Abstract

One of the most interesting applications of photopolymers is as holographic recording materials for holographic memories. One of the basic requirements for this application is that the recording material thickness must be 500 µm or thicker. In recent years many 2-dimensional models have been proposed for the analysis of photopolymers. Good agreement between theoretical simulations and experimental results has been obtained for layers thinner than 200 µm. The attenuation of the light inside the material by Beer’s law results in an attenuation of the index profile inside the material and in some cases the effective optical thickness of the material is lower than the physical thickness. This is an important and fundamental limitation in achieving high capacity holographic memories using photopolymers and cannot be analyzed using 2-D diffusion models. In this paper a model is proposed to describe the behavior of the photopolymers in 3-D. This model is applied to simulate the formation of profiles in depth for different photopolymer viscosities and different intensity attenuations inside the material.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

Appl. Opt.

Appl. Phys. B

M. Ortuño, S. Gallego, C. García, C. Neipp, A. Beléndez and I. Pascual, �??Optimization of a 1 mm thick PVA/acrylamide recording material to obtain holographic memories: method of preparation and holographic properties,�?? Appl. Phys. B 76, 851-857 (2003).
[CrossRef]

Appl. Phys. Lett.

S. Blaya, L. Carretero and A. Fimia. �??Highly sensitive photopolymerisable dry film for use in real time holography,�?? Appl. Phys. Lett., 75, 1628-1630 (1998).
[CrossRef]

D. H. Close, A. D. Jacobson, J. D. Margerum, R. G. Brault, and F.J. McClung, �??Hologram recorded on photopolymer holographic recording material,�?? Appl. Phys. Lett. 14, 159-160 (1969).
[CrossRef]

Applied Optics

V. Moreau, Y. Renotte and Y. Lion, �??Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model�??, Applied Optics 41, 3427-3435 (2002).
[CrossRef] [PubMed]

Applied Physics B

S. Blaya, L. Carretero, R. F. Madrigal, M. Ulibarrena, P. Acebal and A. Fimia, �??Photopolymerization model for holographic gratings formation in photopolymers�??, Applied Physics B 77, 639-662 (2003).
[CrossRef]

J. Im. Science and Technology

D. A. Walkman, H-Y. S. Li and M. G. Horner, �??Volume Shrinkage in Slant Fringe Gratings of a Cationic Ring-Opening Holographic Recording Material,�?? J. Im. Science and Technology 41, 497-514 (1997).

J. Mod. Opt.

G. Zhao and P. Mouroulis, �??Diffusion model of hologram formation in dry photopolymers materials,�?? J. Mod. Opt. 41, 1929-1939 (1994).
[CrossRef]

I. Aubrecht, M. Miler y I. Koudela, �??Recording of holographic diffraction gratings in photopolymers: theoretical modelling and real-time monitoring of grating growth,�?? J. Mod. Opt. 45, 1465-1477 (1998).
[CrossRef]

S. Gallego, C. Neipp, M. Ortuño, A. Beléndez and I. Pascual �??Stabilization of volume gratings recorded in PVA/acrylamide photopolymers with diffraction efficiencies higher than 90%,�?? J. Mod. Opt. 51, 491-503 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. T. Sheridan and J. R. Lawrence, �??Nonlocal-response diffusion model of holographic recording in photopolymer�??, J. Opt. Soc. Am. A 17, 1008-1014 (2000).
[CrossRef]

N. Uchida, �??Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,�?? J. Opt. Soc. Am. A 63, 280-285 (1973).
[CrossRef]

J. Opt. Soc. Am. B

Journal of Applied Physics

V. L Colvin, R. G. Larson, A. L. Harris and M. L. Schilling, �??Quantitative model of volume hologram formation in photopolymers�??, Journal of Applied Physics 81, 5913-5923 (1997).
[CrossRef]

Microwave Optics Technology Letters

R. R. Adhami, D. J. Lanteigne and D. A. Gregory, �??Photopolymer hologram formation theory�??, Microwave Optics Technology Letters 4, 106-109 (1991).
[CrossRef]

Opt. Comm.

C. Neipp, J. T. Sheridan, S. Gallego, M. Ortuño, A. Márquez, I. Pascual and A. Beléndez, �??Effect of a depth attenuated refractive index profile in the angular responses of the efficiency of higher orders in volume gratings recorded in a PVA/Acrylamide photopolymer�?? Opt. Comm. 233, 311-322 (2004).
[CrossRef]

Opt. Eng.

A. Pu, K. Curtis and P. Psaltis, �??Exposure schedule for multiplexing holograms in photopolymer films,�?? Opt. Eng. 35, 2824-2829 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Optics Communications

G. M. Karpov, V. V. Obukhovsky, T. N. Smirnova and V. V. Lemeshko, �??Spatial transfer of matter as method of holographic recording in photoformers�??, Optics Communications 174, 391-404 (2000).
[CrossRef]

Optik

J. R. Lawrence, F. T. O�??Neill and J. T. Sheridan, �??Photopolymer holographic recording material,�?? Optik, 112, 449-463 (2001).
[CrossRef]

Proc. SPIE

T. Ingwall and M. Troll, �??The mechanism of hologram formation in DMP-128 photopolymer, in Holographic Optics: Design and Applications,�?? Proc. SPIE 883, 94 (1988).

Pure and Appl. Opt.

J. Lougnot, P. Jost and L. Lavielle, �??Polymers for holographic recording: VI. Some Basic ideas for modelling the Kinetics of the recording process�??, Pure and Appl. Opt. 6, 225-245 (1997).
[CrossRef]

J. Lougnot, P. Jost y L. Lavielle, �??Polymers for holographic recording: VI. Some Basic ideas for modeling the Kinetics of the recording process,�?? Pure and Appl. Opt. 6, 225-245 (1997).
[CrossRef]

Other

H. J. Coufal, D. Psaltis, Holographic Data Storage, G. T. Sincerbox, Springer-Verlag, New York, 2000.

S. Gallego, C. Neipp, M. Ortuño, A. Márquez, I. Pascual and A. Beléndez �??Optical and physical thickness of holographic diffraction gratings recorded in photopolymers,�?? Opto Ireland, SPIE Europe.

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Figures (12)

Fig. 1.
Fig. 1.

Transmission of a.800 µm thick layer as function of exposure time.

Fig. 2.
Fig. 2.

Holographic grating structure

Fig. 3.
Fig. 3.

Refractive index distribution within the photopolymer for three different recording times (15 s, 40 s and 100 s) for standard parameters (D~10-11cm2/s and R~1.25).

Fig. 4.
Fig. 4.

Refractive index modulation distribution within the photopolymer versus thickness and time for standard parameters (D~10-11cm2/s and R~1.25).

Fig. 5.
Fig. 5.

Refractive index distribution within the photopolymer for three different recording times (15 s, 40 s and 100 s) for usual parameters of viscous photopolymers: D~2×10-13cm2/s and R~0.02.

Fig. 6.
Fig. 6.

Refractive index distribution within the photopolymer versus thickness and time for usual parameters of viscous photopolymers: D~2×10-13 cm2/s and R~0.02.

Fig. 7.
Fig. 7.

Refractive index distribution within the photopolymer for three different recording times (15 s, 40 s and 100 s) for usual parameters of liquid systems: D~5×10-9cm2/s and R~60.

Fig. 8.
Fig. 8.

Refractive index distribution within the photopolymer as function of thickness and time for usual parameters of liquid systems: D~5×10-9cm2/s and R~60.

Fig. 9.
Fig. 9.

Refractive index distribution within the photopolymer for three different recording times (15 s, 40 s and 100 s) and for a high dye concentration (α=0.01 µm-1).

Fig. 10.
Fig. 10.

Refractive index distribution within the photopolymer as function of thickness and time for high dye concentration (α=0.01 µm-1).

Fig. 11.
Fig. 11.

Refractive index distribution within the photopolymer for three different recording times (15 s, 40 s and 100 s) and α=0.003 µm-1.

Fig. 12.
Fig. 12.

Refractive index distribution within the photopolymer as function of thickness and time with α=0.003 µm-1.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

I ( x ) = I 0 [ 1 + V cos ( K g x ) ]
I ( x , z ) = I 0 [ 1 + V cos ( K g x ) ] e α ( t ) z
α ( t ) = α 0 e K α I 0 β t
[ M ] ( x , z , t ) t = x D [ M ] ( x , z , t ) x k R ( t ) I γ ( x , z , t ) [ M ] ( x , z , t ) + z D [ M ] ( x , z , t ) z ,
[ P ] ( x , z , t ) t = k R ( t ) I γ ( x , z , t ) [ M ] ( x , z , t )
k R ( t ) = k R exp ( φ I 0 t )
τ D = 1 D K g 2
[ M ] ( x , z , t ) x [ M ] ( x , z , t ) z
d = g = 1 G d g
n 1 = ( n dark 2 + 2 ) 2 6 n dark [ ( n m 2 1 n m 2 + 2 n b 2 1 n b 2 + 2 ) 2 [ M ] 1 + ( n p 2 1 n p 2 + 2 n b 2 1 n b 2 + 2 ) [ P ] 1 ]
R = D K g 2 k R I 0

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