Abstract

We present theoretical results for angular responses of transmitted and diffracted beams in mixed amplitude–phase holographic gratings. Experimental results for gratings recorded in photographic emulsions and developed without a bleaching bath, with diffraction efficiencies of >20%, are also presented. The model shows an angular shift between minimum transmittance and maximum diffraction efficiency when both index modulation and absorption coefficient modulation are present. Also, the Borrmann effect was found outside the Bragg angle. This method can be extended to a study of the mechanism of image formation in materials such as bacteriorhodopsin and azo-dye-doped polymers that exhibit both types of modulations (index and absorption).

© 2001 Optical Society of America

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References

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  1. H. Kogelnik, Bell. Syst. Tech. J. 48, 2909 (1969).
    [CrossRef]
  2. D. M. Burland, G. C. Bjorklund, and D. C. Álvarez, J. Am. Chem. Soc. 102, 7117 (1980).
    [CrossRef]
  3. D. M. Burland and C. Brauchle, J. Chem. Phys. 76, 4502 (1982).
  4. S. Blaya, L. Carretero, R. Mallavia, A. Fimia, and R. F. Madrigal, Appl. Opt. 38, 955 (1999).
    [CrossRef]
  5. Y. Barmenkov and N. Kozhevnikov, Sov. Tech. Phys. Lett. 16, 28 (1990).
  6. G. E. Scrivener and M. Tubbs, Opt. Commun. 10, 32 (1974).
    [CrossRef]
  7. O. Salminen, A. Ozols, and P. Riihola, J. Mod. Opt. 41, 1507 (1994).
    [CrossRef]
  8. P. Russell and L. Solymar, Appl. Phys. 22, 335 (1980).
  9. A. Beléndez, R. F. Madrigal, I. Pascual, and A. Fimia, Proc. SPIE 3956, 376 (2000).
    [CrossRef]

2000 (1)

A. Beléndez, R. F. Madrigal, I. Pascual, and A. Fimia, Proc. SPIE 3956, 376 (2000).
[CrossRef]

1999 (1)

1994 (1)

O. Salminen, A. Ozols, and P. Riihola, J. Mod. Opt. 41, 1507 (1994).
[CrossRef]

1990 (1)

Y. Barmenkov and N. Kozhevnikov, Sov. Tech. Phys. Lett. 16, 28 (1990).

1982 (1)

D. M. Burland and C. Brauchle, J. Chem. Phys. 76, 4502 (1982).

1980 (2)

P. Russell and L. Solymar, Appl. Phys. 22, 335 (1980).

D. M. Burland, G. C. Bjorklund, and D. C. Álvarez, J. Am. Chem. Soc. 102, 7117 (1980).
[CrossRef]

1974 (1)

G. E. Scrivener and M. Tubbs, Opt. Commun. 10, 32 (1974).
[CrossRef]

1969 (1)

H. Kogelnik, Bell. Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Álvarez, D. C.

D. M. Burland, G. C. Bjorklund, and D. C. Álvarez, J. Am. Chem. Soc. 102, 7117 (1980).
[CrossRef]

Barmenkov, Y.

Y. Barmenkov and N. Kozhevnikov, Sov. Tech. Phys. Lett. 16, 28 (1990).

Beléndez, A.

A. Beléndez, R. F. Madrigal, I. Pascual, and A. Fimia, Proc. SPIE 3956, 376 (2000).
[CrossRef]

Bjorklund, G. C.

D. M. Burland, G. C. Bjorklund, and D. C. Álvarez, J. Am. Chem. Soc. 102, 7117 (1980).
[CrossRef]

Blaya, S.

Brauchle, C.

D. M. Burland and C. Brauchle, J. Chem. Phys. 76, 4502 (1982).

Burland, D. M.

D. M. Burland and C. Brauchle, J. Chem. Phys. 76, 4502 (1982).

D. M. Burland, G. C. Bjorklund, and D. C. Álvarez, J. Am. Chem. Soc. 102, 7117 (1980).
[CrossRef]

Carretero, L.

Fimia, A.

A. Beléndez, R. F. Madrigal, I. Pascual, and A. Fimia, Proc. SPIE 3956, 376 (2000).
[CrossRef]

S. Blaya, L. Carretero, R. Mallavia, A. Fimia, and R. F. Madrigal, Appl. Opt. 38, 955 (1999).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell. Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Kozhevnikov, N.

Y. Barmenkov and N. Kozhevnikov, Sov. Tech. Phys. Lett. 16, 28 (1990).

Madrigal, R. F.

A. Beléndez, R. F. Madrigal, I. Pascual, and A. Fimia, Proc. SPIE 3956, 376 (2000).
[CrossRef]

S. Blaya, L. Carretero, R. Mallavia, A. Fimia, and R. F. Madrigal, Appl. Opt. 38, 955 (1999).
[CrossRef]

Mallavia, R.

Ozols, A.

O. Salminen, A. Ozols, and P. Riihola, J. Mod. Opt. 41, 1507 (1994).
[CrossRef]

Pascual, I.

A. Beléndez, R. F. Madrigal, I. Pascual, and A. Fimia, Proc. SPIE 3956, 376 (2000).
[CrossRef]

Riihola, P.

O. Salminen, A. Ozols, and P. Riihola, J. Mod. Opt. 41, 1507 (1994).
[CrossRef]

Russell, P.

P. Russell and L. Solymar, Appl. Phys. 22, 335 (1980).

Salminen, O.

O. Salminen, A. Ozols, and P. Riihola, J. Mod. Opt. 41, 1507 (1994).
[CrossRef]

Scrivener, G. E.

G. E. Scrivener and M. Tubbs, Opt. Commun. 10, 32 (1974).
[CrossRef]

Solymar, L.

P. Russell and L. Solymar, Appl. Phys. 22, 335 (1980).

Tubbs, M.

G. E. Scrivener and M. Tubbs, Opt. Commun. 10, 32 (1974).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

P. Russell and L. Solymar, Appl. Phys. 22, 335 (1980).

Bell. Syst. Tech. J. (1)

H. Kogelnik, Bell. Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

J. Am. Chem. Soc. (1)

D. M. Burland, G. C. Bjorklund, and D. C. Álvarez, J. Am. Chem. Soc. 102, 7117 (1980).
[CrossRef]

J. Chem. Phys. (1)

D. M. Burland and C. Brauchle, J. Chem. Phys. 76, 4502 (1982).

J. Mod. Opt. (1)

O. Salminen, A. Ozols, and P. Riihola, J. Mod. Opt. 41, 1507 (1994).
[CrossRef]

Opt. Commun. (1)

G. E. Scrivener and M. Tubbs, Opt. Commun. 10, 32 (1974).
[CrossRef]

Proc. SPIE (1)

A. Beléndez, R. F. Madrigal, I. Pascual, and A. Fimia, Proc. SPIE 3956, 376 (2000).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

Y. Barmenkov and N. Kozhevnikov, Sov. Tech. Phys. Lett. 16, 28 (1990).

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Figures (3)

Fig. 1
Fig. 1

Theoretical curves of the angular behavior of the normalized diffraction and transmission efficiencies of a pure absorption holographic grating recorded in symmetrical geometry with a thickness of 10 μm, n1=0, α=1000 cm-1, α1=0.7α, θb=22.5 deg, and λ=633 nm. The origin of θ is θb.

Fig. 2
Fig. 2

Theoretical study of the effect of the modulation of absorption in the angular responses of the diffraction and transmission efficiencies of a mixed absorption–phase holographic grating recorded in symmetrical geometry with a thickness of 10 μm, n1=0.02, α=1000 cm-1, θb=22.5 deg, and λ=633 nm. The origin of θ is θb.

Fig. 3
Fig. 3

Experimental curves of the angular behavior of the diffraction and transmission efficiency of a mixed absorption–phase holographic grating recorded in photographic emulsions by use of symmetrical setup with a thickness of 7 μm, θb=22.5 deg, λ=633 nm. The origin of θ is θb.

Equations (9)

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R=κ2csγ1-γ2expγ2dcrγ2+α-expγ1dcrγ1+α,
S=iκcsγ1-γ2expγ2d-expγ1d.
κ=πn1λ-iα12,
γ1,2=-12αcr+αcs+iϑcs±12αcr-αcs-iϑcs2-4κ2crcs1/2,
ϑ=4πn0sinθbλsinθ-sinθb,
z0=[(ϑ2+4κ12-κ222+8κ1κ22]1/2,
ψ0=arccos-ϑ2+4κ12-κ22z0,
ηdθ=exp-2αdcosθκ12+κ22z0×2coshz0dcosψ0/2cosθ-2cosz0dsinψ0/2cosθ,
ηtθ=exp-2αd/cosθz0×ϑ24+z042coshz0dcosψ0/2cosθ-ϑ24-z042cosz0dsinψ0/2cosθ+ϑz0sinψ02sinhz0dcosψ0/2cosθ-ϑz0cosψ02sinz0dsinψ0/2cosθ.

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