Abstract

This study presents a theoretical analysis and experimental demonstration of an electrically controllable Fresnel lens in a 90° twisted nematic liquid crystal cell. The cell gap was chosen to satisfy the Gooch-Tarry conditions, and therefore, the polarization rotation effect was valid regardless of the incident polarization direction. The polarization sensitivity of the diffraction efficiency of the 90° twisted nematic Fresnel lens was dependent on the applied voltage regime. Theoretical calculations effectively explain the experimental results.

© 2015 Optical Society of America

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References

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  1. H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
    [Crossref]
  2. T.-H. Lin, Y. Huang, A. Y. G. Fuh, and S.-T. Wu, “Polarization controllable Fresnel lens using dye-doped liquid crystals,” Opt. Express 14(6), 2359–2364 (2006).
    [Crossref] [PubMed]
  3. K.-T. Cheng, C.-K. Liu, C. L. Ting, and A. Y.-G. Fuh, “Electrically switchable and optically rewritable reflective Fresnel zone plate in dye-doped cholesteric liquid crystals,” Opt. Express 15(21), 14078–14085 (2007).
    [Crossref] [PubMed]
  4. C.-H. Lin, Y.-Y. Wang, and C.-W. Hsieh, “Polarization-independent and high-diffraction-efficiency Fresnel lenses based on blue phase liquid crystals,” Opt. Lett. 36(4), 502–504 (2011).
    [Crossref] [PubMed]
  5. H.-C. Yeh, Y.-C. Kuo, S.-H. Lin, J.-D. Lin, T.-S. Mo, and S.-Y. Huang, “Optically controllable and focus-tunable Fresnel lens in azo-dye-doped liquid crystals using a Sagnac interferometer,” Opt. Lett. 36(8), 1311–1313 (2011).
    [Crossref] [PubMed]
  6. G.-S. Chen and H.-C. Yeh, “Polarization-selective color-filter Fresnel lens in polymer-stabilized cholesteric liquid crystals,” J. Appl. Phys. 112(5), 054501 (2012).
    [Crossref]
  7. A. K. Srivastava, X. Wang, S. Q. Gong, D. Shen, Y. Q. Lu, V. G. Chigrinov, and H. S. Kwok, “Micro-patterned photo-aligned ferroelectric liquid crystal Fresnel zone lens,” Opt. Lett. 40(8), 1643–1646 (2015).
    [Crossref] [PubMed]
  8. J. S. Patel and S.-D. Lee, “Electrically tunable and polarization insensitive Fabry–Perot étalon with a liquid-crystal film,” Appl. Phys. Lett. 58(22), 2491–2493 (1991).
    [Crossref]
  9. C.-H. Lin, H.-Y. Huang, and J.-Y. Wang, “Polarization-independent liquid-crystal Fresnel lenses based on surface-mode switching of 90° twisted-nematic liquid crystals,” IEEE Photonics Technol. Lett. 22(3), 137–139 (2010).
    [Crossref]
  10. S. T. Wu and C. S. Wu, “Mixed-mode twisted-nematic cell for transmissive liquid crystal display,” Displays 20(5), 231–236 (1999).
    [Crossref]
  11. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, 1999), Chap. 5.
  12. Y. Huang, T. X. Wu, and S.-T. Wu, “Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method,” J. Appl. Phys. 93(5), 2490–2495 (2003).
    [Crossref]
  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(11), 1347–1354 (1991).
    [Crossref] [PubMed]
  14. W.-C. Hung, Y.-J. Chen, C.-H. Lin, I. M. Jiang, and T. F. Hsu, “Sensitive voltage-dependent diffraction of a liquid crystal Fresnel lens,” Appl. Opt. 48(11), 2094–2098 (2009).
    [Crossref] [PubMed]

2015 (1)

2012 (1)

G.-S. Chen and H.-C. Yeh, “Polarization-selective color-filter Fresnel lens in polymer-stabilized cholesteric liquid crystals,” J. Appl. Phys. 112(5), 054501 (2012).
[Crossref]

2011 (2)

2010 (1)

C.-H. Lin, H.-Y. Huang, and J.-Y. Wang, “Polarization-independent liquid-crystal Fresnel lenses based on surface-mode switching of 90° twisted-nematic liquid crystals,” IEEE Photonics Technol. Lett. 22(3), 137–139 (2010).
[Crossref]

2009 (1)

2007 (1)

2006 (1)

2003 (2)

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

Y. Huang, T. X. Wu, and S.-T. Wu, “Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method,” J. Appl. Phys. 93(5), 2490–2495 (2003).
[Crossref]

1999 (1)

S. T. Wu and C. S. Wu, “Mixed-mode twisted-nematic cell for transmissive liquid crystal display,” Displays 20(5), 231–236 (1999).
[Crossref]

1991 (2)

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(11), 1347–1354 (1991).
[Crossref] [PubMed]

J. S. Patel and S.-D. Lee, “Electrically tunable and polarization insensitive Fabry–Perot étalon with a liquid-crystal film,” Appl. Phys. Lett. 58(22), 2491–2493 (1991).
[Crossref]

Chen, G.-S.

G.-S. Chen and H.-C. Yeh, “Polarization-selective color-filter Fresnel lens in polymer-stabilized cholesteric liquid crystals,” J. Appl. Phys. 112(5), 054501 (2012).
[Crossref]

Chen, Y.-J.

Cheng, K.-T.

Chigrinov, V. G.

Fan, Y.-H.

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

Fuh, A. Y. G.

Fuh, A. Y.-G.

Gilchrist, H.

Gong, S. Q.

Habiby, S. F.

Hsieh, C.-W.

Hsu, T. F.

Huang, H.-Y.

C.-H. Lin, H.-Y. Huang, and J.-Y. Wang, “Polarization-independent liquid-crystal Fresnel lenses based on surface-mode switching of 90° twisted-nematic liquid crystals,” IEEE Photonics Technol. Lett. 22(3), 137–139 (2010).
[Crossref]

Huang, S.-Y.

Huang, Y.

T.-H. Lin, Y. Huang, A. Y. G. Fuh, and S.-T. Wu, “Polarization controllable Fresnel lens using dye-doped liquid crystals,” Opt. Express 14(6), 2359–2364 (2006).
[Crossref] [PubMed]

Y. Huang, T. X. Wu, and S.-T. Wu, “Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method,” J. Appl. Phys. 93(5), 2490–2495 (2003).
[Crossref]

Hubbard, W. M.

Hung, W.-C.

Jiang, I. M.

Kuo, Y.-C.

Kwok, H. S.

Lee, S.-D.

J. S. Patel and S.-D. Lee, “Electrically tunable and polarization insensitive Fabry–Perot étalon with a liquid-crystal film,” Appl. Phys. Lett. 58(22), 2491–2493 (1991).
[Crossref]

Lin, C.-H.

Lin, J.-D.

Lin, S.-H.

Lin, T.-H.

Liu, C.-K.

Lu, Y. Q.

Marrakchi, A.

Mo, T.-S.

Nahory, R. E.

Patel, J. S.

J. S. Patel and S.-D. Lee, “Electrically tunable and polarization insensitive Fabry–Perot étalon with a liquid-crystal film,” Appl. Phys. Lett. 58(22), 2491–2493 (1991).
[Crossref]

Rastani, K.

Ren, H.

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

Shen, D.

Srivastava, A. K.

Ting, C. L.

Wang, J.-Y.

C.-H. Lin, H.-Y. Huang, and J.-Y. Wang, “Polarization-independent liquid-crystal Fresnel lenses based on surface-mode switching of 90° twisted-nematic liquid crystals,” IEEE Photonics Technol. Lett. 22(3), 137–139 (2010).
[Crossref]

Wang, X.

Wang, Y.-Y.

Wu, C. S.

S. T. Wu and C. S. Wu, “Mixed-mode twisted-nematic cell for transmissive liquid crystal display,” Displays 20(5), 231–236 (1999).
[Crossref]

Wu, S. T.

S. T. Wu and C. S. Wu, “Mixed-mode twisted-nematic cell for transmissive liquid crystal display,” Displays 20(5), 231–236 (1999).
[Crossref]

Wu, S.-T.

T.-H. Lin, Y. Huang, A. Y. G. Fuh, and S.-T. Wu, “Polarization controllable Fresnel lens using dye-doped liquid crystals,” Opt. Express 14(6), 2359–2364 (2006).
[Crossref] [PubMed]

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

Y. Huang, T. X. Wu, and S.-T. Wu, “Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method,” J. Appl. Phys. 93(5), 2490–2495 (2003).
[Crossref]

Wu, T. X.

Y. Huang, T. X. Wu, and S.-T. Wu, “Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method,” J. Appl. Phys. 93(5), 2490–2495 (2003).
[Crossref]

Yeh, H.-C.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

J. S. Patel and S.-D. Lee, “Electrically tunable and polarization insensitive Fabry–Perot étalon with a liquid-crystal film,” Appl. Phys. Lett. 58(22), 2491–2493 (1991).
[Crossref]

Displays (1)

S. T. Wu and C. S. Wu, “Mixed-mode twisted-nematic cell for transmissive liquid crystal display,” Displays 20(5), 231–236 (1999).
[Crossref]

IEEE Photonics Technol. Lett. (1)

C.-H. Lin, H.-Y. Huang, and J.-Y. Wang, “Polarization-independent liquid-crystal Fresnel lenses based on surface-mode switching of 90° twisted-nematic liquid crystals,” IEEE Photonics Technol. Lett. 22(3), 137–139 (2010).
[Crossref]

J. Appl. Phys. (2)

G.-S. Chen and H.-C. Yeh, “Polarization-selective color-filter Fresnel lens in polymer-stabilized cholesteric liquid crystals,” J. Appl. Phys. 112(5), 054501 (2012).
[Crossref]

Y. Huang, T. X. Wu, and S.-T. Wu, “Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method,” J. Appl. Phys. 93(5), 2490–2495 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Other (1)

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, 1999), Chap. 5.

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Figures (7)

Fig. 1
Fig. 1 Schematic of the orientations of the polarizer axes and LC directors of a 90° TN cell in the xy plane.
Fig. 2
Fig. 2 Normalized transmittance T of a 90° TN cell as a function of dΔn /λ and β.
Fig. 3
Fig. 3 Distribution of the (a) tilt angle and (b) twist angle of the LC director in a 90° TN cell along the z axis for different applied voltages.
Fig. 4
Fig. 4 Calculated diffraction efficiency of 90° TN Fresnel lenses with (a) d = 8.8 μm and (b) d = 10 μm as a function of the voltage applied to the odd zones and polarization direction β for the wavelength of 633 nm.
Fig. 5
Fig. 5 Experimental setup for examining the focusing characteristics of the 90° TN Fresnel zone plate. L, lens; I, iris diaphragm; P, polarizer; λ/4 WP, quarter-wave plate for 633 nm; S, sample; AC, alternating-current power supply; D, detector.
Fig. 6
Fig. 6 Microscope images of the 90° TN Fresnel lens under crossed polarizers at (a) 0, (b) 1.4, (c) 2, (d) 3, (e) 4, and (f) 10 V, and a magnified view of images obtained at (g) 3, (h) 4, and (i) 10 V. P and A denote the transmission axes of the polarizer and analyzer, respectively, and R denotes the rubbing direction.
Fig. 7
Fig. 7 (a) Diffraction efficiency of the 90° TN Fresnel lens as a function of the applied voltage and β. (b) The intensity profile and focusing pattern in the focal plane at β = 0° and an applied voltage of 1.4 V.

Equations (7)

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T = cos 2 X+ ( Γ 2X cos2β ) 2 sin 2 X,
dΔn λ = ( q 2 1 4 ) 1/2 ,
V th =π k 11 + ( k 33 2 k 22 ) /4 ε 0 Δε .
r m 2 =m r 1 2 ,
f= r 1 2 λ ,
A n = 1 2 r 1 2 0 2 r 1 2 E out exp( iπn r 2 r 1 2 ) d( r 2 ) = 1 2 r 1 2 [ 0 r 1 2 E outodd exp( iπn r 2 r 1 2 ) d( r 2 )+ r 1 2 2 r 1 2 E outeven exp( iπn r 2 r 1 2 ) d( r 2 ) ],
η= | A 1 | 2 | E in | 2 = | E outodd E outeven | 2 π 2 | E in | 2 ,

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