Abstract

A fly’s-eye lens was fabricated using polymer-dispersed liquid crystals and its optical properties were evaluated. The morphologies were examined under an optical microscope. The forming process has been simulated based on a patterned photo-polymerization technique in which the spatially modulated reaction rate has been coupled with the time-dependent Ginzburg-Landau (TDGL) equations with the free energies relating to isotropic mixing, nematic ordering, and network elasticity incorporated. The simulated results are in good agreement with the experimental results. The beam profile was tested using a CCD. The results showed that this fly’s-eye lens could modulate a Gaussian beam into a mesa-like beam. Such device is potentially useful in beam shaping and many illumination systems that require uniform beam profile.

© 2006 Optical Society of America

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  1. C. -M. Chang, and H. -P. D. Shieh, "Design of illumination and projection optics for projectors with single digital micromirror devices," Appl. Opt. 39, 3202-3208 (2000).
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  4. Y. Masumoto,US Patent 5, 418, 583 (1993).
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    [CrossRef]
  9. Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
    [CrossRef]
  10. R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
    [CrossRef]
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    [CrossRef]
  14. Y. J. Liu, B. Zhang, Y. Jia, and K. S. Xu, "Improvement of the diffraction efficiency in holographic polymer dispersed liquid crystal Bragg gratings," Opt. Commun. 218, 27-32 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. D. Nwabunma, H.-W. Chiu, and T. Kyu, "Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures," J. Chem. Phys. 113, 6429-6436 (2000).
    [CrossRef]
  18. T. Kyu, and D. Nwabunma, "Simulations of microlens arrays formed by pattern-photoplymerization-induced phase separation of liquid crystal/monomer mixtures," Macromolecules 34, 9168-9172 (2001).
    [CrossRef]

2005

Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
[CrossRef]

2003

Y. J. Liu, B. Zhang, Y. Jia, and K. S. Xu, "Improvement of the diffraction efficiency in holographic polymer dispersed liquid crystal Bragg gratings," Opt. Commun. 218, 27-32 (2003).
[CrossRef]

2002

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

2001

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

T. Kyu, and D. Nwabunma, "Simulations of microlens arrays formed by pattern-photoplymerization-induced phase separation of liquid crystal/monomer mixtures," Macromolecules 34, 9168-9172 (2001).
[CrossRef]

2000

D. Nwabunma, H.-W. Chiu, and T. Kyu, "Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures," J. Chem. Phys. 113, 6429-6436 (2000).
[CrossRef]

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

C. -M. Chang, and H. -P. D. Shieh, "Design of illumination and projection optics for projectors with single digital micromirror devices," Appl. Opt. 39, 3202-3208 (2000).
[CrossRef]

1999

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

D. Nwabunma, and T. Kyu, "Phase behavior of mixtures of low molar mass nematic liquid crystal and in situ photo-cross-linked polymer network," Macromolecules 32, 664-674 (1999).
[CrossRef]

1998

J. R. Dorgan, and D. Yan, "Kinetics of spinodal decomposition in liquid crystalline polymers: processing effects on the phase separation morphology," Macromolecules 31, 193-200 (1998).
[CrossRef]

1995

1986

J. W. Doane, N. Z. Vaz, and B. -G. Wu, S. Zumer, "Field controlled light scattering from nematic microdroplets," Appl. Phys. Lett. 48, 269-271 (1986).
[CrossRef]

Adams, W. W.

Bowley, C.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Bowley, C. C.

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

Bunning, T. J.

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, T. J. Bunning, and W. W. Adams, "Volume holographic image storage and electro-optical readout in a polymer-dispersed liquid-crystal film," Opt. Lett. 20, 1325-1327 (1995).
[CrossRef] [PubMed]

Chandra, S.

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

Chang, C. -M.

Chien, L.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Chiu, H.-W.

D. Nwabunma, H.-W. Chiu, and T. Kyu, "Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures," J. Chem. Phys. 113, 6429-6436 (2000).
[CrossRef]

Colegrove, J.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Crawford, G.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Crawford, G. P.

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

Crowther, B. G.

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

Dai, H. T.

Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
[CrossRef]

Doane, J. W.

J. W. Doane, N. Z. Vaz, and B. -G. Wu, S. Zumer, "Field controlled light scattering from nematic microdroplets," Appl. Phys. Lett. 48, 269-271 (1986).
[CrossRef]

Dorgan, J. R.

J. R. Dorgan, and D. Yan, "Kinetics of spinodal decomposition in liquid crystalline polymers: processing effects on the phase separation morphology," Macromolecules 31, 193-200 (1998).
[CrossRef]

Faris, S.

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

Fiske, T.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Fontecchio, A. K.

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

Gotin, R.

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

Gunther, J.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Harned, R.

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

Hu, G.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Jia, Y.

Y. J. Liu, B. Zhang, Y. Jia, and K. S. Xu, "Improvement of the diffraction efficiency in holographic polymer dispersed liquid crystal Bragg gratings," Opt. Commun. 218, 27-32 (2003).
[CrossRef]

Kelly, J.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Koch, D. G.

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

Kunick, J. M.

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

Kyu, T.

T. Kyu, and D. Nwabunma, "Simulations of microlens arrays formed by pattern-photoplymerization-induced phase separation of liquid crystal/monomer mixtures," Macromolecules 34, 9168-9172 (2001).
[CrossRef]

D. Nwabunma, H.-W. Chiu, and T. Kyu, "Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures," J. Chem. Phys. 113, 6429-6436 (2000).
[CrossRef]

D. Nwabunma, and T. Kyu, "Phase behavior of mixtures of low molar mass nematic liquid crystal and in situ photo-cross-linked polymer network," Macromolecules 32, 664-674 (1999).
[CrossRef]

Lewis, A.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Li, L.

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

Lin, J.-J.

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

Liu, J. H.

Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
[CrossRef]

Liu, Y. J.

Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
[CrossRef]

Y. J. Liu, B. Zhang, Y. Jia, and K. S. Xu, "Improvement of the diffraction efficiency in holographic polymer dispersed liquid crystal Bragg gratings," Opt. Commun. 218, 27-32 (2003).
[CrossRef]

McGuire, J. P.

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

Natarajan, L. V.

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, T. J. Bunning, and W. W. Adams, "Volume holographic image storage and electro-optical readout in a polymer-dispersed liquid-crystal film," Opt. Lett. 20, 1325-1327 (1995).
[CrossRef] [PubMed]

Nwabunma, D.

T. Kyu, and D. Nwabunma, "Simulations of microlens arrays formed by pattern-photoplymerization-induced phase separation of liquid crystal/monomer mixtures," Macromolecules 34, 9168-9172 (2001).
[CrossRef]

D. Nwabunma, H.-W. Chiu, and T. Kyu, "Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures," J. Chem. Phys. 113, 6429-6436 (2000).
[CrossRef]

D. Nwabunma, and T. Kyu, "Phase behavior of mixtures of low molar mass nematic liquid crystal and in situ photo-cross-linked polymer network," Macromolecules 32, 664-674 (1999).
[CrossRef]

Shieh, H. -P. D.

Silverstein, L.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Siwecki, S. A.

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

Sun, X. W.

Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
[CrossRef]

Sutherland, R. L.

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, T. J. Bunning, and W. W. Adams, "Volume holographic image storage and electro-optical readout in a polymer-dispersed liquid-crystal film," Opt. Lett. 20, 1325-1327 (1995).
[CrossRef] [PubMed]

Tondiglia, V. P.

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

V. P. Tondiglia, L. V. Natarajan, R. L. Sutherland, T. J. Bunning, and W. W. Adams, "Volume holographic image storage and electro-optical readout in a polymer-dispersed liquid-crystal film," Opt. Lett. 20, 1325-1327 (1995).
[CrossRef] [PubMed]

Vaz, N. Z.

J. W. Doane, N. Z. Vaz, and B. -G. Wu, S. Zumer, "Field controlled light scattering from nematic microdroplets," Appl. Phys. Lett. 48, 269-271 (1986).
[CrossRef]

Wu, B. -G.

J. W. Doane, N. Z. Vaz, and B. -G. Wu, S. Zumer, "Field controlled light scattering from nematic microdroplets," Appl. Phys. Lett. 48, 269-271 (1986).
[CrossRef]

Xu, K. S.

Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
[CrossRef]

Y. J. Liu, B. Zhang, Y. Jia, and K. S. Xu, "Improvement of the diffraction efficiency in holographic polymer dispersed liquid crystal Bragg gratings," Opt. Commun. 218, 27-32 (2003).
[CrossRef]

Yan, D.

J. R. Dorgan, and D. Yan, "Kinetics of spinodal decomposition in liquid crystalline polymers: processing effects on the phase separation morphology," Macromolecules 31, 193-200 (1998).
[CrossRef]

Yuan, H.

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

Zhang, B.

Y. J. Liu, B. Zhang, Y. Jia, and K. S. Xu, "Improvement of the diffraction efficiency in holographic polymer dispersed liquid crystal Bragg gratings," Opt. Commun. 218, 27-32 (2003).
[CrossRef]

Zumer, S.

J. W. Doane, N. Z. Vaz, and B. -G. Wu, S. Zumer, "Field controlled light scattering from nematic microdroplets," Appl. Phys. Lett. 48, 269-271 (1986).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. W. Doane, N. Z. Vaz, and B. -G. Wu, S. Zumer, "Field controlled light scattering from nematic microdroplets," Appl. Phys. Lett. 48, 269-271 (1986).
[CrossRef]

Y. J. Liu, X. W. Sun, J. H. Liu, H. T. Dai, and K. S. Xu, "A polarization insensitive 2 × 2 optical switch fabricated by liquid crystal-polymer composite," Appl. Phys. Lett. 86, 041115 (2005).
[CrossRef]

C. C. Bowley, A. K. Fontecchio, G. P. Crawford, J.-J. Lin, L. Li, and S. Faris, "Multiple gratings simultaneously formed in holographic polymer-dispersed liquid-crystal displays," Appl. Phys. Lett. 76, 523-525 (2000).
[CrossRef]

J. Chem. Phys.

D. Nwabunma, H.-W. Chiu, and T. Kyu, "Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures," J. Chem. Phys. 113, 6429-6436 (2000).
[CrossRef]

Macromolecules

T. Kyu, and D. Nwabunma, "Simulations of microlens arrays formed by pattern-photoplymerization-induced phase separation of liquid crystal/monomer mixtures," Macromolecules 34, 9168-9172 (2001).
[CrossRef]

J. R. Dorgan, and D. Yan, "Kinetics of spinodal decomposition in liquid crystalline polymers: processing effects on the phase separation morphology," Macromolecules 31, 193-200 (1998).
[CrossRef]

D. Nwabunma, and T. Kyu, "Phase behavior of mixtures of low molar mass nematic liquid crystal and in situ photo-cross-linked polymer network," Macromolecules 32, 664-674 (1999).
[CrossRef]

Opt. Commun.

Y. J. Liu, B. Zhang, Y. Jia, and K. S. Xu, "Improvement of the diffraction efficiency in holographic polymer dispersed liquid crystal Bragg gratings," Opt. Commun. 218, 27-32 (2003).
[CrossRef]

Opt. Lett.

Proc. SPIE

H. Yuan, J. Colegrove, G. Hu, T. Fiske, A. Lewis, J. Gunther, L. Silverstein, C. Bowley, G. Crawford, L. Chien, and J. Kelly, "HPDLC color reflective displays," Proc. SPIE 3690, 196-206 (1999).
[CrossRef]

R. L. Sutherland, L. V. Natarajan, V. P. Tondiglia, S. A. Siwecki, S. Chandra, and T. J. Bunning, "Switchable holograms for displays and telecommunications," Proc. SPIE 4463, 1-10 (2001).
[CrossRef]

B. G. Crowther, D. G. Koch, J. M. Kunick, J. P. McGuire, R. Harned, and R. Gotin, "A fly’s eye condenser system for uniform illumination," Proc. SPIE 4832, 302-310 (2002).
[CrossRef]

Other

A. H. J. van den Brandt, and W. A. G. Timmers, US Patent 5, 098, 184 (1990).

Y. Masumoto,US Patent 5, 418, 583 (1993).

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[CrossRef]

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[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

The experimental setup to fabricate the PDLC fly’s-eye lens. L1, L2 and L3 are all lenses. L1 and L2 are used to generate a collimated laser beam. L3 is used to minimize the pattern.

Fig. 2.
Fig. 2.

The evolution of a hypothetical patterned PDLC fly’s-eye lens showing the array patterns. Parameters used were φL =0.75, T=30°C, k 0=10-4, I 0=1.0. The upper row shows the case for Nx =Ny =100, while the lower row represents that for Nx =100, and Ny =150.

Fig. 3.
Fig. 3.

The micrographs (a), (b), and (c) are obtained under the optical microscope. The insets are the theoretical simulations, which show the similar morphologies.

Fig. 4.
Fig. 4.

The overall micrograph of the patterned PDLC fly’s-eye lens, (a), and its Fourier transform pattern, (b).

Fig. 5.
Fig. 5.

The near field (a) and far field (b) patterns of the fly’s-eye lens, which are obtained by a CCD 10 mm and 20 cm away from the fly’s-eye lens when the laser beam passes through it, respectively.

Fig. 6.
Fig. 6.

The intensity distribution of the incoming light (a), the output light without voltage (b), and with voltage applied (c), respectively.

Equations (3)

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ϕ M t = [ Λ G ϕ M ] + η ϕ M or ϕ P t = [ Λ G ϕ P ] + η ϕ P
ϕ L t = [ Λ G ϕ L ] + η ϕ L
S t = [ Λ G S ] + η S

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