Abstract

A peculiar bifurcation phenomenon in the diffraction spectra of volume holograms is investigated. A linear expansion model modulated by a random number was built to explain the phenomenon. In our model, a random number was first introduced to describe the random property of swelling or shrinking of the emulsion during the process after exposure. The calculated results show good consistency with the experimental observations.

© 2006 Optical Society of America

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References

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  2. R. J. Collier, Optical Holography (Academic, 1971), Chap. 9.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. G. Wang, C. Tan, Y. Yi, and H. Shan, J. Mod. Opt. 50, 2155 (2003).
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    [CrossRef]
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    [CrossRef]
  15. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 10, p. 295.
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    [CrossRef]
  17. M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980).

2005 (1)

L. Cui, H. Gao, P. Dong, and D. Liu, Optik (Stuttgart) 116, 118 (2005).
[CrossRef]

2004 (2)

V. M. Petrov, S. Lichtenberg, J. Petter, and T. Tschudi, Opt. Commun. 229, 131 (2004).
[CrossRef]

L. Cui, F. Wang, J. Wang, Z. Wang, and D. Liu, Phys. Lett. A 324, 489 (2004).
[CrossRef]

2003 (1)

G. Wang, C. Tan, Y. Yi, and H. Shan, J. Mod. Opt. 50, 2155 (2003).

2000 (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

1997 (1)

V. Berger, O. Gauthier-Lafaye, and E. Costard, J. Appl. Phys. 82, 60 (1997).
[CrossRef]

1995 (1)

D. Liu, G. Manivannan, H. H. Arsenault, and R. A. Lessard, J. Mod. Opt. 42, 639 (1995).
[CrossRef]

1994 (1)

D. Liu, Opt. Commun. 107, 471 (1994).
[CrossRef]

1992 (1)

D. Liu, W. Tang, W. Huang, and Z. Liang, Opt. Eng. 31, 809 (1992).
[CrossRef]

1984 (1)

S. Sjölinder, Opt. Acta 31, 1001 (1984).
[CrossRef]

1981 (1)

1977 (1)

1972 (1)

1969 (1)

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

Arsenault, H. H.

D. Liu, G. Manivannan, H. H. Arsenault, and R. A. Lessard, J. Mod. Opt. 42, 639 (1995).
[CrossRef]

Berger, V.

V. Berger, O. Gauthier-Lafaye, and E. Costard, J. Appl. Phys. 82, 60 (1997).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980).

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 10, p. 295.

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 10, p. 295.

R. J. Collier, Optical Holography (Academic, 1971), Chap. 9.

Costard, E.

V. Berger, O. Gauthier-Lafaye, and E. Costard, J. Appl. Phys. 82, 60 (1997).
[CrossRef]

Cui, L.

L. Cui, H. Gao, P. Dong, and D. Liu, Optik (Stuttgart) 116, 118 (2005).
[CrossRef]

L. Cui, F. Wang, J. Wang, Z. Wang, and D. Liu, Phys. Lett. A 324, 489 (2004).
[CrossRef]

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Dong, P.

L. Cui, H. Gao, P. Dong, and D. Liu, Optik (Stuttgart) 116, 118 (2005).
[CrossRef]

Gao, H.

L. Cui, H. Gao, P. Dong, and D. Liu, Optik (Stuttgart) 116, 118 (2005).
[CrossRef]

Gauthier-Lafaye, O.

V. Berger, O. Gauthier-Lafaye, and E. Costard, J. Appl. Phys. 82, 60 (1997).
[CrossRef]

Gaylord, T. K.

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Huang, W.

D. Liu, W. Tang, W. Huang, and Z. Liang, Opt. Eng. 31, 809 (1992).
[CrossRef]

Kaspar, F. G.

Kogelnik, H.

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

Lessard, R. A.

D. Liu, G. Manivannan, H. H. Arsenault, and R. A. Lessard, J. Mod. Opt. 42, 639 (1995).
[CrossRef]

Liang, Z.

D. Liu, W. Tang, W. Huang, and Z. Liang, Opt. Eng. 31, 809 (1992).
[CrossRef]

Lichtenberg, S.

V. M. Petrov, S. Lichtenberg, J. Petter, and T. Tschudi, Opt. Commun. 229, 131 (2004).
[CrossRef]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 10, p. 295.

Liu, D.

L. Cui, H. Gao, P. Dong, and D. Liu, Optik (Stuttgart) 116, 118 (2005).
[CrossRef]

L. Cui, F. Wang, J. Wang, Z. Wang, and D. Liu, Phys. Lett. A 324, 489 (2004).
[CrossRef]

D. Liu, G. Manivannan, H. H. Arsenault, and R. A. Lessard, J. Mod. Opt. 42, 639 (1995).
[CrossRef]

D. Liu, Opt. Commun. 107, 471 (1994).
[CrossRef]

D. Liu, W. Tang, W. Huang, and Z. Liang, Opt. Eng. 31, 809 (1992).
[CrossRef]

Mangnusson, R.

Manivannan, G.

D. Liu, G. Manivannan, H. H. Arsenault, and R. A. Lessard, J. Mod. Opt. 42, 639 (1995).
[CrossRef]

Moharam, M. G.

Petrov, V. M.

V. M. Petrov, S. Lichtenberg, J. Petter, and T. Tschudi, Opt. Commun. 229, 131 (2004).
[CrossRef]

Petter, J.

V. M. Petrov, S. Lichtenberg, J. Petter, and T. Tschudi, Opt. Commun. 229, 131 (2004).
[CrossRef]

Shan, H.

G. Wang, C. Tan, Y. Yi, and H. Shan, J. Mod. Opt. 50, 2155 (2003).

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Sjölinder, S.

S. Sjölinder, Opt. Acta 31, 1001 (1984).
[CrossRef]

Tan, C.

G. Wang, C. Tan, Y. Yi, and H. Shan, J. Mod. Opt. 50, 2155 (2003).

Tang, W.

D. Liu, W. Tang, W. Huang, and Z. Liang, Opt. Eng. 31, 809 (1992).
[CrossRef]

Tschudi, T.

V. M. Petrov, S. Lichtenberg, J. Petter, and T. Tschudi, Opt. Commun. 229, 131 (2004).
[CrossRef]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Wang, F.

L. Cui, F. Wang, J. Wang, Z. Wang, and D. Liu, Phys. Lett. A 324, 489 (2004).
[CrossRef]

Wang, G.

G. Wang, C. Tan, Y. Yi, and H. Shan, J. Mod. Opt. 50, 2155 (2003).

Wang, J.

L. Cui, F. Wang, J. Wang, Z. Wang, and D. Liu, Phys. Lett. A 324, 489 (2004).
[CrossRef]

Wang, Z.

L. Cui, F. Wang, J. Wang, Z. Wang, and D. Liu, Phys. Lett. A 324, 489 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980).

Yi, Y.

G. Wang, C. Tan, Y. Yi, and H. Shan, J. Mod. Opt. 50, 2155 (2003).

Bell Syst. Tech. J. (1)

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

J. Appl. Phys. (1)

V. Berger, O. Gauthier-Lafaye, and E. Costard, J. Appl. Phys. 82, 60 (1997).
[CrossRef]

J. Mod. Opt. (2)

D. Liu, G. Manivannan, H. H. Arsenault, and R. A. Lessard, J. Mod. Opt. 42, 639 (1995).
[CrossRef]

G. Wang, C. Tan, Y. Yi, and H. Shan, J. Mod. Opt. 50, 2155 (2003).

J. Opt. Soc. Am. (3)

Nature (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Opt. Acta (1)

S. Sjölinder, Opt. Acta 31, 1001 (1984).
[CrossRef]

Opt. Commun. (2)

D. Liu, Opt. Commun. 107, 471 (1994).
[CrossRef]

V. M. Petrov, S. Lichtenberg, J. Petter, and T. Tschudi, Opt. Commun. 229, 131 (2004).
[CrossRef]

Opt. Eng. (1)

D. Liu, W. Tang, W. Huang, and Z. Liang, Opt. Eng. 31, 809 (1992).
[CrossRef]

Optik (Stuttgart) (1)

L. Cui, H. Gao, P. Dong, and D. Liu, Optik (Stuttgart) 116, 118 (2005).
[CrossRef]

Phys. Lett. A (1)

L. Cui, F. Wang, J. Wang, Z. Wang, and D. Liu, Phys. Lett. A 324, 489 (2004).
[CrossRef]

Other (3)

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 10, p. 295.

M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980).

R. J. Collier, Optical Holography (Academic, 1971), Chap. 9.

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Figures (5)

Fig. 1
Fig. 1

Experimental layout: L, convex lens; M, mirror; E, recording material (DCG); P, photomultiplier tube; H, volume hologram. (a) Setup for recording the volume hologram. (b) Measurement setup for the volume hologram.

Fig. 2
Fig. 2

Diffraction spectra of the reflection hologram grating made of DCG with the thickness of 36 μ m when the light waves are normally incident. The wavelength of the recording beam was 488 nm .

Fig. 3
Fig. 3

(a) Periodic structure of the volume hologram, without considering the expansion of DCG. (b) Changes of the refractive index in the volume hologram for the linear expansion model.

Fig. 4
Fig. 4

Calculated spectra of the volume hologram (upper row) with various random series (lower row). The values of the parameters are M 1 = 1.12 , M N = 1 , α g = 0.018 , a = 50 , N = 212 (almost 36 μ m ), n 0 = 1.52 , Δ n 1 = 0.04 , Δ n 2 = 0.07 .

Fig. 5
Fig. 5

Simulation with the parameters a = 100 , M 1 = 1.08 , M N = 1 and with other parameters unchanged from those in Fig. 4. (a) Calculated spectrum. (b) Expansion model.

Equations (2)

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M z , j = M 1 ( M 1 M N ) j N + r j a ,
n = n 0 + Δ n 1 exp ( α g T 2 ) cosh { α g [ Λ ( N 2 j + 1 ) z ] } + Δ n 2 exp ( α g T 2 ) cos ( k j z ) .

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