Abstract

Blue phase liquid crystal Dammann grating is demonstrated as an optical array generator. The phase profile is formed by the alternation of isotropic refractive index and vertical field induced ordinary index. Periodical Dammann grating can generate equal energy distributed optical array. When forked dislocations are introduced, multiple optical vortex beams with different topological charges are generated. This approach supplies a novel design for fast-response optical array generator, which has great potentials in array illumination, beam shaping and optical communications.

© 2016 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (1)

2015 (5)

J. Yu, C. Zhou, W. Jia, J. Wu, L. Zhu, Y. Lu, C. Xiang, and S. Li, “Generation of controllable rotating petal-like modes using composited Dammann vortex gratings,” Appl. Opt. 54(7), 1667–1672 (2015).
[Crossref]

D. Xu, G. Tan, and S. T. Wu, “Large-angle and high-efficiency tunable phase grating using fringe field switching liquid crystal,” Opt. Express 23(9), 12274–12285 (2015).
[Crossref] [PubMed]

J. Yan, Y. Xing, and Q. Li, “Dual-period tunable phase grating using polymer stabilized blue phase liquid crystal,” Opt. Lett. 40(19), 4520–4523 (2015).
[Crossref] [PubMed]

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133 (2015).
[Crossref]

2014 (5)

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S. T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

Y. Liu, Y. Lan, Q. Hong, and S. T. Wu, “Compensation film designs for high contrast wide-view blue phase liquid crystal displays,” J. Disp. Technol. 10(1), 3–6 (2014).
[Crossref]

S. C. Chen, P. C. Wu, and W. Lee, “Dielectric and phase behaviors of blue-phase liquid crystals,” Opt. Mater. Express 4(11), 2392–2400 (2014).
[Crossref]

S. J. Ge, W. Ji, G. X. Cui, B. Y. Wei, W. Hu, and Y. Q. Lu, “Fast switchable optical vortex generator based on blue phase liquid crystal fork grating,” Opt. Mater. Express 4(12), 2535–2541 (2014).
[Crossref]

2013 (2)

D. Luo, H. T. Dai, and X. W. Sun, “Polarization-independent electrically tunable/switchable Airy beam based on polymer-stabilized blue phase liquid crystal,” Opt. Express 21(25), 31318–31323 (2013).
[Crossref] [PubMed]

Y. T. Lin, H. C. Jau, and T. H. Lin, “Polarization-independent rapidly responding phase grating based on hybrid blue phase liquid crystal,” J. Appl. Phys. 113(6), 063103 (2013).
[Crossref]

2012 (5)

G. Zhu, J. N. Li, X. W. Lin, H. F. Wang, W. Hu, Z. G. Zheng, H. Q. Cui, D. Shen, and Y. Q. Lu, “Polarization-independent blue phase liquid crystal gratings driven by vertical electric field,” J. Soc. Inf. Disp. 20(6), 341–346 (2012).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

J. L. Zhu, J. G. Lu, J. Qiang, E. W. Zhong, Z. C. Ye, Z. He, X. Guo, C. Y. Dong, Y. Su, and H. P. D. Shieh, “1D/2D switchable grating based on field-induced polymer stabilized blue phase liquid crystal,” J. Appl. Phys. 111(3), 033101 (2012).
[Crossref]

J. Yu, C. Zhou, W. Jia, A. Hu, W. Cao, J. Wu, and S. Wang, “Three-dimensional Dammann vortex array with tunable topological charge,” Appl. Opt. 51(13), 2485–2490 (2012).
[Crossref] [PubMed]

H. Wu, W. Hu, H. C. Hu, X. W. Lin, G. Zhu, J. W. Choi, V. Chigrinov, and Y. Q. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20(15), 16684–16689 (2012).
[Crossref]

2011 (4)

2010 (5)

Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

J. Yan, H. C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S. T. Wu, “Extended Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett. 96(7), 071105 (2010).
[Crossref]

L. Rao, Z. Ge, S. Gauza, K. M. Chen, and S. T. Wu, “Emerging liquid crystal displays based on the Kerr effect,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 527(1), 30–42 (2010).
[Crossref]

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X. C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35(10), 1536–1538 (2010).
[Crossref] [PubMed]

N. Zhang, X. C. Yuan, and R. E. Burge, “Extending the detection range of optical vortices by Dammann vortex gratings,” Opt. Lett. 35(20), 3495–3497 (2010).
[Crossref] [PubMed]

2009 (1)

Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu, “Electro-optics of polymer-stabilized blue phase liquid crystal displays,” Appl. Phys. Lett. 94(10), 101104 (2009).
[Crossref]

2004 (1)

2002 (1)

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[Crossref] [PubMed]

1995 (1)

1989 (1)

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36(12), 1559–1573 (1989).
[Crossref]

1986 (1)

1977 (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of 2-dimensional periodic structures,” Opt. Acta (Lond.) 24(4), 505–515 (1977).
[Crossref]

1972 (1)

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Barnett, S.

Boivin, L. P.

Burge, R. E.

Cao, W.

Chen, H. S.

Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

Chen, K. M.

L. Rao, Z. Ge, S. Gauza, K. M. Chen, and S. T. Wu, “Emerging liquid crystal displays based on the Kerr effect,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 527(1), 30–42 (2010).
[Crossref]

Chen, P.

W. Duan, P. Chen, B. Y. Wei, S. J. Ge, X. Liang, W. Hu, and Y. Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6(2), 597–602 (2016).
[Crossref]

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133 (2015).
[Crossref]

Chen, S. C.

Chen, Y.

D. Xu, J. Yan, J. Yuan, F. Peng, Y. Chen, and S. T. Wu, “Electro-optic response of polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 105(1), 011119 (2014).
[Crossref]

Y. Chen, J. Yan, J. Sun, S. T. Wu, X. Liang, S. H. Liu, P. J. Hsieh, K. L. Cheng, and J. W. Shiu, “A microsecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 99(20), 201105 (2011).
[Crossref]

Cheng, H. C.

J. Yan, H. C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S. T. Wu, “Extended Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett. 96(7), 071105 (2010).
[Crossref]

Cheng, K. L.

Y. Chen, J. Yan, J. Sun, S. T. Wu, X. Liang, S. H. Liu, P. J. Hsieh, K. L. Cheng, and J. W. Shiu, “A microsecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 99(20), 201105 (2011).
[Crossref]

Chigrinov, V.

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133 (2015).
[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

H. Wu, W. Hu, H. C. Hu, X. W. Lin, G. Zhu, J. W. Choi, V. Chigrinov, and Y. Q. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20(15), 16684–16689 (2012).
[Crossref]

Choi, J. W.

Cottrell, D. M.

Courtial, J.

Cui, G. X.

Cui, H. Q.

G. Zhu, J. N. Li, X. W. Lin, H. F. Wang, W. Hu, Z. G. Zheng, H. Q. Cui, D. Shen, and Y. Q. Lu, “Polarization-independent blue phase liquid crystal gratings driven by vertical electric field,” J. Soc. Inf. Disp. 20(6), 341–346 (2012).
[Crossref]

Dai, H. T.

Dammann, H.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of 2-dimensional periodic structures,” Opt. Acta (Lond.) 24(4), 505–515 (1977).
[Crossref]

Davis, J. A.

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dong, C. Y.

J. L. Zhu, J. G. Lu, J. Qiang, E. W. Zhong, Z. C. Ye, Z. He, X. Guo, C. Y. Dong, Y. Su, and H. P. D. Shieh, “1D/2D switchable grating based on field-induced polymer stabilized blue phase liquid crystal,” J. Appl. Phys. 111(3), 033101 (2012).
[Crossref]

Duan, W.

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Franke-Arnold, S.

Gauza, S.

J. Yan, H. C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S. T. Wu, “Extended Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett. 96(7), 071105 (2010).
[Crossref]

L. Rao, Z. Ge, S. Gauza, K. M. Chen, and S. T. Wu, “Emerging liquid crystal displays based on the Kerr effect,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 527(1), 30–42 (2010).
[Crossref]

Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu, “Electro-optics of polymer-stabilized blue phase liquid crystal displays,” Appl. Phys. Lett. 94(10), 101104 (2009).
[Crossref]

Ge, S. J.

Ge, Z.

L. Rao, Z. Ge, S. Gauza, K. M. Chen, and S. T. Wu, “Emerging liquid crystal displays based on the Kerr effect,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 527(1), 30–42 (2010).
[Crossref]

Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu, “Electro-optics of polymer-stabilized blue phase liquid crystal displays,” Appl. Phys. Lett. 94(10), 101104 (2009).
[Crossref]

Gibson, G.

Guo, X.

J. L. Zhu, J. G. Lu, J. Qiang, E. W. Zhong, Z. C. Ye, Z. He, X. Guo, C. Y. Dong, Y. Su, and H. P. D. Shieh, “1D/2D switchable grating based on field-induced polymer stabilized blue phase liquid crystal,” J. Appl. Phys. 111(3), 033101 (2012).
[Crossref]

He, Z.

J. L. Zhu, J. G. Lu, J. Qiang, E. W. Zhong, Z. C. Ye, Z. He, X. Guo, C. Y. Dong, Y. Su, and H. P. D. Shieh, “1D/2D switchable grating based on field-induced polymer stabilized blue phase liquid crystal,” J. Appl. Phys. 111(3), 033101 (2012).
[Crossref]

Hisakado, Y.

H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
[Crossref] [PubMed]

Hong, Q.

Y. Liu, Y. Lan, Q. Hong, and S. T. Wu, “Compensation film designs for high contrast wide-view blue phase liquid crystal displays,” J. Disp. Technol. 10(1), 3–6 (2014).
[Crossref]

Hsieh, P. J.

Y. Chen, J. Yan, J. Sun, S. T. Wu, X. Liang, S. H. Liu, P. J. Hsieh, K. L. Cheng, and J. W. Shiu, “A microsecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 99(20), 201105 (2011).
[Crossref]

Hsu, H. K.

Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

Hu, A.

Hu, H. C.

Hu, W.

W. Duan, P. Chen, B. Y. Wei, S. J. Ge, X. Liang, W. Hu, and Y. Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6(2), 597–602 (2016).
[Crossref]

P. Chen, B. Y. Wei, W. Ji, S. J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133 (2015).
[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
[Crossref] [PubMed]

S. J. Ge, W. Ji, G. X. Cui, B. Y. Wei, W. Hu, and Y. Q. Lu, “Fast switchable optical vortex generator based on blue phase liquid crystal fork grating,” Opt. Mater. Express 4(12), 2535–2541 (2014).
[Crossref]

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[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26(10), 1590–1595 (2014).
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S. J. Ge, W. Ji, G. X. Cui, B. Y. Wei, W. Hu, and Y. Q. Lu, “Fast switchable optical vortex generator based on blue phase liquid crystal fork grating,” Opt. Mater. Express 4(12), 2535–2541 (2014).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002).
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T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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Figures (3)

Fig. 1
Fig. 1 Phase structures of (a) DG and (e) DVG, where black for 0 and white for π. Micrographs of (b) DG and (f) DVG patterned electrodes. Micrographs of PSBPLC cells at (c), (g) voltage-off state and (d), (h) voltage-on state with 180 V applied. The scale bars are all 100 μm.
Fig. 2
Fig. 2 Light energy distribution in the 1 × 7 diffraction orders of (a) DG and (b) DVG. The insets are corresponding photos of diffraction patterns with 180 V applied.
Fig. 3
Fig. 3 EO response of the BPLC DVG. The voltage-off state is shown as inset.

Equations (6)

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T DG (x)= n= C n exp(in 2π Λ x) ,
T DG (x,θ)= n= C n exp[ in( 2π Λ x+mθ) ] .
C n ={ iΛ 2nπ [ 1+2 k=1 N1 (1) k exp(i2πn x k ) + (1) N exp(i2πn x N ) ] n0 Λ[ 2 k=1 N1 (1) k x k + (1) N x N ] n=0 ,
Δn(E)=Δ n sat ( 1exp[ ( E E S ) 2 ] ),
n o (E)= n i Δn(E) 3 ,
Γ= 2π λ [ n i n o (E)]d,

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