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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References

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  1. H.-S. Ji, J.-H. Kim, and S. Kumar, “Electrically controllable microlens array fabricated by anisotropic phase separation from liquid-crystal and polymer composite materials,” Opt. Lett. 28, 1147–1149 (2003).
    [Crossref] [PubMed]
  2. M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
    [Crossref]
  3. H.-W. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, “Tunable-focus cylindrical liquid crystal lens,” Jpn. J. Appl. Phys. 43, 652–653 (2004).
    [Crossref]
  4. H.-W. Ren and S.-T. Wu, “Tunable electronic lens using polymer network liquid crystals,” Appl. Phys. Lett. 82, 22–24 (2003).
    [Crossref]
  5. F. H. Yu, J. Chen, S. T. Tang, and H. S. Kwok, “Reflective twisted nematic liquid crystal displays. II. Elimination of retardation film and rear polarizer,” J. Appl. Phys. 82, 5287–5294 (1997).
    [Crossref]
  6. V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
    [Crossref]
  7. H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
    [Crossref]

2004 (2)

H.-W. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, “Tunable-focus cylindrical liquid crystal lens,” Jpn. J. Appl. Phys. 43, 652–653 (2004).
[Crossref]

H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
[Crossref]

2003 (2)

2002 (1)

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[Crossref]

1998 (1)

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[Crossref]

1997 (1)

F. H. Yu, J. Chen, S. T. Tang, and H. S. Kwok, “Reflective twisted nematic liquid crystal displays. II. Elimination of retardation film and rear polarizer,” J. Appl. Phys. 82, 5287–5294 (1997).
[Crossref]

Chen, J.

F. H. Yu, J. Chen, S. T. Tang, and H. S. Kwok, “Reflective twisted nematic liquid crystal displays. II. Elimination of retardation film and rear polarizer,” J. Appl. Phys. 82, 5287–5294 (1997).
[Crossref]

Dai, H.-T.

H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
[Crossref]

Fan, Y.-H.

H.-W. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, “Tunable-focus cylindrical liquid crystal lens,” Jpn. J. Appl. Phys. 43, 652–653 (2004).
[Crossref]

Gauza, S.

H.-W. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, “Tunable-focus cylindrical liquid crystal lens,” Jpn. J. Appl. Phys. 43, 652–653 (2004).
[Crossref]

Ji, H.-S.

Kim, J.-H.

Kumar, S.

Kwok, H. S.

F. H. Yu, J. Chen, S. T. Tang, and H. S. Kwok, “Reflective twisted nematic liquid crystal displays. II. Elimination of retardation film and rear polarizer,” J. Appl. Phys. 82, 5287–5294 (1997).
[Crossref]

Laude, V.

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[Crossref]

Liu, J.-H.

H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
[Crossref]

Liu, Y.-J.

H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
[Crossref]

Ren, H.-W.

H.-W. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, “Tunable-focus cylindrical liquid crystal lens,” Jpn. J. Appl. Phys. 43, 652–653 (2004).
[Crossref]

H.-W. Ren and S.-T. Wu, “Tunable electronic lens using polymer network liquid crystals,” Appl. Phys. Lett. 82, 22–24 (2003).
[Crossref]

Sato, S.

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[Crossref]

Tang, S. T.

F. H. Yu, J. Chen, S. T. Tang, and H. S. Kwok, “Reflective twisted nematic liquid crystal displays. II. Elimination of retardation film and rear polarizer,” J. Appl. Phys. 82, 5287–5294 (1997).
[Crossref]

Wang, X.

H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
[Crossref]

Wu, S.-T.

H.-W. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, “Tunable-focus cylindrical liquid crystal lens,” Jpn. J. Appl. Phys. 43, 652–653 (2004).
[Crossref]

H.-W. Ren and S.-T. Wu, “Tunable electronic lens using polymer network liquid crystals,” Appl. Phys. Lett. 82, 22–24 (2003).
[Crossref]

Xu, K.-S

H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
[Crossref]

Ye, M.

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[Crossref]

Yu, F. H.

F. H. Yu, J. Chen, S. T. Tang, and H. S. Kwok, “Reflective twisted nematic liquid crystal displays. II. Elimination of retardation film and rear polarizer,” J. Appl. Phys. 82, 5287–5294 (1997).
[Crossref]

Appl. Phys. Lett. (1)

H.-W. Ren and S.-T. Wu, “Tunable electronic lens using polymer network liquid crystals,” Appl. Phys. Lett. 82, 22–24 (2003).
[Crossref]

J. Appl. Phys. (1)

F. H. Yu, J. Chen, S. T. Tang, and H. S. Kwok, “Reflective twisted nematic liquid crystal displays. II. Elimination of retardation film and rear polarizer,” J. Appl. Phys. 82, 5287–5294 (1997).
[Crossref]

Jpn. J. Appl. Phys. (2)

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41, L571–L573 (2002).
[Crossref]

H.-W. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, “Tunable-focus cylindrical liquid crystal lens,” Jpn. J. Appl. Phys. 43, 652–653 (2004).
[Crossref]

Opt. Commun. (2)

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[Crossref]

H.-T. Dai, K.-S Xu, Y.-J. Liu, X. Wang, and J.-H. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269–276 (2004).
[Crossref]

Opt. Lett. (1)

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Figures (9)

Fig. 1.
Fig. 1. Construction of LCOS.
Fig. 2.
Fig. 2. Beam path of a LCOS SLM.
Fig. 3.
Fig. 3. Phase transformation of a LCOS lens.
Fig. 4.
Fig. 4. Phase-shift voltage curve of LC film.
Fig. 5.
Fig. 5. Phase-shift red value curve of LCOS.
Fig. 6.
Fig. 6. Red maps for lens arrays and their focusing images.
Fig. 7.
Fig. 7. Red value pixel for different focal lengths.
Fig. 8.
Fig. 8. Fine tuning at a 1-m focal length.
Fig. 9.
Fig. 9. Intensity pixel curve for focusing quality.

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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