Abstract

A varied-line-spacing switchable holographic grating is demonstrated through a changeable interference pattern recorded in polymer-dispersed liquid crystal. The pattern is generated by the interference between one plane wave and another cylindrical wave. The line spacing and the period of grating can be controlled by varying the distance between the cylindrical lens and the grating sample and by changing the exposure angle between the two beams. Experimental period measurements and calculations show good agreement with the theoretical results. High diffraction efficiency of more than 80% for the middle period of the grating has been achieved under appropriate exposure time of 120 s and intensity of 19.1  mW/cm2. In addition, the diffraction can be switched on and off by virtue of the external driving voltage of approximately 120 V. The grating also possesses a fast response with a rise time of 300 μs and a fall time of 750 μs. This grating, which can change the period in the grating structure to allow switchable diffraction of transmitted light, shows great potential application for diffractive optics.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2015 (1)

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

2014 (2)

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

P. C. Wu, E. R. Yeh, V. Y. Zyryanov, and W. Lee, “Spatial and electrical switching of defect modes in a photonic bandgap device with a polymer-dispersed liquid crystal defect layer,” Opt. Express 22, 20278–20283 (2014).
[Crossref]

2013 (2)

M. H. Zhang, J. H. Zheng, K. Gui, K. N. Wang, C. H. Guo, X. P. Wei, and S. L. Zhuang, “Electro-optical characteristics of holographic polymer dispersed liquid crystal gratings doped with nanosilver,” Appl. Opt. 52, 7411–7418 (2013).
[Crossref]

S. Bronnikov, S. Kostromin, and V. Zuev, “Polymer-dispersed liquid crystals: progress in preparation, investigation, and application,” J. Macromol. Sci. Part B 52, 1718–1735 (2013).
[Crossref]

2012 (2)

2011 (1)

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbuaian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[Crossref]

2008 (2)

Y. J. Liu and X. W. Sun, “Holographic polymer-dispersed liquid crystals: materials, formation, and applications,” Adv. Optoelectron. 2008, 1–52 (2008).
[Crossref]

A. Y. Fuh and T. H. Lin, “Electrically switchable spatial filter based on polymer-dispersed liquid crystal film,” J. Appl. Phys. 96, 5402–5404 (2008).
[Crossref]

2007 (1)

2006 (2)

J. Lou, S. J. Fu, X. D. Xu, and S. P. He, “Design and fabrication of holographic variable line-spacing gratings for position sensor,” Acta Phys. Sin. 55, 6405–6409 (2006).

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
[Crossref]

2005 (1)

H. F. Zhu, J. W. Chen, H. Y. Gao, H. L. Xie, and Z. Z. Xu, “A new method to produce high spatial frequency grating with variable spacing,” Acta Phys. Sin. 54, 682–686 (2005).

2004 (2)

Y. J. Xie, X. D. Xu, Y. L. Hong, Y. Liu, S. J. Fu, S. P. He, and B. K. Jin, “Fabrication of varied-line-spacing grating by elastic medium,” Opt. Express 12, 3894–3899 (2004).
[Crossref]

J. Lou, Y. Liu, S. J. Fu, X. D. Xu, and S. P. He, “Design of variable line-space plane gratings with holographic recording,” Proc. SPIE 5636, 551–559 (2004).
[Crossref]

2003 (1)

L. Petti, P. Mormile, and W. J. Blau, “Fast electro-optical switching and high contrast ratio in epoxy-based polymer dispersed liquid crystals,” Opt. Laser Eng. 39, 369–377 (2003).
[Crossref]

2000 (2)

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[Crossref]

L. Poletto and G. Tondello, “Spherical-grating monochromator with a variable-line-spaced grating for synchrotron radiation,” Appl. Opt. 39, 5671–5678 (2000).
[Crossref]

1997 (1)

1986 (1)

J. W. Chen, S. F. Fu, D. K. Zhang, Z. F. Qi, S. Yang, and Z. J. Wang, “Producing grating with variable spacing,” Chin. J. Lasers 13, 291–295 (1986).

Blau, W. J.

L. Petti, P. Mormile, and W. J. Blau, “Fast electro-optical switching and high contrast ratio in epoxy-based polymer dispersed liquid crystals,” Opt. Laser Eng. 39, 369–377 (2003).
[Crossref]

Bronnikov, S.

S. Bronnikov, S. Kostromin, and V. Zuev, “Polymer-dispersed liquid crystals: progress in preparation, investigation, and application,” J. Macromol. Sci. Part B 52, 1718–1735 (2013).
[Crossref]

Bunning, T. J.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[Crossref]

Chen, J. W.

H. F. Zhu, J. W. Chen, H. Y. Gao, H. L. Xie, and Z. Z. Xu, “A new method to produce high spatial frequency grating with variable spacing,” Acta Phys. Sin. 54, 682–686 (2005).

J. W. Chen, S. F. Fu, D. K. Zhang, Z. F. Qi, S. Yang, and Z. J. Wang, “Producing grating with variable spacing,” Chin. J. Lasers 13, 291–295 (1986).

Chiuzbuaian, G. S.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbuaian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[Crossref]

Diao, Z. H.

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

Flechsig, U.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbuaian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[Crossref]

Fontecchio, A. K.

Fox, A. E.

Fu, S. F.

J. W. Chen, S. F. Fu, D. K. Zhang, Z. F. Qi, S. Yang, and Z. J. Wang, “Producing grating with variable spacing,” Chin. J. Lasers 13, 291–295 (1986).

Fu, S. J.

J. Lou, S. J. Fu, X. D. Xu, and S. P. He, “Design and fabrication of holographic variable line-spacing gratings for position sensor,” Acta Phys. Sin. 55, 6405–6409 (2006).

J. Lou, Y. Liu, S. J. Fu, X. D. Xu, and S. P. He, “Design of variable line-space plane gratings with holographic recording,” Proc. SPIE 5636, 551–559 (2004).
[Crossref]

Y. J. Xie, X. D. Xu, Y. L. Hong, Y. Liu, S. J. Fu, S. P. He, and B. K. Jin, “Fabrication of varied-line-spacing grating by elastic medium,” Opt. Express 12, 3894–3899 (2004).
[Crossref]

Fuh, A. Y.

M. S. Li, A. Y. Fuh, J. H. Liu, and S. T. Wu, “Bichromatic optical switch of diffractive light from a BCT photonic crystal based on an azo component-doped HPDLC,” Opt. Express 20, 25545–25553 (2012).
[Crossref]

A. Y. Fuh and T. H. Lin, “Electrically switchable spatial filter based on polymer-dispersed liquid crystal film,” J. Appl. Phys. 96, 5402–5404 (2008).
[Crossref]

Gao, H. Y.

H. F. Zhu, J. W. Chen, H. Y. Gao, H. L. Xie, and Z. Z. Xu, “A new method to produce high spatial frequency grating with variable spacing,” Acta Phys. Sin. 54, 682–686 (2005).

Gui, K.

Guo, C. H.

He, S. P.

J. Lou, S. J. Fu, X. D. Xu, and S. P. He, “Design and fabrication of holographic variable line-spacing gratings for position sensor,” Acta Phys. Sin. 55, 6405–6409 (2006).

Y. J. Xie, X. D. Xu, Y. L. Hong, Y. Liu, S. J. Fu, S. P. He, and B. K. Jin, “Fabrication of varied-line-spacing grating by elastic medium,” Opt. Express 12, 3894–3899 (2004).
[Crossref]

J. Lou, Y. Liu, S. J. Fu, X. D. Xu, and S. P. He, “Design of variable line-space plane gratings with holographic recording,” Proc. SPIE 5636, 551–559 (2004).
[Crossref]

Hong, Y. L.

Hu, L. F.

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

Huang, W. B.

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

Jannesari, A.

Jashnsaz, H.

Jin, B. K.

Kostromin, S.

S. Bronnikov, S. Kostromin, and V. Zuev, “Polymer-dispersed liquid crystals: progress in preparation, investigation, and application,” J. Macromol. Sci. Part B 52, 1718–1735 (2013).
[Crossref]

Lee, W.

Li, M. S.

Lin, T. H.

A. Y. Fuh and T. H. Lin, “Electrically switchable spatial filter based on polymer-dispersed liquid crystal film,” J. Appl. Phys. 96, 5402–5404 (2008).
[Crossref]

Liu, J. H.

Liu, L. J.

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

Liu, M. H.

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

Liu, Y.

J. Lou, Y. Liu, S. J. Fu, X. D. Xu, and S. P. He, “Design of variable line-space plane gratings with holographic recording,” Proc. SPIE 5636, 551–559 (2004).
[Crossref]

Y. J. Xie, X. D. Xu, Y. L. Hong, Y. Liu, S. J. Fu, S. P. He, and B. K. Jin, “Fabrication of varied-line-spacing grating by elastic medium,” Opt. Express 12, 3894–3899 (2004).
[Crossref]

Liu, Y. G.

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

Liu, Y. J.

Y. J. Liu and X. W. Sun, “Holographic polymer-dispersed liquid crystals: materials, formation, and applications,” Adv. Optoelectron. 2008, 1–52 (2008).
[Crossref]

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
[Crossref]

Lou, J.

J. Lou, S. J. Fu, X. D. Xu, and S. P. He, “Design and fabrication of holographic variable line-spacing gratings for position sensor,” Acta Phys. Sin. 55, 6405–6409 (2006).

J. Lou, Y. Liu, S. J. Fu, X. D. Xu, and S. P. He, “Design of variable line-space plane gratings with holographic recording,” Proc. SPIE 5636, 551–559 (2004).
[Crossref]

Ma, J.

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

Mohajerani, E.

Moike, M.

Mormile, P.

L. Petti, P. Mormile, and W. J. Blau, “Fast electro-optical switching and high contrast ratio in epoxy-based polymer dispersed liquid crystals,” Opt. Laser Eng. 39, 369–377 (2003).
[Crossref]

Mu, Q. Q.

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

Namioka, T.

Nataj, N. H.

Natarajan, L. V.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[Crossref]

Patthey, L.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbuaian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[Crossref]

Peng, Z. H.

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

Petti, L.

L. Petti, P. Mormile, and W. J. Blau, “Fast electro-optical switching and high contrast ratio in epoxy-based polymer dispersed liquid crystals,” Opt. Laser Eng. 39, 369–377 (2003).
[Crossref]

Poletto, L.

Qi, Z. F.

J. W. Chen, S. F. Fu, D. K. Zhang, Z. F. Qi, S. Yang, and Z. J. Wang, “Producing grating with variable spacing,” Chin. J. Lasers 13, 291–295 (1986).

Rai, K.

Schmitt, T.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbuaian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[Crossref]

Strocov, V. N.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbuaian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[Crossref]

Sun, X. W.

Y. J. Liu and X. W. Sun, “Holographic polymer-dispersed liquid crystals: materials, formation, and applications,” Adv. Optoelectron. 2008, 1–52 (2008).
[Crossref]

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006).
[Crossref]

Sutherland, R. L.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[Crossref]

Tondello, G.

Tondiglia, V. P.

T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30, 83–115 (2000).
[Crossref]

Wang, K. N.

Wang, Z. J.

J. W. Chen, S. F. Fu, D. K. Zhang, Z. F. Qi, S. Yang, and Z. J. Wang, “Producing grating with variable spacing,” Chin. J. Lasers 13, 291–295 (1986).

Wei, X. P.

Wu, P. C.

Wu, S. T.

Xie, H. L.

H. F. Zhu, J. W. Chen, H. Y. Gao, H. L. Xie, and Z. Z. Xu, “A new method to produce high spatial frequency grating with variable spacing,” Acta Phys. Sin. 54, 682–686 (2005).

Xie, Y. J.

Xu, X. D.

J. Lou, S. J. Fu, X. D. Xu, and S. P. He, “Design and fabrication of holographic variable line-spacing gratings for position sensor,” Acta Phys. Sin. 55, 6405–6409 (2006).

Y. J. Xie, X. D. Xu, Y. L. Hong, Y. Liu, S. J. Fu, S. P. He, and B. K. Jin, “Fabrication of varied-line-spacing grating by elastic medium,” Opt. Express 12, 3894–3899 (2004).
[Crossref]

J. Lou, Y. Liu, S. J. Fu, X. D. Xu, and S. P. He, “Design of variable line-space plane gratings with holographic recording,” Proc. SPIE 5636, 551–559 (2004).
[Crossref]

Xu, Z. Z.

H. F. Zhu, J. W. Chen, H. Y. Gao, H. L. Xie, and Z. Z. Xu, “A new method to produce high spatial frequency grating with variable spacing,” Acta Phys. Sin. 54, 682–686 (2005).

Xuan, L.

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

Z. H. Diao, W. B. Huang, Z. H. Peng, Q. Q. Mu, Y. G. Liu, J. Ma, and L. Xuan, “Anisotropic waveguide theory for electrically tunable distributed feedback laser from dye-doped holographic polymer dispersed liquid crystal,” Liq. Cryst. 41, 239–246 (2014).
[Crossref]

Yang, S.

J. W. Chen, S. F. Fu, D. K. Zhang, Z. F. Qi, S. Yang, and Z. J. Wang, “Producing grating with variable spacing,” Chin. J. Lasers 13, 291–295 (1986).

Yeh, E. R.

Zhang, D. K.

J. W. Chen, S. F. Fu, D. K. Zhang, Z. F. Qi, S. Yang, and Z. J. Wang, “Producing grating with variable spacing,” Chin. J. Lasers 13, 291–295 (1986).

Zhang, G. Y.

L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

Zhang, M. H.

Zheng, J. H.

Zhu, H. F.

H. F. Zhu, J. W. Chen, H. Y. Gao, H. L. Xie, and Z. Z. Xu, “A new method to produce high spatial frequency grating with variable spacing,” Acta Phys. Sin. 54, 682–686 (2005).

Zhuang, S. L.

Zuev, V.

S. Bronnikov, S. Kostromin, and V. Zuev, “Polymer-dispersed liquid crystals: progress in preparation, investigation, and application,” J. Macromol. Sci. Part B 52, 1718–1735 (2013).
[Crossref]

Zyryanov, V. Y.

Acta Phys. Sin. (2)

J. Lou, S. J. Fu, X. D. Xu, and S. P. He, “Design and fabrication of holographic variable line-spacing gratings for position sensor,” Acta Phys. Sin. 55, 6405–6409 (2006).

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Adv. Optoelectron. (1)

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[Crossref]

Appl. Opt. (5)

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[Crossref]

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J. Appl. Phys. (1)

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[Crossref]

J. Macromol. Sci. Part B (1)

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[Crossref]

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L. J. Liu, L. Xuan, G. Y. Zhang, M. H. Liu, L. F. Hu, Y. G. Liu, and J. Ma, “Enhancement of pump efficiency for an organic distributed feedback laser based on a holographic polymer dispersed liquid crystal as an external light feedback layer,” J. Mater. Chem. C 3, 5566–5572 (2015).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic illustration of the experimental setup for fabricating VLS H-PDLC gratings. (b) Interference pattern showing the varied strip within PDLC. (c) Diagram of varied exposure angles interacting on the sample surface.
Fig. 2.
Fig. 2. Diffraction patterns of VLS H-PDLC gratings. We detected the diffraction on different positions of grating with x i = 6.4 , 4, 2.5, 0.7 , 3 , and 6.1    mm .
Fig. 3.
Fig. 3. AFM images of VLS H-PDLC grating samples: (a)  Λ 1 = 1851    nm ( x i = 3.3    mm ), (b)  Λ 2 = 1695    nm ( x i = 3.1    mm ), and (c)  Λ 3 = 1587    nm ( x i = 7.7    mm ).
Fig. 4.
Fig. 4. Grating period as a function of the (a) exposure angle and (b) distance between the cylindrical lens and the sample. The lines represent theoretical results and the dots show experimental results.
Fig. 5.
Fig. 5. Diffraction efficiency of gratings as a function of (a) exposure time and (b) recording optical intensity, as well as average diffraction efficiency values versus (c) exposure times and (d) exposure intensity.
Fig. 6.
Fig. 6. Measurements for electro-optic characteristics of VLS H-PDLC gratings: (a) measured diffraction efficiency as a function of bias voltage and (b) measured rise and fall time.

Equations (6)

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Λ = λ sin θ ,
U 0 ( x , y ) = A exp [ i k ( n 1 ) x 2 2 R ] ,
U 1 ( x i , y i ) = A i λ D P ( x , y ) exp [ i k ( n 1 ) x 2 2 R ] · exp { i k 2 D [ ( x i x ) 2 + ( y i y ) 2 ] } d x d y ,
U 2 ( x i , y i ) = A exp [ i 2 π λ x i sin θ 0 ] .
I ( x i , y i ) = | U 1 ( x i , y i ) + U 2 ( x i , y i ) | 2 .
Λ = λ ( n 1 ) · x i D ( n 1 ) R + sin θ 0 .

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