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Physical and effective optical thickness of holographic diffraction gratings recorded in photopolymers

S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. T. Sheridan

Open Access Open Access

Abstract

In recent years the interest in thick holographic recording materials for storage applications has increased. In particular, photopolymers are interesting materials for obtaining inexpensive thick dry layers with low noise and high diffraction efficiencies. Nonetheless, as will be demonstrated in this work, the attenuation in depth of light during the recording limits dramatically the effective optical thickness of the material. This effect must be taken into account whenever thick diffraction gratings are recorded in photopolymer materials. In this work the differences between optical and physical thickness are analyzed, applying a method based on the Rigorous Coupled Wave Theory and taking into account the attenuation in depth of the refractive index profile. By doing this the maximum optical thickness that can be achieved can be calculated. When the effective thickness is known, then the real storage capacity of the material can be obtained.

©2005 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Experimental setup. Where Mi are the mirrors. Li are the lenses. SFi the spatial filters to expand the beams. Di represent the diaphragms. BS is the beam splitter.

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Fig. 2.
Fig. 2. Photopolymer Type 1. The experimental angular scan around the first Bragg angle (20.8°) is plotted for two layers with different physical thickness 220 µm (circles) and 180 µm (triangles).

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Fig. 3.
Fig. 3. The experimental angular scan around the first Bragg angle is plotted for six layers with different physical thicknesses: 40 µm (composition Type 1), 70 µm (composition Type 1),, 110 µm (composition Type 1), 250 µm (composition Type 2), 750 µm (composition Type 3) and 1000 µm (composition Type 4).

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Fig. 4.
Fig. 4. The theoretical angular scan around the first Bragg angle (20.8°) is simulated using the depth attenuated algorithm for different physical thickness (70 µm, 100 µm, 220 µm and 400 µm).

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Fig. 5.
Fig. 5. The exponential decay of n1 , modulation of the refractive index, divided by the index modulation in the surface (n10 ) as function of depth is plotted for thin layers (α=0.015 µm-1).

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Fig. 6.
Fig. 6. The exponential decay of n1 , modulation of the refractive index, divided by the index modulation in the surface (n10 ) as function of depth is plotted for thick layers (α=0.003 µm-1).

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Fig. 7.
Fig. 7. The theoretical angular scans around the first Bragg angle (20.8°) is simulated using depth attenuated algorithm for different physical thickness (100 µm, 220 µm, 400 µm 600 µm 800 µm and 1200 µm).

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Fig. 8.
Fig. 8. The theoretical angular scans around the first Bragg angle (20.8°) is simulated using depth attenuated algorithm for different physical thickness (600 µm 800 µm, 1200 µm and 2400 µm).

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Tables (1)

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Table 1. Concentration and components of the different layer compositions

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Equations (9)

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ε ( x , z ) = ∑ h ε h ( z ) exp [ jhKx ]
K = 2 π Λ
ε h ( z ) = ε h , 0 exp [ − α z ]
d = ∑ g = 1 G d g
ε g ( x ) = ∑ h ε g , h exp [ jhKx ]
ε g , h = ε 0 , h exp [ − α ∑ g ′ = 1 g d g ′ ]
n leff = arcsin { [ η e ⁄ ( η e + t e ) ] 1 ⁄ 2 } λ cos θ ′ π d
n 1 eff = 1 d ∫ 0 d n 1 , 0 exp ( − α z ) dz
n 1 , 0 = n 1 eff α d 1 − exp ( − α d )
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