Abstract

Detailed analysis of the relationship between the experimental geometry and the holographic contrast in photorefractive polymers is important for applications, such as angle multiplexing in holographic data storage. In this paper the field dependent photogeneration efficiency is introduced into the complete reorientational model to provide a full account of the electric field and geometrical dependence of the index contrast. The interaction of a local grating and the photorefractive grating is also considered. A simplification for acute angles between writing beams is described. Experimental verification by use of four-wave mixing and transmission ellipsometry reveals an excellent agreement between theory and measurement.

© 2002 Optical Society of America

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References

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  1. K. Meerholz, B. L. Volodin, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
    [CrossRef]
  2. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  3. G. J. Steckman, R. Bittner, K. Meerholz, D. Psaltis, “Holographic multiplexing in photorefractive polymers,” Opt. Commun. 185, 13–17 (2000).
    [CrossRef]
  4. K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
    [CrossRef]
  5. W. E. Moerner, S. M. Silence, F. Hache, G. C. Bjorklund, “Orientationally enhanced photorefractive effect in polymers,” J. Opt. Soc. Am. B 11, 320–330 (1994).
    [CrossRef]
  6. N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  7. N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
    [CrossRef]
  8. K. Khand, D. J. Binks, D. P. West, “Effect of field-dependent photogeneration on holographic contrast in photorefractive polymers,” J. Appl. Phys. 89, 2516–2519 (2001).
    [CrossRef]
  9. L. Onsager, “Deviation from Ohm’s law in weak electrolytes,” J. Chem. Phys. 2, 599–615 (1934).
    [CrossRef]
  10. T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
    [CrossRef]
  11. C. L. Braun, “Electric field assisted dissociation of charge transfer states as a mechanism of photocarrier production,” J. Chem. Phys. 80, 4162–4161 (1984).
    [CrossRef]
  12. M. R. Spiegel, Mathematical Handbook of Formulas and Tables (McGraw-Hill, New York, 1968) p. 143.
  13. M. A. Smith, “Grating interactions in photorefractive polymers,” Ph.D. dissertation (Reading University, Reading, United Kingdom, 1999).
  14. J. D. Shakos, M. D. Rahn, D. P. West, K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
    [CrossRef]

2001 (1)

K. Khand, D. J. Binks, D. P. West, “Effect of field-dependent photogeneration on holographic contrast in photorefractive polymers,” J. Appl. Phys. 89, 2516–2519 (2001).
[CrossRef]

2000 (3)

T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
[CrossRef]

G. J. Steckman, R. Bittner, K. Meerholz, D. Psaltis, “Holographic multiplexing in photorefractive polymers,” Opt. Commun. 185, 13–17 (2000).
[CrossRef]

J. D. Shakos, M. D. Rahn, D. P. West, K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

1998 (1)

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

1994 (2)

W. E. Moerner, S. M. Silence, F. Hache, G. C. Bjorklund, “Orientationally enhanced photorefractive effect in polymers,” J. Opt. Soc. Am. B 11, 320–330 (1994).
[CrossRef]

K. Meerholz, B. L. Volodin, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

1984 (1)

C. L. Braun, “Electric field assisted dissociation of charge transfer states as a mechanism of photocarrier production,” J. Chem. Phys. 80, 4162–4161 (1984).
[CrossRef]

1979 (2)

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

1934 (1)

L. Onsager, “Deviation from Ohm’s law in weak electrolytes,” J. Chem. Phys. 2, 599–615 (1934).
[CrossRef]

Binks, D. J.

K. Khand, D. J. Binks, D. P. West, “Effect of field-dependent photogeneration on holographic contrast in photorefractive polymers,” J. Appl. Phys. 89, 2516–2519 (2001).
[CrossRef]

Bittner, R.

T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
[CrossRef]

G. J. Steckman, R. Bittner, K. Meerholz, D. Psaltis, “Holographic multiplexing in photorefractive polymers,” Opt. Commun. 185, 13–17 (2000).
[CrossRef]

Bjorklund, G. C.

Braun, C. L.

C. L. Braun, “Electric field assisted dissociation of charge transfer states as a mechanism of photocarrier production,” J. Chem. Phys. 80, 4162–4161 (1984).
[CrossRef]

Cimrova, V.

T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
[CrossRef]

Daubler, T. K.

T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
[CrossRef]

Hache, F.

Khand, K.

K. Khand, D. J. Binks, D. P. West, “Effect of field-dependent photogeneration on holographic contrast in photorefractive polymers,” J. Appl. Phys. 89, 2516–2519 (2001).
[CrossRef]

J. D. Shakos, M. D. Rahn, D. P. West, K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

King, T. A.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Kukhatarev, N. V.

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Markov, V. B.

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Meerholz, K.

G. J. Steckman, R. Bittner, K. Meerholz, D. Psaltis, “Holographic multiplexing in photorefractive polymers,” Opt. Commun. 185, 13–17 (2000).
[CrossRef]

T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
[CrossRef]

K. Meerholz, B. L. Volodin, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Moerner, W. E.

Neher, D.

T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
[CrossRef]

Onsager, L.

L. Onsager, “Deviation from Ohm’s law in weak electrolytes,” J. Chem. Phys. 2, 599–615 (1934).
[CrossRef]

Psaltis, D.

G. J. Steckman, R. Bittner, K. Meerholz, D. Psaltis, “Holographic multiplexing in photorefractive polymers,” Opt. Commun. 185, 13–17 (2000).
[CrossRef]

Rahn, M. D.

J. D. Shakos, M. D. Rahn, D. P. West, K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Shakos, J. D.

J. D. Shakos, M. D. Rahn, D. P. West, K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Silence, S. M.

Smith, M. A.

M. A. Smith, “Grating interactions in photorefractive polymers,” Ph.D. dissertation (Reading University, Reading, United Kingdom, 1999).

Soskin, M.

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Spiegel, M. R.

M. R. Spiegel, Mathematical Handbook of Formulas and Tables (McGraw-Hill, New York, 1968) p. 143.

Steckman, G. J.

G. J. Steckman, R. Bittner, K. Meerholz, D. Psaltis, “Holographic multiplexing in photorefractive polymers,” Opt. Commun. 185, 13–17 (2000).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Volodin, B. L.

K. Meerholz, B. L. Volodin, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Wade, F. A.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

West, D. P.

K. Khand, D. J. Binks, D. P. West, “Effect of field-dependent photogeneration on holographic contrast in photorefractive polymers,” J. Appl. Phys. 89, 2516–2519 (2001).
[CrossRef]

J. D. Shakos, M. D. Rahn, D. P. West, K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

West, K. S.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Ferroelectrics (2)

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhatarev, V. B. Markov, M. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling-light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

J. Appl. Phys. (2)

K. Khand, D. J. Binks, D. P. West, “Effect of field-dependent photogeneration on holographic contrast in photorefractive polymers,” J. Appl. Phys. 89, 2516–2519 (2001).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

J. Chem. Phys. (2)

L. Onsager, “Deviation from Ohm’s law in weak electrolytes,” J. Chem. Phys. 2, 599–615 (1934).
[CrossRef]

C. L. Braun, “Electric field assisted dissociation of charge transfer states as a mechanism of photocarrier production,” J. Chem. Phys. 80, 4162–4161 (1984).
[CrossRef]

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

Nature (1)

K. Meerholz, B. L. Volodin, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Opt. Commun. (1)

G. J. Steckman, R. Bittner, K. Meerholz, D. Psaltis, “Holographic multiplexing in photorefractive polymers,” Opt. Commun. 185, 13–17 (2000).
[CrossRef]

Phys. Rev. B (1)

T. K. Daubler, R. Bittner, K. Meerholz, V. Cimrova, D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B 61, 13515–13527 (2000).
[CrossRef]

Other (3)

R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

M. R. Spiegel, Mathematical Handbook of Formulas and Tables (McGraw-Hill, New York, 1968) p. 143.

M. A. Smith, “Grating interactions in photorefractive polymers,” Ph.D. dissertation (Reading University, Reading, United Kingdom, 1999).

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Figures (5)

Fig. 1
Fig. 1

Illustration of the experimental geometry, showing the electric fields present in the material and their relative angles. The dashed lines depict the grating maxima. Vector addition of the space-charge field, E sc, and the applied field, E 0, gives the resultant, E res. The interaction between the probe field, E in, and scattered field, E out is brought about by the effect of the resultant field on the refractive index profile of the medium.

Fig. 2
Fig. 2

Plot of p against the square of the poling field at room temperature, for varying ratios of the relaxation rate, k f , to the zero-field dissociation rate, k d (0), by use of Eqs. (2)–(5). The upper line corresponds to negligible photogeneration efficiency, which occurs when k f k d (0). The remaining lines correspond to increasing photogeneration efficiency with ratios of k f /k d (0) = 5, 10, and 20, respectively.

Fig. 3
Fig. 3

Plot of the full and simplified versions of the geometrical factor, where the simplified version is the lower line in each case for varying angles between the applied and space-charge fields. The ratio of electro-optic coefficients used is A/(C - A) = -0.296. The dashed lines correspond to an external scatter angle of 40°, and the solid lines to 10°. In the 10° case, use of the simplified geometrical version introduces only a small error.

Fig. 4
Fig. 4

Linear fits of the holographic contrast against the products of the space-charge and applied fields after 190 s writing time. The three geometries had 40° external scatter angles, and angles between the bisector of the writing beams and the sample normal of 20°, 35°, and 50°. The space-charge field, E sc is calculated from Eq. (1), and the field E 0 applied over a range 0 to 5 kV. The gradient is the product of the geometrical factor k, calculated from Eq. (13), and the material parameter S. The zero field contrast is approximately constant for varying angles and is assumed to be the size of the local grating throughout.

Fig. 5
Fig. 5

Linear fit of the birefringence from transmission ellipsometry against the square of the poling field E 0, after 190 s rise time. The gradient is half the coefficient S and therefore allows verification of the analysis of index contrast.

Equations (21)

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pE=dΦdEE0Φ.
Esc= E0 cos θ1+p cos2 θ,
Φ=kdEkdE+kf= 11+kf/kdE.
kdE=2kd0I12b2b,
b=e3E8πεε0k2T2,
p=1-Φ2bI18bI28b.
I1xI2xexpx2πx1/2.
Δn= 12nEout*·Δχ·Ein,
Δχ=A000A000CEres2.
Δnp-pol= 12nC cosα-βcos2θ-β-α+A sinα-βsin2θ-α-βEres2.
Δnp-pol= 12nC-AEres2 cos ΔβAC-A+cos2β-α-0.5 tan Δβ sin2β-α.
Eres2=E02+Esc2 cos2Kz+ψ+2E0·Esc cosKz+ψ,
Δn1K|p-pol= 12nC-A2E0Esck,
k=cos Δβ A cos θC-A +cosθ-βcos β+0.5 tan Δβ sin2β-θ.
ΔnPR=SEscE0k,
S=C-An.
k=cos Δβ A cos θC-A+cosθ-βcos β.
AC-A-0.296.
Δn=ΔnPR2+Δn02+2ΔnPRΔn0 cosπ-ψ1/2.
ψ=tan-1-E0Eq1+p cos2 θ,
Δn=SEscE0k+Δn0,

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