuration,” Appl. Opt. 16, 1807–1809 (1977).
    [CrossRef] [PubMed]
  6. P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
    [CrossRef]
  7. S. Mallick, D. Rouède, and A. Apostolidis, “Efficiency and polarization characteristics of photorefractive diffraction in a BSO crystal,” J. Opt. Soc. Am. B 4, 1247–1259 (1987).
    [CrossRef]
  8. P. Günter and J. P. Huignard, eds., Photorefractive Materials and Their Applications II (Springer-Verlag, Berlin, 1989).
  9. L. B. Au and L. Solymar, “Space-charge field in photorefractive materials at large modulation,” Opt. Lett. 13, 660–667 (1988).
    [CrossRef] [PubMed]
  10. S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–41 (1994).
    [CrossRef]
  11. K. Nakagawa, K. Arita, K. Kitamura, and T. Minemoto, “Comparison of photorefractive response in BSO crystals with different absorption,” presented at the 1997 Topical Meeting on Photorefractive Materials, Effects and Devices, June 11–13, 1997, Chiba, Japan.
  12. N. V. Kukhtarev, V. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  13. J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during phorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686–5690 (1995).
    [CrossRef]
  14. J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of strong modulation on beam coupling gain in photorefractive materials,” J. Opt. Soc. Am. B 15, 2092–2098 (1998).
    [CrossRef]
  15. F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994).
  16. I. Casar and L. F. Magaña, “Effects of absorption on beam coupling gain in photorefractive materials (BSO) under strong modulation with an external applied electric field,” Rev. Mex. Fis. 44, 319–322 (1998).
  17. I. Casar and L. F. Magaña, “Calculation of beam coupling gain and fringe bending in the photorefractive material bismuth silicon oxide under electric fields and strong modulations,” Phys. Rev. B 58, 9591–9594 (1998).
    [CrossRef]
  18. K. Nonaka, “Diffraction efficiency analysis in hologram gratings recorded by counterpropagating-type geometry,” J. Appl. Phys. 78, 4345–4352 (1995).
    [CrossRef]
  19. E. Ochoa, F. Vachss, and L. Hesselink, “Higher-order analysis of the photorefractive effect for large modulation depths,” J. Opt. Soc. Am. A 3, 181–187 (1986).
    [CrossRef]

1998 (3)

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of strong modulation on beam coupling gain in photorefractive materials,” J. Opt. Soc. Am. B 15, 2092–2098 (1998).
[CrossRef]

I. Casar and L. F. Magaña, “Effects of absorption on beam coupling gain in photorefractive materials (BSO) under strong modulation with an external applied electric field,” Rev. Mex. Fis. 44, 319–322 (1998).

I. Casar and L. F. Magaña, “Calculation of beam coupling gain and fringe bending in the photorefractive material bismuth silicon oxide under electric fields and strong modulations,” Phys. Rev. B 58, 9591–9594 (1998).
[CrossRef]

1995 (2)

K. Nonaka, “Diffraction efficiency analysis in hologram gratings recorded by counterpropagating-type geometry,” J. Appl. Phys. 78, 4345–4352 (1995).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during phorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686–5690 (1995).
[CrossRef]

1994 (1)

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–41 (1994).
[CrossRef]

1988 (1)

1987 (2)

P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
[CrossRef]

S. Mallick, D. Rouède, and A. Apostolidis, “Efficiency and polarization characteristics of photorefractive diffraction in a BSO crystal,” J. Opt. Soc. Am. B 4, 1247–1259 (1987).
[CrossRef]

1986 (1)

1984 (1)

J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
[CrossRef]

1979 (1)

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

1977 (2)

M. Peltier and F. Micheron, “Volume hologram recording and charge transfer process in BSO and BGO,” J. Appl. Phys. 48, 3683–3690 (1977).
[CrossRef]

J. P. Huignard and J. P. Herriau, “Real time double exposure interferometry with BSO crystals in transverse electrooptic configuration,” Appl. Opt. 16, 1807–1809 (1977).
[CrossRef] [PubMed]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Agulló-López, F.

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of strong modulation on beam coupling gain in photorefractive materials,” J. Opt. Soc. Am. B 15, 2092–2098 (1998).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during phorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686–5690 (1995).
[CrossRef]

Apostolidis, A.

Au, L. B.

Bassat, J. M.

P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
[CrossRef]

Carrascosa, M.

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of strong modulation on beam coupling gain in photorefractive materials,” J. Opt. Soc. Am. B 15, 2092–2098 (1998).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during phorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686–5690 (1995).
[CrossRef]

Casar, I.

I. Casar and L. F. Magaña, “Effects of absorption on beam coupling gain in photorefractive materials (BSO) under strong modulation with an external applied electric field,” Rev. Mex. Fis. 44, 319–322 (1998).

I. Casar and L. F. Magaña, “Calculation of beam coupling gain and fringe bending in the photorefractive material bismuth silicon oxide under electric fields and strong modulations,” Phys. Rev. B 58, 9591–9594 (1998).
[CrossRef]

Heaton, J. M.

J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
[CrossRef]

Herriau, J. P.

Herriau, P.

P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
[CrossRef]

Hesselink, L.

Huignard, J. P.

P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
[CrossRef]

J. P. Huignard and J. P. Herriau, “Real time double exposure interferometry with BSO crystals in transverse electrooptic configuration,” Appl. Opt. 16, 1807–1809 (1977).
[CrossRef] [PubMed]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kukhtarev, N. V.

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

Launey, J. C.

P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
[CrossRef]

Magaña, L. F.

I. Casar and L. F. Magaña, “Effects of absorption on beam coupling gain in photorefractive materials (BSO) under strong modulation with an external applied electric field,” Rev. Mex. Fis. 44, 319–322 (1998).

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of strong modulation on beam coupling gain in photorefractive materials,” J. Opt. Soc. Am. B 15, 2092–2098 (1998).
[CrossRef]

I. Casar and L. F. Magaña, “Calculation of beam coupling gain and fringe bending in the photorefractive material bismuth silicon oxide under electric fields and strong modulations,” Phys. Rev. B 58, 9591–9594 (1998).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during phorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686–5690 (1995).
[CrossRef]

Mallick, S.

Markov, V.

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

Micheron, F.

M. Peltier and F. Micheron, “Volume hologram recording and charge transfer process in BSO and BGO,” J. Appl. Phys. 48, 3683–3690 (1977).
[CrossRef]

Mill, P. A.

J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
[CrossRef]

Murillo, J. G.

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of strong modulation on beam coupling gain in photorefractive materials,” J. Opt. Soc. Am. B 15, 2092–2098 (1998).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during phorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686–5690 (1995).
[CrossRef]

Nonaka, K.

K. Nonaka, “Diffraction efficiency analysis in hologram gratings recorded by counterpropagating-type geometry,” J. Appl. Phys. 78, 4345–4352 (1995).
[CrossRef]

Ochoa, E.

Odulov, S. G.

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

Paige, E. G.

J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
[CrossRef]

Peltier, M.

M. Peltier and F. Micheron, “Volume hologram recording and charge transfer process in BSO and BGO,” J. Appl. Phys. 48, 3683–3690 (1977).
[CrossRef]

Rojas, D.

P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
[CrossRef]

Rouède, D.

Solymar, L.

L. B. Au and L. Solymar, “Space-charge field in photorefractive materials at large modulation,” Opt. Lett. 13, 660–667 (1988).
[CrossRef] [PubMed]

J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
[CrossRef]

Soskin, M. S.

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

Stepanov, S. I.

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–41 (1994).
[CrossRef]

Vachss, F.

Vinetskii, V. L.

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

Wilson, T.

J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Ferroelectrics (2)

P. Herriau, D. Rojas, J. P. Huignard, J. M. Bassat, and J. C. Launey, “Highly efficient diffraction in photorefractive BSO–BGO crystals at large applied fields,” Ferroelectrics 75, 271–279 (1987).
[CrossRef]

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

J. Appl. Phys. (3)

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during phorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686–5690 (1995).
[CrossRef]

M. Peltier and F. Micheron, “Volume hologram recording and charge transfer process in BSO and BGO,” J. Appl. Phys. 48, 3683–3690 (1977).
[CrossRef]

K. Nonaka, “Diffraction efficiency analysis in hologram gratings recorded by counterpropagating-type geometry,” J. Appl. Phys. 78, 4345–4352 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Opt. Acta (1)

J. M. Heaton, P. A. Mill, E. G. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–891 (1984).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

I. Casar and L. F. Magaña, “Calculation of beam coupling gain and fringe bending in the photorefractive material bismuth silicon oxide under electric fields and strong modulations,” Phys. Rev. B 58, 9591–9594 (1998).
[CrossRef]

Rep. Prog. Phys. (1)

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–41 (1994).
[CrossRef]

Rev. Mex. Fis. (1)

I. Casar and L. F. Magaña, “Effects of absorption on beam coupling gain in photorefractive materials (BSO) under strong modulation with an external applied electric field,” Rev. Mex. Fis. 44, 319–322 (1998).

Other (4)

K. Nakagawa, K. Arita, K. Kitamura, and T. Minemoto, “Comparison of photorefractive response in BSO crystals with different absorption,” presented at the 1997 Topical Meeting on Photorefractive Materials, Effects and Devices, June 11–13, 1997, Chiba, Japan.

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994).

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).

P. Günter and J. P. Huignard, eds., Photorefractive Materials and Their Applications II (Springer-Verlag, Berlin, 1989).

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Figures (8)

Fig. 1
Fig. 1

Diagram of the experimental configuration for (a) recording and (b) reading.

Fig. 2
Fig. 2

Beam-coupling evolution with z of the intensities of the incident and diffracted beams for an applied field of 5 kV/cm and light modulation m=0.9. Dashed curves, no absorption; continuous curves, results for an absorption coefficient of 1.5 cm-1.

Fig. 3
Fig. 3

Coupling parameter as a function of z for 10 kV/cm. Continuous curves, no absorption for several values of light-modulation depth; dashed curves, an absorption coefficient of 1.5 cm-1.

Fig. 4
Fig. 4

Refractive index as a function of z for 10 and 5 kV/cm. Dashed curves, no absorption; continuous curves, an absorption coefficient of 1.5 cm-1.

Fig. 5
Fig. 5

Variation of diffraction efficiency with z for a very small value of m with an absorption coefficient of 1.5 cm-1 and for an applied field of 10 kV/cm. Dashed curve, result for the linear approach; continuous curve, the result of our numerical approach.

Fig. 6
Fig. 6

Variation of diffraction efficiency with z for an absorption coefficient of 1.5 cm-1 and several values of light modulation. (A, m=1; B, m=0.9; C, m=0.6; D, m=0.3). Dashed curves, the linear approach; continuous curves, the numerical calculation. The applied dc field is 10 kV/cm.

Fig. 7
Fig. 7

Variation of diffraction efficiency with z for a light modulation of m=0.9, an absorption coefficient of 1.5 cm-1, and various values of the applied dc field.

Fig. 8
Fig. 8

Variation of diffraction efficiency for different applied fields. Continuous curve, maximum attainable diffraction efficiency; dashed curve, diffraction efficiency obtained at a fixed thickness of 10 mm.

Tables (1)

Tables Icon

Table 1 Values of the Physical Parameters for BSO Used in the Numerical Solution of the Material Rate Equations

Equations (11)

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

m(z)=2[I1(z)I2(z)]1/2I0.
Δn(x, z)=½n03rE1[x,m(z)]=½n03rE1(x, z),
dAidz+iκAd+αAi=0,
dAddz+iκAi+αAd=0,
Ii=|Ai·Ai*|,Id=|Ad·Ad*|,κ=πΔnλ cos θ,
Ii(z)=Ii(0)exp(-αz)cos2(κz),
Id(z)=I,(0)exp(-αz)sin2(κz).
η=Id(z)Ii(0),
η=exp(-αz)sin2 κz,
Id(z)=exp(-az)Id(z0)*[cos2 κ(z-z0)-sin2 κ(z-z0)]+I0 sin2 κ(z-z0)+sin κ(z-z0)* cos κ(z-z0)*Id(z0)z+αIi(z0).
I(z)=Ii(z)+Id(z)=exp(-az)[I0(0)].

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