Abstract

We demonstrated a highly efficient, polarization-independent and electrically tunable Fresnel lens based on dye-doped liquid crystal using double-side photoalignment technique. The maximum diffraction efficiency reaches 37%, which approaches the theoretical limit ~41%. Such a lens functions as a half-wave plate, and this feature could be well preserved under the applied voltage. In addition, the device is simple to fabricate, and has fast switching responses between focusing and defocusing state.

© 2007 Optical Society of America

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  1. X. Ren, S. Liu, and X. Zhang, "Fabrication of off-axis holographic Fresnel lens used as muntiplexer/ demulltiplexer in optical communication," Proc. SPIE 5456, 391-398 (2004).
    [CrossRef]
  2. F. Sobel, L. Wentworth, and J. C. Wiltse, "Quasi-optical surface waveguide and other components for the 100-to- 300-Ge region," IRE Trans. Microwave Theory Tech. 9, 512-518 (1961).
    [CrossRef]
  3. N. Kitaura, S. Ogata, and Y. Mori, "Spectrometer employing a micro-Fresnel lens," Opt. Eng. (Bellingham) 34, 584-588. (1995).
    [CrossRef]
  4. M. Ferstl and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
    [CrossRef]
  5. M. Hain, W. Spiegle, M. Schmiedchen, T. Tschudi, and B. Javidi, "3D integral imaging using diffractive Fresnel lens arrays," Opt. Express 13, 315-326. (2005).
    [CrossRef] [PubMed]
  6. T. Fujita, H. Nishihara, and J. Koyama, "Fabrication of micro lenses using electron- beam lithography," Opt. Lett. 6, 613-615 (1981).
    [CrossRef] [PubMed]
  7. J. Jahns and S. J. Walker, "Two-dimensional array of diffractive microlenses fabricated by thin film deposition," Appl. Opt. 29, 931-936 (1990).
    [CrossRef] [PubMed]
  8. Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
    [CrossRef] [PubMed]
  9. Ho. Ren, Y.-H. Fan, and S.-T. Wu, "Tunable Fresnel lens using nanoscale polymer-stabilized liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
    [CrossRef]
  10. D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
    [CrossRef]
  11. T.-H. Lin, Y. H., A. Y.-G. Fuh, and S.-T. Wu, "Polarization controllable Fresnel lens using dye-doped liquid crystals," Opt. Express 14, 2359-2364 (2006).
    [CrossRef] [PubMed]
  12. J. S. Patel and K. Rastani, "Electrically controlled polarization-independent liquid-crystal Fresnel lens arrays," Opt. Lett. 16, 532-534 (1991).
    [CrossRef] [PubMed]
  13. K. Rastani, A. Marrakchi, S. F. Habiby, W. M. Hubbard, H. Gilchrist, and R. E. Nahory, "Binary phase Fresnel lenses for generation of two-dimensional beam arrays," Appl. Opt. 30, 1347-1354 (1991).
    [CrossRef] [PubMed]
  14. A. Y.-G. Fuh and K.-T. Cheng, "Partially erasable photoalignment layer formed in dye-doped liquid crystal films," Jpn. J. Appl. Phys. 45, 8778-8781 (2006).
    [CrossRef]
  15. C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
    [CrossRef]
  16. C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
    [CrossRef]
  17. S.-Y. Huang, S.-T. Wu, A. Y.-G. Fuh, "Optically switchable twist nematic grating based on a dye-doped liquid crystal film," Appl. Phys. Lett. 88, 0411041-0411043 (2006)
    [CrossRef]

2006

D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
[CrossRef]

T.-H. Lin, Y. H., A. Y.-G. Fuh, and S.-T. Wu, "Polarization controllable Fresnel lens using dye-doped liquid crystals," Opt. Express 14, 2359-2364 (2006).
[CrossRef] [PubMed]

A. Y.-G. Fuh and K.-T. Cheng, "Partially erasable photoalignment layer formed in dye-doped liquid crystal films," Jpn. J. Appl. Phys. 45, 8778-8781 (2006).
[CrossRef]

S.-Y. Huang, S.-T. Wu, A. Y.-G. Fuh, "Optically switchable twist nematic grating based on a dye-doped liquid crystal film," Appl. Phys. Lett. 88, 0411041-0411043 (2006)
[CrossRef]

2005

2004

X. Ren, S. Liu, and X. Zhang, "Fabrication of off-axis holographic Fresnel lens used as muntiplexer/ demulltiplexer in optical communication," Proc. SPIE 5456, 391-398 (2004).
[CrossRef]

C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
[CrossRef]

2003

C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
[CrossRef]

Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
[CrossRef] [PubMed]

Ho. Ren, Y.-H. Fan, and S.-T. Wu, "Tunable Fresnel lens using nanoscale polymer-stabilized liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

1996

M. Ferstl and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

1995

N. Kitaura, S. Ogata, and Y. Mori, "Spectrometer employing a micro-Fresnel lens," Opt. Eng. (Bellingham) 34, 584-588. (1995).
[CrossRef]

1991

1990

1981

1961

F. Sobel, L. Wentworth, and J. C. Wiltse, "Quasi-optical surface waveguide and other components for the 100-to- 300-Ge region," IRE Trans. Microwave Theory Tech. 9, 512-518 (1961).
[CrossRef]

Cheng, K. T.

C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
[CrossRef]

C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
[CrossRef]

Cheng, K.-T.

A. Y.-G. Fuh and K.-T. Cheng, "Partially erasable photoalignment layer formed in dye-doped liquid crystal films," Jpn. J. Appl. Phys. 45, 8778-8781 (2006).
[CrossRef]

Fan, Y.-H.

Ferstl, M.

M. Ferstl and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

Frisch, A.-M.

M. Ferstl and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

Fu, T. L.

C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
[CrossRef]

C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
[CrossRef]

Fuh, A. Y. -G.

C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
[CrossRef]

C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
[CrossRef]

Fuh, A. Y.-G.

S.-Y. Huang, S.-T. Wu, A. Y.-G. Fuh, "Optically switchable twist nematic grating based on a dye-doped liquid crystal film," Appl. Phys. Lett. 88, 0411041-0411043 (2006)
[CrossRef]

A. Y.-G. Fuh and K.-T. Cheng, "Partially erasable photoalignment layer formed in dye-doped liquid crystal films," Jpn. J. Appl. Phys. 45, 8778-8781 (2006).
[CrossRef]

Fujita, T.

Gilchrist, H.

Habiby, S. F.

Hain, M.

Huang, S.-Y.

S.-Y. Huang, S.-T. Wu, A. Y.-G. Fuh, "Optically switchable twist nematic grating based on a dye-doped liquid crystal film," Appl. Phys. Lett. 88, 0411041-0411043 (2006)
[CrossRef]

Hubbard, W. M.

Jahns, J.

Javidi, B.

Kim, D.-W.

D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
[CrossRef]

Kim, H.-R.

D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
[CrossRef]

Kim, S.-J.

D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
[CrossRef]

Kitaura, N.

N. Kitaura, S. Ogata, and Y. Mori, "Spectrometer employing a micro-Fresnel lens," Opt. Eng. (Bellingham) 34, 584-588. (1995).
[CrossRef]

Koyama, J.

Lee, C. R.

C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
[CrossRef]

C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
[CrossRef]

Lee, S.-D.

D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
[CrossRef]

Lin, T.-H.

Liu, S.

X. Ren, S. Liu, and X. Zhang, "Fabrication of off-axis holographic Fresnel lens used as muntiplexer/ demulltiplexer in optical communication," Proc. SPIE 5456, 391-398 (2004).
[CrossRef]

Marrakchi, A.

Mo, T. S.

C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
[CrossRef]

C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
[CrossRef]

Mori, Y.

N. Kitaura, S. Ogata, and Y. Mori, "Spectrometer employing a micro-Fresnel lens," Opt. Eng. (Bellingham) 34, 584-588. (1995).
[CrossRef]

Nahory, R. E.

Nishihara, H.

Ogata, S.

N. Kitaura, S. Ogata, and Y. Mori, "Spectrometer employing a micro-Fresnel lens," Opt. Eng. (Bellingham) 34, 584-588. (1995).
[CrossRef]

Patel, J. S.

Rastani, K.

Ren, H.

Ren, X.

X. Ren, S. Liu, and X. Zhang, "Fabrication of off-axis holographic Fresnel lens used as muntiplexer/ demulltiplexer in optical communication," Proc. SPIE 5456, 391-398 (2004).
[CrossRef]

Schmiedchen, M.

Sobel, F.

F. Sobel, L. Wentworth, and J. C. Wiltse, "Quasi-optical surface waveguide and other components for the 100-to- 300-Ge region," IRE Trans. Microwave Theory Tech. 9, 512-518 (1961).
[CrossRef]

Spiegle, W.

Tschudi, T.

Walker, S. J.

Wentworth, L.

F. Sobel, L. Wentworth, and J. C. Wiltse, "Quasi-optical surface waveguide and other components for the 100-to- 300-Ge region," IRE Trans. Microwave Theory Tech. 9, 512-518 (1961).
[CrossRef]

Wiltse, J. C.

F. Sobel, L. Wentworth, and J. C. Wiltse, "Quasi-optical surface waveguide and other components for the 100-to- 300-Ge region," IRE Trans. Microwave Theory Tech. 9, 512-518 (1961).
[CrossRef]

Wu, S.-T.

S.-Y. Huang, S.-T. Wu, A. Y.-G. Fuh, "Optically switchable twist nematic grating based on a dye-doped liquid crystal film," Appl. Phys. Lett. 88, 0411041-0411043 (2006)
[CrossRef]

Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003).
[CrossRef] [PubMed]

Yu, C.-J.

D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
[CrossRef]

Zhang, X.

X. Ren, S. Liu, and X. Zhang, "Fabrication of off-axis holographic Fresnel lens used as muntiplexer/ demulltiplexer in optical communication," Proc. SPIE 5456, 391-398 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

C. R. Lee, T. S. Mo, K. T. Cheng, T. L. Fu, and A. Y. -G. Fuh, "Electrically switchable and thermally erasable biphotonic holographic gratings in dye-doped liquid crystal films," Appl. Phys. Lett. 83, 4285-4287 (2003).
[CrossRef]

S.-Y. Huang, S.-T. Wu, A. Y.-G. Fuh, "Optically switchable twist nematic grating based on a dye-doped liquid crystal film," Appl. Phys. Lett. 88, 0411041-0411043 (2006)
[CrossRef]

Ho. Ren, Y.-H. Fan, and S.-T. Wu, "Tunable Fresnel lens using nanoscale polymer-stabilized liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

D.-W. Kim, C.-J. Yu, H.-R. Kim, S.-J. Kim, and S.-D. Lee, "Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration," Appl. Phys. Lett. 88, 203505-203507 (2006).
[CrossRef]

IRE Trans. Microwave Theory Tech.

F. Sobel, L. Wentworth, and J. C. Wiltse, "Quasi-optical surface waveguide and other components for the 100-to- 300-Ge region," IRE Trans. Microwave Theory Tech. 9, 512-518 (1961).
[CrossRef]

J. Mod. Opt.

M. Ferstl and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

Jpn. J. Appl. Phys.

A. Y.-G. Fuh and K.-T. Cheng, "Partially erasable photoalignment layer formed in dye-doped liquid crystal films," Jpn. J. Appl. Phys. 45, 8778-8781 (2006).
[CrossRef]

Opt. Eng. (Bellingham)

N. Kitaura, S. Ogata, and Y. Mori, "Spectrometer employing a micro-Fresnel lens," Opt. Eng. (Bellingham) 34, 584-588. (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

C. R. Lee, T. L. Fu, K. T. Cheng, T. S. Mo, and A. Y. -G. Fuh, "Surface-assisted photoalignment in dye-doped polymer-ball-liquid-crystal films," Phys. Rev. E 69, 031704-031709 (2004).
[CrossRef]

Proc. SPIE

X. Ren, S. Liu, and X. Zhang, "Fabrication of off-axis holographic Fresnel lens used as muntiplexer/ demulltiplexer in optical communication," Proc. SPIE 5456, 391-398 (2004).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic fabrication method of the DDLC Fresnel lens.

Fig. 2.
Fig. 2.

Schematic diagram of the orthogonally alternating binary configuration of the DDLC Fresnel lens. The top layer is a Fresnel zone plate mask.

Fig. 3.
Fig. 3.

Microscopic images of the fabricated DDLC Fresnel lens observed under a crossed-polarizer optical microscope with the rubbing direction of the cell making an angle of, (a) 0°, and (b) 45° to the polarizer axis.

Fig. 4.
Fig. 4.

Schematic experimental setup for analyzing the focusing properties of the DDLC Fresnel lens.

Fig. 5.
Fig. 5.

The measured primary diffraction efficiency of the DDLC Fresnel lens as a function of the applied voltage.

Fig. 6.
Fig. 6.

The measured intensity of the DDLC Fresnel lens as a function of the analyzer axis in reference to the director axis of LCs in the odd zones under various voltages.

Fig. 7.
Fig. 7.

Measured diffraction efficiency at the primary focal point of the DDLC Fresnel lens as a function of the incident linearly polarization angle at the applied voltages of V = 0Vrms and 1.8 Vrms.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

[ T in ] = [ E o cos θ E o sin θ ] ; [ T out ] odd zone = [ E o cos θ e in o 2 π λ d E o sin θ e in e 2 π λ d ] ; [ T out ] even zone = [ E o cos θ e in e 2 π λ d E o sin θ e in o 2 π λ d ]
D m = 1 2 A 1 0 2 A 1 [ T out ] e i 2 m π A 2 A 1 dA
= 1 2 πr 1 2 0 2 π 0 r 1 [ T out ] odd zone e im π r 2 r 1 2 rdrd θ + 0 2 π r 1 2 r 1 [ T out ] even zone e im π r 2 r 1 2 rdrd θ
= 1 im π e in o 2 π λ d ( e i ( n e n o ) 2 π λ d 1 ) [ E o cos θ E o sin θ ] , m = odd integers
η m = D m T in 2 2 = D m 2 E 0 2 = ( sin ( n e n o ) 2 π λ d 2 m π 2 ) 2 , m = odd integers

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