Abstract

A coupled wave model is used to describe the replay of two transmission gratings (G1 and G2) which have been recorded in dichromated gelatin at high exposure energies. As a consequence of material nonlinearities, a third grating G3, which has a spatial frequency equal to the difference of the two primary recordings, is also recorded. The model assumes multiple interactions between each of the three gratings and is used to match experimental data where the recording angles were (a) far apart so as to minimize interactions and (b) close together to enhance grating interactions. Good theoretical agreement was found with experiment for both cases.

© 1991 Optical Society of America

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References

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  1. S. K. Case, “Coupled-Wave Theory for Multiply Exposed Thick Holographic Gratings,” J. Opt. Soc. Am. 65, 724–729 (1975).
    [CrossRef]
  2. R. Kowarschik, “Diffraction Efficiency of Sequentially Stored Gratings in Transmission Volume Holograms,” Opt. Acta 25, 67 (1978).
    [CrossRef]
  3. C. W. Slinger, R. R. A. Syms, L. Solymar, “Multiple Holographic Transmission Gratings in Silver Halide Emulsion,” Appl. Phys. B 42, 121 (1987).
    [CrossRef]
  4. A. A. Friesem, J. S. Zelenka, “Effects of Film Nonlinearities in Holography,” Appl. Opt. 6, 1755–1759 (1967).
    [CrossRef] [PubMed]
  5. C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear Recording in Silver Halide Planar Volume Holograms,” Appl. Phys. B 36, 217 (1985).
    [CrossRef]
  6. S. K. Case, R. Alferness, “Index Modulation and Spatial Harmonic Generation in Dichromated Gelatin Films,” Appl. Phys. 10, 41 (1976).
    [CrossRef]
  7. B. J. Chang, C. D. Leonard, “Dichromated Gelatin for the Fabrication of Holographic Elements,” Appl. Opt. 18, 2407–2417 (1979).
    [CrossRef] [PubMed]
  8. J. C. W. Newell, “Optical Holography in Dichromated Gelatin,” Ph.D. Thesis, Department of Engineering Science, U. Oxford (1987).
  9. L. T. Blair, L. Solymar, J. Takacs, “Nonlinear Recording in Dichromated Gelatin,” Proc. Soc. Photo-Opt. Instrum. Eng. 1136 (1989).
  10. C. W. Slinger, L. Solymar, “Grating Interactions in Holograms Recorded with Two Object Waves,” Appl. Opt. 25, 3283–3287 (1986).
    [CrossRef] [PubMed]
  11. L. T. Blair, “Evaluation of Volume Holographic Optical Elements in Dichromated Gelatin,” Ph.D. Thesis, Department of Engineering Science, U. Oxford (1989).
  12. J. C. W. Newell, L. Solymar, “Nonuniformities in Dichromated Gelatin Reflection Gratings,” J. Mod. Opt. 36, 751 (1989).
    [CrossRef]

1989 (2)

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear Recording in Dichromated Gelatin,” Proc. Soc. Photo-Opt. Instrum. Eng. 1136 (1989).

J. C. W. Newell, L. Solymar, “Nonuniformities in Dichromated Gelatin Reflection Gratings,” J. Mod. Opt. 36, 751 (1989).
[CrossRef]

1987 (1)

C. W. Slinger, R. R. A. Syms, L. Solymar, “Multiple Holographic Transmission Gratings in Silver Halide Emulsion,” Appl. Phys. B 42, 121 (1987).
[CrossRef]

1986 (1)

1985 (1)

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear Recording in Silver Halide Planar Volume Holograms,” Appl. Phys. B 36, 217 (1985).
[CrossRef]

1979 (1)

1978 (1)

R. Kowarschik, “Diffraction Efficiency of Sequentially Stored Gratings in Transmission Volume Holograms,” Opt. Acta 25, 67 (1978).
[CrossRef]

1976 (1)

S. K. Case, R. Alferness, “Index Modulation and Spatial Harmonic Generation in Dichromated Gelatin Films,” Appl. Phys. 10, 41 (1976).
[CrossRef]

1975 (1)

1967 (1)

Alferness, R.

S. K. Case, R. Alferness, “Index Modulation and Spatial Harmonic Generation in Dichromated Gelatin Films,” Appl. Phys. 10, 41 (1976).
[CrossRef]

Blair, L. T.

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear Recording in Dichromated Gelatin,” Proc. Soc. Photo-Opt. Instrum. Eng. 1136 (1989).

L. T. Blair, “Evaluation of Volume Holographic Optical Elements in Dichromated Gelatin,” Ph.D. Thesis, Department of Engineering Science, U. Oxford (1989).

Case, S. K.

S. K. Case, R. Alferness, “Index Modulation and Spatial Harmonic Generation in Dichromated Gelatin Films,” Appl. Phys. 10, 41 (1976).
[CrossRef]

S. K. Case, “Coupled-Wave Theory for Multiply Exposed Thick Holographic Gratings,” J. Opt. Soc. Am. 65, 724–729 (1975).
[CrossRef]

Chang, B. J.

Friesem, A. A.

Kowarschik, R.

R. Kowarschik, “Diffraction Efficiency of Sequentially Stored Gratings in Transmission Volume Holograms,” Opt. Acta 25, 67 (1978).
[CrossRef]

Leonard, C. D.

Newell, J. C. W.

J. C. W. Newell, L. Solymar, “Nonuniformities in Dichromated Gelatin Reflection Gratings,” J. Mod. Opt. 36, 751 (1989).
[CrossRef]

J. C. W. Newell, “Optical Holography in Dichromated Gelatin,” Ph.D. Thesis, Department of Engineering Science, U. Oxford (1987).

Slinger, C. W.

C. W. Slinger, R. R. A. Syms, L. Solymar, “Multiple Holographic Transmission Gratings in Silver Halide Emulsion,” Appl. Phys. B 42, 121 (1987).
[CrossRef]

C. W. Slinger, L. Solymar, “Grating Interactions in Holograms Recorded with Two Object Waves,” Appl. Opt. 25, 3283–3287 (1986).
[CrossRef] [PubMed]

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear Recording in Silver Halide Planar Volume Holograms,” Appl. Phys. B 36, 217 (1985).
[CrossRef]

Solymar, L.

J. C. W. Newell, L. Solymar, “Nonuniformities in Dichromated Gelatin Reflection Gratings,” J. Mod. Opt. 36, 751 (1989).
[CrossRef]

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear Recording in Dichromated Gelatin,” Proc. Soc. Photo-Opt. Instrum. Eng. 1136 (1989).

C. W. Slinger, R. R. A. Syms, L. Solymar, “Multiple Holographic Transmission Gratings in Silver Halide Emulsion,” Appl. Phys. B 42, 121 (1987).
[CrossRef]

C. W. Slinger, L. Solymar, “Grating Interactions in Holograms Recorded with Two Object Waves,” Appl. Opt. 25, 3283–3287 (1986).
[CrossRef] [PubMed]

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear Recording in Silver Halide Planar Volume Holograms,” Appl. Phys. B 36, 217 (1985).
[CrossRef]

Syms, R. R. A.

C. W. Slinger, R. R. A. Syms, L. Solymar, “Multiple Holographic Transmission Gratings in Silver Halide Emulsion,” Appl. Phys. B 42, 121 (1987).
[CrossRef]

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear Recording in Silver Halide Planar Volume Holograms,” Appl. Phys. B 36, 217 (1985).
[CrossRef]

Takacs, J.

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear Recording in Dichromated Gelatin,” Proc. Soc. Photo-Opt. Instrum. Eng. 1136 (1989).

Zelenka, J. S.

Appl. Opt. (3)

Appl. Phys. (1)

S. K. Case, R. Alferness, “Index Modulation and Spatial Harmonic Generation in Dichromated Gelatin Films,” Appl. Phys. 10, 41 (1976).
[CrossRef]

Appl. Phys. B (2)

C. W. Slinger, R. R. A. Syms, L. Solymar, “Multiple Holographic Transmission Gratings in Silver Halide Emulsion,” Appl. Phys. B 42, 121 (1987).
[CrossRef]

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear Recording in Silver Halide Planar Volume Holograms,” Appl. Phys. B 36, 217 (1985).
[CrossRef]

J. Mod. Opt. (1)

J. C. W. Newell, L. Solymar, “Nonuniformities in Dichromated Gelatin Reflection Gratings,” J. Mod. Opt. 36, 751 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

R. Kowarschik, “Diffraction Efficiency of Sequentially Stored Gratings in Transmission Volume Holograms,” Opt. Acta 25, 67 (1978).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

L. T. Blair, L. Solymar, J. Takacs, “Nonlinear Recording in Dichromated Gelatin,” Proc. Soc. Photo-Opt. Instrum. Eng. 1136 (1989).

Other (2)

L. T. Blair, “Evaluation of Volume Holographic Optical Elements in Dichromated Gelatin,” Ph.D. Thesis, Department of Engineering Science, U. Oxford (1989).

J. C. W. Newell, “Optical Holography in Dichromated Gelatin,” Ph.D. Thesis, Department of Engineering Science, U. Oxford (1987).

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Figures (5)

Fig. 1
Fig. 1

Recording geometry for sequential double exposure transmission gratings.

Fig. 2
Fig. 2

Ewald circle representation of wave interactions considered in the theoretical model. (Wave vectors are always asummed positive, grating vectors are assumed positive in the y-direction, and off-Bragg parameters are assumed positive in the x-direction.)

Fig. 3
Fig. 3

Theoretical matching of experimental angular transmittance scans for gratings recorded at ±18 and ±23° in an index matching tank.

Fig. 4
Fig. 4

Theoretical matching of experimental angular transmittance scans for gratings recorded at ±20 and ±21° in an index matching tank.

Fig. 5
Fig. 5

Plot of refractive index modulation vs replay wavelength for experimental data when (a) assuming and (b) neglecting grating interactions.

Equations (3)

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n = n 0 + n 1 cos ( K 1 r ¯ + ϕ 1 ) + n 2 cos ( K 2 r ¯ + ϕ 2 ) + n 3 cos ( K 3 r ¯ + ϕ 3 ) ,
( a ) n 1 = 0 . 0059 , n 2 = 0 . 0065 , n 3 = 0 ; ( b ) n 1 = 0 . 0067 , n 2 = 0 . 0074 , n 3 = 0 . 0017 ; and ( c ) n 1 = 0 . 0071 , n 2 = 0 . 0071 , n 3 = 0 . 0021
( a ) n 1 = 0 . 0056 , n 2 = 0 . 0053 , n 3 = 0 ; ( b ) n 1 = 0 . 0076 , n 2 = 0 . 0076 , n 3 = 0 . 0017 ; ( c ) n 1 = 0 . 0073 , n 2 = 0 . 0070 , n 3 = 0 . 00195 .

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