Abstract

Diffractive optical devices using low-molar-mass liquid crystals are of great important for realizing numerical optical functions such as optical memory and information systems. In the present study the liquid crystalline gratings have been fabricated using a pair of photo-alignment substrates, and effects of the phase shift between the two photo-alignment substrates on the diffraction properties have been investigated. The liquid crystalline grating has been constructed with variable polarization dependence that can be controlled by the phase shift between the two photo-alignment substrates and twisted angles of the nematic directors. The theoretical considerations were also performed using the elastic continuum theory, Jones calculus, and diffraction theory. A guiding principle that controls the diffraction properties of the liquid crystalline grating cell was successfully presented.

© 2009 Optical Society of America

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  1. J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
    [CrossRef]
  2. C.-J. Yu, J.-H. Park, J. Kim, M.-S. Jung, and S.-D. Lee, “Design of binary diffraction gratings of liquid crystals in a linearly graded phase model,” Appl. Opt. 43, 1783-1788 (2004).
    [CrossRef] [PubMed]
  3. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
    [CrossRef]
  4. T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Liquid-crystal phase gratings using photoregulated photocrosslinkable polymer liquid crystal,” Appl. Phys. Lett. 87, 161112(2005).
    [CrossRef]
  5. V. Kapoustine, A. Kazakevitch, V. So, and R. Tam, “Simple method of formation of switchable liquid crystal gratings by introducing periodic photoalignment pattern into liquid crystal cell,” Opt. Commun. 266, 1-5 (2006).
    [CrossRef]
  6. V. Presnyakov, K. Asatryan, T. Galstian, and V. Chigrinov, “Optical polarization grating induced liquid crystal micro-structure using azo-dye command layer,” Opt. Express 14, 10558-10564 (2006).
    [CrossRef] [PubMed]
  7. R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701 (2007).
    [CrossRef]
  8. H. Ono, S. Oikawa, and N. Kawatsuki, “Effects of anchoring strength on diffraction properties of liquid crystal phase gratings formed on photoalignment polymer films,” J. Appl. Phys. 101, 123523 (2007).
    [CrossRef]
  9. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Electrically tunable two-dimensional liquid crystals gratings induced by polarization holography,” Opt. Express 15, 5872-5878 (2007).
    [CrossRef] [PubMed]
  10. T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Diffraction properties of nematic phase gratings with photoregulated liquid crystal cells,” Jpn. J. Appl. Phys. 46, 698-702 (2007).
    [CrossRef]
  11. W. Y. Wu, M. S. Li, H. C. Lin, and A. Y.-G. Fuh, “Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films,” J. Appl. Phys. 103, 083119 (2008).
    [CrossRef]

2008 (1)

W. Y. Wu, M. S. Li, H. C. Lin, and A. Y.-G. Fuh, “Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films,” J. Appl. Phys. 103, 083119 (2008).
[CrossRef]

2007 (4)

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701 (2007).
[CrossRef]

H. Ono, S. Oikawa, and N. Kawatsuki, “Effects of anchoring strength on diffraction properties of liquid crystal phase gratings formed on photoalignment polymer films,” J. Appl. Phys. 101, 123523 (2007).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Diffraction properties of nematic phase gratings with photoregulated liquid crystal cells,” Jpn. J. Appl. Phys. 46, 698-702 (2007).
[CrossRef]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Electrically tunable two-dimensional liquid crystals gratings induced by polarization holography,” Opt. Express 15, 5872-5878 (2007).
[CrossRef] [PubMed]

2006 (2)

V. Presnyakov, K. Asatryan, T. Galstian, and V. Chigrinov, “Optical polarization grating induced liquid crystal micro-structure using azo-dye command layer,” Opt. Express 14, 10558-10564 (2006).
[CrossRef] [PubMed]

V. Kapoustine, A. Kazakevitch, V. So, and R. Tam, “Simple method of formation of switchable liquid crystal gratings by introducing periodic photoalignment pattern into liquid crystal cell,” Opt. Commun. 266, 1-5 (2006).
[CrossRef]

2005 (2)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Liquid-crystal phase gratings using photoregulated photocrosslinkable polymer liquid crystal,” Appl. Phys. Lett. 87, 161112(2005).
[CrossRef]

2004 (1)

2003 (1)

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
[CrossRef]

Asatryan, K.

Callan-Jones, A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Chigrinov, V.

Chung, S.-Y.

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
[CrossRef]

Cipparrone, G.

Crawford, G. P.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Eakin, J. N.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Escuti, M. J.

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701 (2007).
[CrossRef]

Fuh, A. Y.-G.

W. Y. Wu, M. S. Li, H. C. Lin, and A. Y.-G. Fuh, “Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films,” J. Appl. Phys. 103, 083119 (2008).
[CrossRef]

Galstian, T.

Jung, M.-S.

Kapoustine, V.

V. Kapoustine, A. Kazakevitch, V. So, and R. Tam, “Simple method of formation of switchable liquid crystal gratings by introducing periodic photoalignment pattern into liquid crystal cell,” Opt. Commun. 266, 1-5 (2006).
[CrossRef]

Kawatsuki, N.

H. Ono, S. Oikawa, and N. Kawatsuki, “Effects of anchoring strength on diffraction properties of liquid crystal phase gratings formed on photoalignment polymer films,” J. Appl. Phys. 101, 123523 (2007).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Diffraction properties of nematic phase gratings with photoregulated liquid crystal cells,” Jpn. J. Appl. Phys. 46, 698-702 (2007).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Liquid-crystal phase gratings using photoregulated photocrosslinkable polymer liquid crystal,” Appl. Phys. Lett. 87, 161112(2005).
[CrossRef]

Kazakevitch, A.

V. Kapoustine, A. Kazakevitch, V. So, and R. Tam, “Simple method of formation of switchable liquid crystal gratings by introducing periodic photoalignment pattern into liquid crystal cell,” Opt. Commun. 266, 1-5 (2006).
[CrossRef]

Kim, J.

C.-J. Yu, J.-H. Park, J. Kim, M.-S. Jung, and S.-D. Lee, “Design of binary diffraction gratings of liquid crystals in a linearly graded phase model,” Appl. Opt. 43, 1783-1788 (2004).
[CrossRef] [PubMed]

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
[CrossRef]

Komanduri, R. K.

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701 (2007).
[CrossRef]

Kuwabara, M.

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Diffraction properties of nematic phase gratings with photoregulated liquid crystal cells,” Jpn. J. Appl. Phys. 46, 698-702 (2007).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Liquid-crystal phase gratings using photoregulated photocrosslinkable polymer liquid crystal,” Appl. Phys. Lett. 87, 161112(2005).
[CrossRef]

Lee, S.-D.

C.-J. Yu, J.-H. Park, J. Kim, M.-S. Jung, and S.-D. Lee, “Design of binary diffraction gratings of liquid crystals in a linearly graded phase model,” Appl. Opt. 43, 1783-1788 (2004).
[CrossRef] [PubMed]

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
[CrossRef]

Li, M. S.

W. Y. Wu, M. S. Li, H. C. Lin, and A. Y.-G. Fuh, “Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films,” J. Appl. Phys. 103, 083119 (2008).
[CrossRef]

Lin, H. C.

W. Y. Wu, M. S. Li, H. C. Lin, and A. Y.-G. Fuh, “Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films,” J. Appl. Phys. 103, 083119 (2008).
[CrossRef]

Oikawa, S.

H. Ono, S. Oikawa, and N. Kawatsuki, “Effects of anchoring strength on diffraction properties of liquid crystal phase gratings formed on photoalignment polymer films,” J. Appl. Phys. 101, 123523 (2007).
[CrossRef]

Ono, H.

H. Ono, S. Oikawa, and N. Kawatsuki, “Effects of anchoring strength on diffraction properties of liquid crystal phase gratings formed on photoalignment polymer films,” J. Appl. Phys. 101, 123523 (2007).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Diffraction properties of nematic phase gratings with photoregulated liquid crystal cells,” Jpn. J. Appl. Phys. 46, 698-702 (2007).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Liquid-crystal phase gratings using photoregulated photocrosslinkable polymer liquid crystal,” Appl. Phys. Lett. 87, 161112(2005).
[CrossRef]

Pagliusi, P.

Park, J.-H.

C.-J. Yu, J.-H. Park, J. Kim, M.-S. Jung, and S.-D. Lee, “Design of binary diffraction gratings of liquid crystals in a linearly graded phase model,” Appl. Opt. 43, 1783-1788 (2004).
[CrossRef] [PubMed]

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
[CrossRef]

Pelcovits, R. A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Presnyakov, V.

Provenzano, C.

Radcliffe, M. D.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Sasaki, T.

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Diffraction properties of nematic phase gratings with photoregulated liquid crystal cells,” Jpn. J. Appl. Phys. 46, 698-702 (2007).
[CrossRef]

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Liquid-crystal phase gratings using photoregulated photocrosslinkable polymer liquid crystal,” Appl. Phys. Lett. 87, 161112(2005).
[CrossRef]

So, V.

V. Kapoustine, A. Kazakevitch, V. So, and R. Tam, “Simple method of formation of switchable liquid crystal gratings by introducing periodic photoalignment pattern into liquid crystal cell,” Opt. Commun. 266, 1-5 (2006).
[CrossRef]

Tam, R.

V. Kapoustine, A. Kazakevitch, V. So, and R. Tam, “Simple method of formation of switchable liquid crystal gratings by introducing periodic photoalignment pattern into liquid crystal cell,” Opt. Commun. 266, 1-5 (2006).
[CrossRef]

Wu, W. Y.

W. Y. Wu, M. S. Li, H. C. Lin, and A. Y.-G. Fuh, “Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films,” J. Appl. Phys. 103, 083119 (2008).
[CrossRef]

Yu, C.-J.

C.-J. Yu, J.-H. Park, J. Kim, M.-S. Jung, and S.-D. Lee, “Design of binary diffraction gratings of liquid crystals in a linearly graded phase model,” Appl. Opt. 43, 1783-1788 (2004).
[CrossRef] [PubMed]

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Liquid-crystal phase gratings using photoregulated photocrosslinkable polymer liquid crystal,” Appl. Phys. Lett. 87, 161112(2005).
[CrossRef]

J.-H. Park, C.-J. Yu, J. Kim, S.-Y. Chung, and S.-D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83, 1918-1920 (2003).
[CrossRef]

J. Appl. Phys. (3)

H. Ono, S. Oikawa, and N. Kawatsuki, “Effects of anchoring strength on diffraction properties of liquid crystal phase gratings formed on photoalignment polymer films,” J. Appl. Phys. 101, 123523 (2007).
[CrossRef]

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

W. Y. Wu, M. S. Li, H. C. Lin, and A. Y.-G. Fuh, “Two-dimensional holographic polarization grating formed on azo-dye-doped polyvinyl alcohol films,” J. Appl. Phys. 103, 083119 (2008).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Sasaki, H. Ono, N. Kawatsuki, and M. Kuwabara, “Diffraction properties of nematic phase gratings with photoregulated liquid crystal cells,” Jpn. J. Appl. Phys. 46, 698-702 (2007).
[CrossRef]

Opt. Commun. (1)

V. Kapoustine, A. Kazakevitch, V. So, and R. Tam, “Simple method of formation of switchable liquid crystal gratings by introducing periodic photoalignment pattern into liquid crystal cell,” Opt. Commun. 266, 1-5 (2006).
[CrossRef]

Opt. Express (2)

Phys. Rev. E (1)

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701 (2007).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic view for the liquid crystalline grating cell.

Fig. 2
Fig. 2

Spatial distribution of the director calculated using the elastic continuum theory (left-hand side pictures). The horizontal lines represent the projections of the director. The right-hand side pictures show the photograph of the liquid crystalline grating cells under polarization optical microscope. The directions of the analyzer and polarizer are indicated as arrows in each picture. The twisted angle was set to be 90 degrees. The phase shift between two photo-alignment substrates was (a) 0, (b)  0.2 π , and (c) π.

Fig. 3
Fig. 3

Diffraction efficiency versus polarization azimuth angle between the grating vector and polarization direction of the probe beam on varying the phase shift between two photo-alignment substrates. Open and filled circles represent the negative and positive first-order diffraction efficiency, respectively. The solid and dotted curves show the theoretical calculation. The twisted angle was set to be 90 degrees. The phase shift between two photo-alignment substrates was (a) 0, (b)  0.2 π , and (c) π.

Fig. 4
Fig. 4

Diffraction efficiency versus polarization azimuth angle between the grating vector and polarization direction of the probe beam on varying the twisted angle. Open and filled circles represent the negative and positive first-order diffraction efficiency, respectively. The solid and dotted curves show the theoretical calculation. The phase shift between two photo-alignment substrates was set to be 0.2 π . The twisted angle was (a) 90, (b) 45, and (c) 60 degrees.

Fig. 5
Fig. 5

Summary of the polarization dependence (left-hand side pictures) and maximum efficiency for the light diffraction in liquid crystalline gratings. Open and filled circles represent the negative and positive first-order diffraction efficiency, respectively. The solid and dotted curves show the theoretical calculation. The twisted angle was (a) 90, (b) 45, and (c) 60 degrees.

Equations (13)

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f elas = 1 2 K 11 ( · n ) 2 + 1 2 K 22 ( n · ( × n ) ) 2 + 1 2 K 33 ( n × ( × n ) ) 2 ,
n = ( cos ϕ , sin ϕ , 0 ) ,
f elas = 1 2 ( K 11 sin 2 ϕ + K 33 cos 2 ϕ ) ( ϕ x ) 2 + 1 2 K 22 ( ϕ z ) 2 .
F = f elas d x d z .
F ϕ = 0.
W = m = 1 N W m ,
W m = R ( ϕ m ) · W 0 · R ( ϕ m ) ,
R ( ϕ m ) = ( cos ϕ m sin ϕ m - sin ϕ m cos ϕ m ) ,
W 0 = ( e i Γ m / 2 0 0 e i Γ m / 2 ) .
Γ m = 2 π d m Δ n λ .
E out = W · E in ( E x E y ) ,
E in = ( cos χ sin χ ) ,
α = 1 η min η max ,

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