Abstract

We introduce a model describing real-time grating formation in holographic photopolymers, under the assumption that the diffusion of free monomers is much faster than the grating formation. This model, which combines polymerization kinetics with results from coupled-wave theory, indicates that the grating formation time depends sublinearly on the average holographic recording intensity, and the beam intensity ratio controls the grating index modulation at saturation. We validate the model by comparing its predictions with the results of experiments in which DuPont HRF-150X001 photopolymer was used.

© 1996 Optical Society of America

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References

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  1. W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keyes, Proc. SPIE 1212, 20 (1990).
    [CrossRef]
  2. G. Odian, Principles of Polymerization (McGraw-Hill, New York, 1970).
  3. G. C. Bjorklund, D. M. Burland, D. C. Alvarez, J. Chem. Phys. 9, 93 (1980).
  4. T. Todorov, P. Markoski, N. Tomova, V. Dragostinva, Opt. Quantum Electron. 16, 471 (1984).
    [CrossRef]
  5. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  6. K. Curtis, D. Psaltis, Appl. Opt. 31, 725 (1992).
    [CrossRef]
  7. G. Zhao, P. Mourolis, J. Mod. Opt. 41, 1929 (1994).
    [CrossRef]
  8. U. Rhee, H. J. Caulfield, C. S. Vikram, J. Shamir, Appl. Opt. 34, 846 (1995).
    [CrossRef] [PubMed]

1995

1994

G. Zhao, P. Mourolis, J. Mod. Opt. 41, 1929 (1994).
[CrossRef]

1992

K. Curtis, D. Psaltis, Appl. Opt. 31, 725 (1992).
[CrossRef]

1990

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keyes, Proc. SPIE 1212, 20 (1990).
[CrossRef]

1984

T. Todorov, P. Markoski, N. Tomova, V. Dragostinva, Opt. Quantum Electron. 16, 471 (1984).
[CrossRef]

1980

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, J. Chem. Phys. 9, 93 (1980).

1969

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

Alvarez, D. C.

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, J. Chem. Phys. 9, 93 (1980).

Bjorklund, G. C.

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, J. Chem. Phys. 9, 93 (1980).

Burland, D. M.

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, J. Chem. Phys. 9, 93 (1980).

Caulfield, H. J.

Curtis, K.

K. Curtis, D. Psaltis, Appl. Opt. 31, 725 (1992).
[CrossRef]

Dragostinva, V.

T. Todorov, P. Markoski, N. Tomova, V. Dragostinva, Opt. Quantum Electron. 16, 471 (1984).
[CrossRef]

Keyes, D. E.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keyes, Proc. SPIE 1212, 20 (1990).
[CrossRef]

Kogelnik, H.

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

Markoski, P.

T. Todorov, P. Markoski, N. Tomova, V. Dragostinva, Opt. Quantum Electron. 16, 471 (1984).
[CrossRef]

Monroe, B. M.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keyes, Proc. SPIE 1212, 20 (1990).
[CrossRef]

Mourolis, P.

G. Zhao, P. Mourolis, J. Mod. Opt. 41, 1929 (1994).
[CrossRef]

Odian, G.

G. Odian, Principles of Polymerization (McGraw-Hill, New York, 1970).

Psaltis, D.

K. Curtis, D. Psaltis, Appl. Opt. 31, 725 (1992).
[CrossRef]

Rhee, U.

Shamir, J.

Smothers, W. K.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keyes, Proc. SPIE 1212, 20 (1990).
[CrossRef]

Todorov, T.

T. Todorov, P. Markoski, N. Tomova, V. Dragostinva, Opt. Quantum Electron. 16, 471 (1984).
[CrossRef]

Tomova, N.

T. Todorov, P. Markoski, N. Tomova, V. Dragostinva, Opt. Quantum Electron. 16, 471 (1984).
[CrossRef]

Vikram, C. S.

Weber, A. M.

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keyes, Proc. SPIE 1212, 20 (1990).
[CrossRef]

Zhao, G.

G. Zhao, P. Mourolis, J. Mod. Opt. 41, 1929 (1994).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

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

J. Chem. Phys.

G. C. Bjorklund, D. M. Burland, D. C. Alvarez, J. Chem. Phys. 9, 93 (1980).

J. Mod. Opt.

G. Zhao, P. Mourolis, J. Mod. Opt. 41, 1929 (1994).
[CrossRef]

Opt. Quantum Electron.

T. Todorov, P. Markoski, N. Tomova, V. Dragostinva, Opt. Quantum Electron. 16, 471 (1984).
[CrossRef]

Proc. SPIE

W. K. Smothers, B. M. Monroe, A. M. Weber, D. E. Keyes, Proc. SPIE 1212, 20 (1990).
[CrossRef]

Other

G. Odian, Principles of Polymerization (McGraw-Hill, New York, 1970).

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Figures (5)

Fig. 1
Fig. 1

Experimental grating formation in holograms recorded with I0 = 81.5 mW/cm2 and beam intensity ratio K as a parameter.

Fig. 2
Fig. 2

Comparison of experimental (open circles) and theoretical (solid curve) saturation diffraction efficiencies. (I0 = 81.5 mW/cm2.)

Fig. 3
Fig. 3

Experimental grating formation in holograms recorded with K = 4 and the average recording intensity I0 as a parameter.

Fig. 4
Fig. 4

Experimental diffraction efficiency of holograms recorded with K = 4 and I0 as a parameter, as a function of the pseudoexposure I 0 δ t. Results are shown for only one hologram for each value of I0.

Fig. 5
Fig. 5

Prediction of the diffraction efficiency of holograms recorded with K = 4 and I0 as a parameter. First, the values for γ = 1.6, τ = 13.7 s are extracted from the leftmost curves of Fig. 3 at K = 4, I0 = 97.3 mW/cm2; then, using the model of Eq. (10) ff., we calculate the time constants at different I0 values; finally, the predictions (solid curves) and measured values (filled circles) are plotted and compared.

Equations (10)

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t [ M ] ( x , t ) = k R ( t ) [ M ] ( x , t ) I ( x ) δ ,
t n ( x , t ) = c n k R ( t ) [ M ] ( x , t ) I ( x ) δ ,
d d t Δ n ( t ) = 2 δ c n k R ( t ) [ M ] ( t ) I 0 δ ( I m / I 0 ) .
d d t [ M ] ( t ) = k R ( t ) [ M ] ( t ) I 0 δ .
Δ n ( t ) = Δ n M [ 2 K / ( K + 1 ) ] × { 1 exp [ I 0 δ 0 t k R ( τ ) d τ ] } ,
Δ n sat = Δ n M [ 2 K / ( K + 1 ) ] ,
η ( t ) = 100 × sin 2 { π Δ n ( t ) T / [ λ b cos ( θ b ) ] } ,
η sat = 100 × sin 2 [ 2 β K / ( K + 1 ) ] ,
k R ( t ) = k 0 exp ( ϕ I 0 δ t ) ,
Δ n ( t ) = Δ n M [ 2 K / ( K + 1 ) ] × ( 1 exp { γ [ 1 exp ( t / τ ) ] } ) ,

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