Abstract

The Coupled Wave Theory of Kogelnik has given a well-established basis for the comprehension of how light propagates inside a hologram. This theory gives an accurate approximation for the diffraction efficiency of volume phase holograms and volume absorption holograms as well. Mixed holograms (phase and absorption) have been also treated from the point of view of this theory. For instance, Guibelalde theoretically described the diffraction efficiency of out of phase mixed volume gratings. In this work we will show that when using fixation-free rehalogenating bleaches, out of phase mixed volume gratings can be recorded on the hologram at high exposures. This is due to the oxidation products of the developer and the bleaching agent. The effects described theoretically for out of phase mixed volume hologram gratings are experimentally observed.

© 2002 Optical Society of America

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References

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  1. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings, (Academic, London 1981).
  2. R. R. A. Syms, Practical Volume Holography, (Clarendon, Oxford 1990).
  3. H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Sys. Tech. J. 48, 2909-47 (1969).
  4. A. Beléndez, T. Beléndez, C. Neipp and I. Pascual, �??Determination of the refractive index and thickness of holographic silver halide materials by the use of polarized reflectances,�?? Appl. Opt. 41, 6802-08 (2002).
    [CrossRef] [PubMed]
  5. E. Guibelalde, �??Coupled wave analysis for out-of-phase mixed thick hologram gratings,�?? Opt. Quantum Electron. 16, 173-178 (1984).
    [CrossRef]
  6. N. J. Phillips, A. A. Ward, R. Cullen and D. Porter, �??Advances in holographic bleaches,�?? Phot. Sci. Eng. 24, 120-4 (1980).
  7. B. J. Chang and C. D. Leonard, �??Dichromated gelatin for the fabrication of holographic optical elements,�?? Appl. Opt. 18, 2407-17 (1979).
    [CrossRef] [PubMed]
  8. K. S. Pennington and J. S. Harper, �??Techniques for producing low-noise, improved efficiency holograms,�?? Appl. Opt. 9, 1643-50 (1970).
    [CrossRef] [PubMed]
  9. H. I. Bjelkhagen, Silver-Halide Recording Materials, (Springer, Berlin 1995).
  10. J. Crespo, A. Fimia and J. A. Quintana, �??Fixation-free methods in bleached reflection holography,�?? Appl. Opt. 25, 1642-5 (1986).
    [CrossRef] [PubMed]
  11. P. Hariharan and C. M. Chidley, �??Rehalogenating bleaches for photographic phase holograms: the influence of halide type and concentration on diffraction efficiency and scattering,�?? Appl. Opt. 26, 3895-8 (1987).
    [CrossRef] [PubMed]
  12. P. Hariharan, �??Rehalogenating bleaches for photographic phase holograms 3: Mechanism of material transfer,�?? Appl. Opt. 29, 2983-5 (1990).
    [CrossRef] [PubMed]
  13. C. Neipp, I. Pascual and A. Beléndez, �??Over modulation effects in fixation-free rehalogenating bleached holograms,�?? Appl. Opt. 40, 3402-3408 (2001).
    [CrossRef]
  14. C. Neipp, I. Pascual and A. Beléndez, �??Optimization of a fixation-free rehalogenating bleach for BB-640 holographic emulsion,�?? J. Mod. Opt. 47, 1671-1679 (2000).
  15. C. Neipp, I. Pascual and A. Beléndez, �??Fixation-free rehalogenating bleached reflection holograms recorded on BB-640 plates,�?? Opt. Commun. 182, 107-114 (2000).
    [CrossRef]
  16. M.Ulibarrena, M. J. Méndez, L. Carretero, R. Madrigal and A. Fimia, �??Comparison of direct, rehalogenating, and solvent bleaching processes with BB-640 plates,�?? Appl. Opt. 41, 4120-4123 (2002).
    [CrossRef] [PubMed]
  17. C. Neipp, C. Pascual and A. Beléndez, �??Mixed phase-amplitude holographic gratings recorded in bleached silver halide materials,�?? J. Phys. D 35, 957-967 (2002).
    [CrossRef]
  18. L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya and A. Beléndez, �??Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,�?? Opt. Lett. 26, 786-7888 (2001).
    [CrossRef]
  19. R. F.Madrigal, L. Carretero, S. Blaya, M. Ulibarrena, A. Beléndez y A. Fimia, �??Diffraction efficiency of unbleached phase and amplitude holograms as a function of volume fraction of metallic silver,�?? Opt. Commun. 201, 279-282 (2002).
    [CrossRef]
  20. C. Neipp, I. Pascual and A. Beléndez, �??Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on Bb-640 emulsions,�?? J. Opt. A 3, 504-513 (2002).
    [CrossRef]

Appl. Opt.

A. Beléndez, T. Beléndez, C. Neipp and I. Pascual, �??Determination of the refractive index and thickness of holographic silver halide materials by the use of polarized reflectances,�?? Appl. Opt. 41, 6802-08 (2002).
[CrossRef] [PubMed]

J. Crespo, A. Fimia and J. A. Quintana, �??Fixation-free methods in bleached reflection holography,�?? Appl. Opt. 25, 1642-5 (1986).
[CrossRef] [PubMed]

P. Hariharan and C. M. Chidley, �??Rehalogenating bleaches for photographic phase holograms: the influence of halide type and concentration on diffraction efficiency and scattering,�?? Appl. Opt. 26, 3895-8 (1987).
[CrossRef] [PubMed]

P. Hariharan, �??Rehalogenating bleaches for photographic phase holograms 3: Mechanism of material transfer,�?? Appl. Opt. 29, 2983-5 (1990).
[CrossRef] [PubMed]

C. Neipp, I. Pascual and A. Beléndez, �??Over modulation effects in fixation-free rehalogenating bleached holograms,�?? Appl. Opt. 40, 3402-3408 (2001).
[CrossRef]

B. J. Chang and C. D. Leonard, �??Dichromated gelatin for the fabrication of holographic optical elements,�?? Appl. Opt. 18, 2407-17 (1979).
[CrossRef] [PubMed]

K. S. Pennington and J. S. Harper, �??Techniques for producing low-noise, improved efficiency holograms,�?? Appl. Opt. 9, 1643-50 (1970).
[CrossRef] [PubMed]

M.Ulibarrena, M. J. Méndez, L. Carretero, R. Madrigal and A. Fimia, �??Comparison of direct, rehalogenating, and solvent bleaching processes with BB-640 plates,�?? Appl. Opt. 41, 4120-4123 (2002).
[CrossRef] [PubMed]

Bell Sys. Tech. J.

H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Sys. Tech. J. 48, 2909-47 (1969).

J. Mod. Opt.

C. Neipp, I. Pascual and A. Beléndez, �??Optimization of a fixation-free rehalogenating bleach for BB-640 holographic emulsion,�?? J. Mod. Opt. 47, 1671-1679 (2000).

J. Opt. A

C. Neipp, I. Pascual and A. Beléndez, �??Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on Bb-640 emulsions,�?? J. Opt. A 3, 504-513 (2002).
[CrossRef]

J. Phys. D

C. Neipp, C. Pascual and A. Beléndez, �??Mixed phase-amplitude holographic gratings recorded in bleached silver halide materials,�?? J. Phys. D 35, 957-967 (2002).
[CrossRef]

Opt. Commun.

R. F.Madrigal, L. Carretero, S. Blaya, M. Ulibarrena, A. Beléndez y A. Fimia, �??Diffraction efficiency of unbleached phase and amplitude holograms as a function of volume fraction of metallic silver,�?? Opt. Commun. 201, 279-282 (2002).
[CrossRef]

C. Neipp, I. Pascual and A. Beléndez, �??Fixation-free rehalogenating bleached reflection holograms recorded on BB-640 plates,�?? Opt. Commun. 182, 107-114 (2000).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

E. Guibelalde, �??Coupled wave analysis for out-of-phase mixed thick hologram gratings,�?? Opt. Quantum Electron. 16, 173-178 (1984).
[CrossRef]

Phot. Sci. Eng.

N. J. Phillips, A. A. Ward, R. Cullen and D. Porter, �??Advances in holographic bleaches,�?? Phot. Sci. Eng. 24, 120-4 (1980).

Other

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

R. R. A. Syms, Practical Volume Holography, (Clarendon, Oxford 1990).

H. I. Bjelkhagen, Silver-Halide Recording Materials, (Springer, Berlin 1995).

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Figures (6)

Fig. 1.
Fig. 1.

Transmission efficiency as a function of the angle for different values of the phase difference, φ. n1 = 0.05, d = 8 μm, α0 = 0.03 μm-1 and α1 = 0.03 μm-1.

Fig. 2.
Fig. 2.

Diffraction efficiency as a function of the phase difference, φ, between the refractive index and the absorption constant for different values of the absorption constant modulation, α1 , n1 = 0.030 and α0 = 0.030 μm-1.

Fig. 3.
Fig. 3.

Experimental set-up.

Fig. 4.
Fig. 4.

Unslanted mixed diffraction gratings.

Fig. 5.
Fig. 5.

- Transmittance as a function of the angle for a mixed diffraction grating. Parameters: n1 = 0.085, d = 6.8 μm, α0 = 0.017 μm-1, α1 = 0.012 μm-1, αs = 0.018 μm-1, φ = 0.25 rad for θ∈ [-45°,0°], φ = 4.3l rad for θ∈ [0°,45°].

Fig. 6.
Fig. 6.

- Transmittance as a function of the angle for a mixed diffraction grating. Parameters: n1 = 0.091, d = 6.8 μm, α0 = 0.019 μm-1, α1 = 0.014 μm-1, αs = 0.014 μm-1, φ = 4.19 rad for θ∈ [-45°,0°], φ = 0.13 rad for θ∈ [0°,45°].

Tables (2)

Tables Icon

Table I. Schedule procedure

Tables Icon

Table II. Bleach bath composition (modified version of R-10)

Equations (20)

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Q = 2 πλd n Λ 2
n = n 0 + n 1 cos ( Kr )
α = α 0 + α 1 cos ( Kr + φ )
R ( z ) = 1 c r ( γ 1 γ 2 ) [ ( c r γ 2 + α 0 ) exp ( γ 1 z ) + ( c r γ 1 + α 0 ) exp ( γ 2 z ) ]
S ( z ) = j χ 2 c s ( γ 1 γ 2 ) [ exp ( γ 1 z ) exp ( γ 2 z ) ]
γ 1,2 = 1 2 [ α 0 c r + α 0 c s + j ϑ c s ] ± 1 2 [ ( α 0 c r α 0 c s j ϑ c s ) 2 4 χ 1 χ 2 c r c s ] 1 2
χ 1 = π n 1 λ j exp ( j φ ) α 1 2
χ 2 = π n 1 λ j exp ( j φ ) α 1 2
η = c s c r S ( d ) S ( d ) *
τ = R ( d ) R ( d ) *
τ = exp ( α s d ) · RR *
S ( d ) = j exp ( α 0 d c r ) ( a j e b ) sin [ ( a j e b ) · ( a bj e ) ] ( a bj e ) · ( a bj e )
a = n 1 λc r
b = α 1 d 2 c r
S ( d ) = j ( c r c s ) 1 2 exp ( α 0 d c r ) sin ( a jb )
η = exp ( 2 α 0 d c r ) · [ sin 2 ( a ) + sinh 2 ( b ) ]
n r = n 0 + n r 1 cos ( Kr + π )
n h = n 0 + n h 1 cos ( Kr )
α = α 0 + α 1 cos ( Kr )
n = n 0 + n 1 cos ( Kr + φ )

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