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3 Dimensional analysis of holographic photopolymers based memories

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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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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)

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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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