Abstract

The dynamic properties of dichromated gelatin plates are investigated during exposure by illuminating them first by a single plane wave and second by two interfering plane waves produced from an argon-ion laser at 514.5 nm. The grating recorded is shown to be a pure absorption grating. The experimental results obtained for the output beam intensities as a function of time are compared with the predictions of a theoretical model, and reasonable agreement is found. It is further shown that owing to the effect of a humid atmosphere, the recorded grating may self-develop into a phase grating of much higher efficiency.

© 1985 Optical Society of America

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References

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  1. T. A. Shankoff, “Phase Holograms in Dichromated Gelatin,” Appl. Opt. 7, 2101 (1968).
    [CrossRef] [PubMed]
  2. D. Meyerhofer, “Spatial Resolution of Relief Holograms in Dichromated Gelatin,” Appl. Opt. 10, 416 (1971).
    [CrossRef] [PubMed]
  3. D. Meyerhofer, “Phase Holograms in Dichromated Gelatin,” RCA Rev. 33, 110 (1972).
  4. S. Calixto, R. A. Lessard, “Real-Time Holography with Undeveloped Dechromated Gelatin Films,” Appl. Opt. 23, 1989 (1984).
    [CrossRef] [PubMed]
  5. W. J. Tomlinson, G. D. Aumiller, “Techniques for Measuring Refractive Index Changes in Photochromic Materials,” Appl. Opt. 14, 1100 (1975).
    [CrossRef] [PubMed]
  6. B. W. Batterman, H. Cole, “Dynamical Diffraction of X-Rays by Perfect Crystals,” Rev. Mod. Phys. 36, 681 (1964).
    [CrossRef]
  7. P. St. J. Russell, L. Solymar, “Borrman-Like Anomalous Effects in Volume Holography,” Appl. Phys. 22, 335 (1980).
    [CrossRef]
  8. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell. Syst. Tech. J. 48, 2909 (1969).
  9. L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).
  10. One could in general determine α0 and α1 by a Fourier expansion of α(x,y,t) in the y direction, but it is rather time-consuming to do so. We used instead an approximate method in which we work out the absorption coefficient only at the maxima [αmax(x,t)] and minima [αmin(x,t)] of the interference pattern and determine α0 and α1 from the relationships α0 = (αmax + αmin)/2 and α1 = (αmax − αmin)/2.
  11. B. J. Chang, C. D. Leonard, “Dichromated Gelatin for the Fabrication of Holographic Optical Elements,” Appl. Opt. 18, 2407 (1979).
    [CrossRef] [PubMed]
  12. R. R. A. Syms, L. Solymar, “Planar Volume Phase Holograms Formed in Bleached Photographic Emulsions,” Appl. Opt. 22, 1479 (1983).
    [CrossRef] [PubMed]

1984 (1)

1983 (1)

1980 (1)

P. St. J. Russell, L. Solymar, “Borrman-Like Anomalous Effects in Volume Holography,” Appl. Phys. 22, 335 (1980).
[CrossRef]

1979 (1)

1975 (1)

1972 (1)

D. Meyerhofer, “Phase Holograms in Dichromated Gelatin,” RCA Rev. 33, 110 (1972).

1971 (1)

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell. Syst. Tech. J. 48, 2909 (1969).

1968 (1)

1964 (1)

B. W. Batterman, H. Cole, “Dynamical Diffraction of X-Rays by Perfect Crystals,” Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Aumiller, G. D.

Batterman, B. W.

B. W. Batterman, H. Cole, “Dynamical Diffraction of X-Rays by Perfect Crystals,” Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Calixto, S.

Chang, B. J.

Cole, H.

B. W. Batterman, H. Cole, “Dynamical Diffraction of X-Rays by Perfect Crystals,” Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Cooke, D. J.

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

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell. Syst. Tech. J. 48, 2909 (1969).

Leonard, C. D.

Lessard, R. A.

Meyerhofer, D.

D. Meyerhofer, “Phase Holograms in Dichromated Gelatin,” RCA Rev. 33, 110 (1972).

D. Meyerhofer, “Spatial Resolution of Relief Holograms in Dichromated Gelatin,” Appl. Opt. 10, 416 (1971).
[CrossRef] [PubMed]

Russell, P. St. J.

P. St. J. Russell, L. Solymar, “Borrman-Like Anomalous Effects in Volume Holography,” Appl. Phys. 22, 335 (1980).
[CrossRef]

Shankoff, T. A.

Solymar, L.

R. R. A. Syms, L. Solymar, “Planar Volume Phase Holograms Formed in Bleached Photographic Emulsions,” Appl. Opt. 22, 1479 (1983).
[CrossRef] [PubMed]

P. St. J. Russell, L. Solymar, “Borrman-Like Anomalous Effects in Volume Holography,” Appl. Phys. 22, 335 (1980).
[CrossRef]

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

Syms, R. R. A.

Tomlinson, W. J.

Appl. Opt. (6)

Appl. Phys. (1)

P. St. J. Russell, L. Solymar, “Borrman-Like Anomalous Effects in Volume Holography,” Appl. Phys. 22, 335 (1980).
[CrossRef]

Bell. Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell. Syst. Tech. J. 48, 2909 (1969).

RCA Rev. (1)

D. Meyerhofer, “Phase Holograms in Dichromated Gelatin,” RCA Rev. 33, 110 (1972).

Rev. Mod. Phys. (1)

B. W. Batterman, H. Cole, “Dynamical Diffraction of X-Rays by Perfect Crystals,” Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Other (2)

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

One could in general determine α0 and α1 by a Fourier expansion of α(x,y,t) in the y direction, but it is rather time-consuming to do so. We used instead an approximate method in which we work out the absorption coefficient only at the maxima [αmax(x,t)] and minima [αmin(x,t)] of the interference pattern and determine α0 and α1 from the relationships α0 = (αmax + αmin)/2 and α1 = (αmax − αmin)/2.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the single-beam experiment.

Fig. 2
Fig. 2

Output beam intensity against time for unexpanded single-beam experiments.

Fig. 3
Fig. 3

Output beam intensity against time for expanded single-beam experiments.

Fig. 4
Fig. 4

Schematic diagram of a two-beam experiment.

Fig. 5
Fig. 5

Diffracted beam intensity against time for a two-beam experiment using 5% sensitization: (a) experiment; (b) theory.

Fig. 6
Fig. 6

Diffracted beam intensity against time for a two-beam experiment using 10% sensitization: (a) experiment; (b) theory.

Fig. 7
Fig. 7

Transmitted beam intensity against time for a two-beam experiment using 5% sensitization: (a) experiment; (b) theory.

Fig. 8
Fig. 8

Transmitted beam intensity against time for a two-beam experiment using 10% sensitization: (a) experiment; (b) theory.

Fig. 9
Fig. 9

Experimentally observed changes in transmitted intensity which occur after grating has been recorded if a phase change is introduced which shifts the fringe pattern relative to the fixed grating.

Fig. 10
Fig. 10

Transmission against angle at 514.5 nm for an undeveloped DCG transmission hologram after 24 h in increased humidity.

Tables (2)

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Table I Values of Parameters used to Model Single-Beam Experiments

Tables Icon

Table II Values of Parameters Used to Model Two-Beam Experiments

Equations (15)

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N 1 ( x , t ) + N 2 ( x , t ) = N 10 .
α i = g N 10 σ 1 , α f = g N 10 σ 2 , α ( x , t ) = g [ N 1 ( x , t ) σ 1 + N 2 ( x , t ) σ 2 ] , }
N 2 t = N 1 t = γ I ( x , t ) [ N 10 N 2 ( x , t ) ] ,
α ( x , t ) t = γ I ( x , t ) [ α f α ( x , t ) ] ,
I ( x , t ) x = 2 α ( x , t ) cos θ I ( x , t ) ,
α ( x , 0 ) = α i and I ( 0 , t ) = I 0 ,
I ( x , 0 ) = I 0 exp [ 2 α i x cos θ ] .
R exp j ( ρ · r ) and S exp j ( σ · r ) ,
I = R 2 + S 2 + 2 R S cos ( K · r ) ,
cos θ R x + α 0 R = α 1 2 S ,
cos θ S x + α 0 S = α 1 2 R ,
α = α 0 + α 1 cos ( K · r ) .
α ( x , y , 0 ) = α i , R ( 0 , t ) = I 1 , S ( 0 , t ) = I 2 ,
R = I 1 exp ( α i x cos θ ) , S = I 2 exp ( α i x cos θ ) ,
R ( 0 , t b ) = I 1 and S ( 0 , t b ) = 0 .

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