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Tunable reflective lens array based on liquid crystal on silicon

Xin Wang, Haitao Dai, and Keshu Xu

Open Access Open Access

Abstract

We use a phase modulation method to form tunable lens arrays on liquid crystal on silicon (LCOS). With independent voltage adjustment on each pixel, LCOS generates a high-resolution gradual phase modulation profile, which makes it possible for the lens array to be freely tunable in focal length and other parameters. A tunable lens array is made on LCOS by use of this method, and we provide details of the theoretical analyses and experimental results.

©2005 Optical Society of America

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Figures (9)
Fig. 1.
Fig. 1. Construction of LCOS.

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Fig. 2.
Fig. 2. Beam path of a LCOS SLM.

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Fig. 3.
Fig. 3. Phase transformation of a LCOS lens.

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Fig. 4.
Fig. 4. Phase-shift voltage curve of LC film.

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Fig. 5.
Fig. 5. Phase-shift red value curve of LCOS.

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Fig. 6.
Fig. 6. Red maps for lens arrays and their focusing images.

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Fig. 7.
Fig. 7. Red value pixel for different focal lengths.

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Fig. 8.
Fig. 8. Fine tuning at a 1-m focal length.

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Fig. 9.
Fig. 9. Intensity pixel curve for focusing quality.

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Equations (10)

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1 n e 2 ( θ ) = cos ⁡ 2 θ n o 2 + sin ⁡ 2 θ n e 2 ,
Δ n = n e ( θ ) − n o .
J ′ R = Pol 2 · Rot ( ϕ ) · LC · Rot ( − ϕ ) · Mir · LC · Pol 1 · J . ,
U ( r ) = A exp [ j k z ] ,
U ′ ( r ) = A exp [ − j k f ] exp [ − j k 2 f r 2 ] ,
R ( r ) = U ′ ( r ) U ( r ) = exp [ − j k 2 f r 2 ] exp k ( − f − z ) ] .
P ( r ) = − π r 2 f λ .
U ( r ) = A exp [ j k p ] exp [ j k 2 p r 2 ] .
U ′ ( r ) = U ( r ) R ( r ) = A exp [ j k ( p − f − z ) ] exp [ − j k 2 q r 2 ] ,
1 f = 1 p + 1 q .
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