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Diffractive lenses recorded in absorbent photopolymers

R. Fernández, S. Gallego, A. Márquez, J. Francés, V. Navarro-Fuster, and I. Pascual

Open Access Open Access

Abstract

Photopolymers can be appealing materials for diffractive optical elements fabrication. In this paper, we present the recording of diffractive lenses in PVA/AA (Polyvinyl alcohol acrylamide) based photopolymers using a liquid crystal device as a master. In addition, we study the viability of using a diffusion model to simulate the lens formation in the material and to study the influence of the different parameters that govern the diffractive formation in photopolymers. Once we control the influence of each parameter, we can fit an optimum recording schedule to record each different diffractive optical element with the optimum focalization power.

© 2016 Optical Society of America

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Supplementary Material (4)

NameDescription
Visualization 1: MP4 (6644 KB)      Video 1
Visualization 2: MP4 (1022 KB)      Video 2
Visualization 3: MP4 (962 KB)      Video 3
Visualization 4: MP4 (533 KB)      Video 4

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Figures (9)
Fig. 1
Fig. 1 Theoretical intensity distribution (horizontal cut) projected onto photopolymer for a focal length of 50 cm.

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Fig. 2
Fig. 2 Experimental setup used to register and analyze in real-time the DOEs (diffractive lenses) D, diaphragm, L, lens, BS, Beam splitter, SF, spatial filter, LP, lineal polarizer, RF, red filter.

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Fig. 3
Fig. 3 (a) Image of the LCoS at the material plane (where the intensity transmittance equivalent lens is displayed) captured by the CCD camera. This plane is where the photopolymer should be placed. (b) Intensity profile across the horizontal line passing through the center of the lens.

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Fig. 4
Fig. 4 Recording simulation for standard material for 120 s, optimum recording time. a) Transverse cut at the focal plane. Visualization 1 b) Transverse cut of the average refractive index distribution. Visualization 2 c) Axial cut of the focal plane, along light propagation. D = 3*10−10 cm2/s. f = 1m.

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Fig. 5
Fig. 5 Intensity at the focal point as a function of the experimental recording and the theoretical simulation for spherical lens f = 0.5 and layer thickness of 95 ± 2 µm. Visualization 3 and Visualization 4.

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Fig. 6
Fig. 6 Intensity at the focal point as a function of recording time for different focal length (2, 1, and 0.5). a) Simulation provided by diffusion model. b) Experimental results with thickness and 85 ± 2 µm and for f = 0.5 m and f = 1m.

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Fig. 7
Fig. 7 Intensity of the focal spot as a function of recording time for different internal monomer diffusivities.

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Fig. 8
Fig. 8 Intensity of the focal point as a function of recording time for different internal relations between intensity and polymerization.

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Fig. 9
Fig. 9 Intensity at the focal point as a function of recording time for different internal dye absorption.

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Tables (1)

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Table 1 Composition of the liquid solution for photopolymer AA.

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Equations (13)

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∂ M ( x , z , t ) ∂   t = ∂ ∂   z D m ( t ) ∂ M ( x , z , t ) ∂ z + ∂ ∂   x D m ( t ) ∂ M ( x , z , t ) ∂ x − F R ( x , z , t ) M ( x , z , t )
∂ P ( x , z , t ) ∂   t = F R ( x , z , t ) M ( x , z , t )
∂ M ( x , y , z , t ) ∂   t = ∂ ∂   z D m ( t ) ∂ M ( x , y , z , t ) ∂ z + ∂ ∂   y D m ( t ) ∂ M ( x , y , z , t ) ∂ y + ∂ ∂   x D m ( t ) ∂ M ( x , y , z , t ) ∂ x − F R ( x , z , t ) M ( x , z , t )
∂ P ( x , y , z , t ) ∂   t = F R ( x , y , z , t ) M ( x , y , z , t )
F R ( x , y , z , t ) = k R ( x , y , z , t ) I ( x , y , z , t ) γ = k R ( x , y , z , t ) I ( x , y ) γ e − α ( t ) γ z
I ( x , y ) = exp [ j π λ f ( x 2 + y 2 ) ]
r m = m ( 2 λ f )
M i , j , k = Δ t Δ x 2 D m ( t ) M i + 1 , j , k − 1 − 2 Δ t Δ x 2 D m ( t ) M i , j , k − 1 + Δ t Δ x 2 D m ( t ) M i − 1 , j , k − 1 + Δ t Δ z 2 D m ( t ) M i , j + 1 , k − 1 − 2 Δ t Δ z 2 D m ( t ) M i , j , k − 1 + Δ t Δ z 2 D m ( t ) M i , j − 1 , k − 1 − Δ t F R i , j , k − 1 M i , j , k .1 + M i , j , k − 1
P i , j , k = P i , j , k + Δ t ⋅ F R i , j , k − 1 ⋅ M i , j , k − 1
M i , l , j , k = Δ t Δ x 2 D m M i + 1 , l , j , k − 1 − 2 Δ t Δ x 2 D m ( t ) M i , l , j , k − 1 + Δ t Δ x 2 D m ( t ) M i − 1 , l , j , k − 1 + Δ t Δ y 2 D m ( t ) M i , l + 1 , j , k − 1 − 2 Δ t Δ y 2 D m ( t ) M i , l , j , k − 1 + Δt Δ y 2 D m ( t ) M i , l − 1 , j , k − 1 +   Δ t Δ z 2 D m ( t ) M i , l , j + 1 , k − 1 − 2 Δ t Δ z 2 D m ( t ) M i , l , j , k − 1 + Δ t Δ z 2 D m ( t ) M i , l , j − 1 , k − 1 = Δ t F R i , l , j , k − 1 M i , l , j , k .1 + M i , l , j , k − 1
F R i , l , j , k = F R i , l , j , k − 1 + Δ t   F R i , l , j , k − 1 M i , l , j , k − 1 + M i , l , j , k − 1
Δ t < 1 2 ( Δ x 2 D m )
n 2 − 1 n 2 + 2 = n m 2 − 1 n m 2 + 2 M + n p 2 − 1 n p 2 + 2 P + n b 2 − 1 n b 2 + 2 ( 1 − M 0 )
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