Abstract

The diffraction properties of reflective anisotropic gratings, which can be recorded in photoanisotropic media with uniaxial birefringence by three-dimensional vector holography, were characterized through the use of coupled-wave analysis (CWA). By investigating the perturbation of the dielectric tensor, we demonstrated that the gratings with sinusoidal distribution of the azimuthal angle of the optic axis diffract polarized light in which the ordinary and extraordinary components are converted for incident light. The polarization conversion was consistent with that calculated by a numerical method. In addition, it was shown that CWA enables highly accurate calculation of the diffraction efficiency with wavelength dispersion when the amplitude of the azimuthal angle is small.

© 2011 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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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2010 (1)

2008 (2)

T. Sasaki, H. Ono, and N. Kawatsuki, “Three-dimensional vector holograms in anisotropic photoreactive liquid-crystal composites,” Appl. Opt. 47, 2192–2200 (2008).
[CrossRef] [PubMed]

H. Ono, T. Sekiguchi, A. Emoto, T. Shioda, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

2007 (1)

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

2006 (4)

2005 (2)

H. Ono, T. Sasaki, A. Emoto, N. Kawatsuki, and E. Uchida, “Polarization gratings in twisted-nematic liquid-crystal composites doped with azobenzene dye,” Opt. Lett. 30, 1950–1952 (2005).
[CrossRef] [PubMed]

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

2003 (1)

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

2002 (2)

F.-L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

F. Ciuchi, A. Mazzulla, and G. Cipparrone, “Permanent polarization gratings in elastomer comparison of layered and mixed samples,” J. Opt. Soc. Am. B 19, 2531–2537 (2002).
[CrossRef]

2001 (1)

1997 (1)

1996 (1)

1993 (2)

T. Huang and K. H. Wagner, “Holographic diffraction in photoanisotropic organic materials,” J. Opt. Soc. Am. A 10, 306–315 (1993).
[CrossRef]

I. C. Khoo, H. Li, and Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447(1993).
[CrossRef]

1990 (1)

A. Lien, “Extended Jones matrix method representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767–2769 (1990).
[CrossRef]

1984 (1)

L. Nikolova and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579–588 (1984).
[CrossRef]

1983 (1)

1982 (1)

T. D. Ebralidze, “Model of an anisotropic diffraction grating,” Opt. Spectrosk. 53, 944–946 (1982).

1972 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Anderson, J. E.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Andruzzi, F.

Berreman, D. W.

Birabassov, R.

Bos, P. J.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Buffeteau, T.

F.-L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Cipparrone, G.

Ciuchi, F.

Cloutier, S. G.

S. P. Gorkhali, S. G. Cloutier, G. P. Crawford, and R. A. Pelcovits, “Stable polarization gratings recorded in azo-dye-doped liquid crystals,” Appl. Phys. Lett. 88, 251113 (2006).
[CrossRef]

Crawford, G. P.

S. P. Gorkhali, S. G. Cloutier, G. P. Crawford, and R. A. Pelcovits, “Stable polarization gratings recorded in azo-dye-doped liquid crystals,” Appl. Phys. Lett. 88, 251113 (2006).
[CrossRef]

Ebralidze, T. D.

T. D. Ebralidze, “Model of an anisotropic diffraction grating,” Opt. Spectrosk. 53, 944–946 (1982).

Emoto, A.

T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation,” Appl. Opt. 49, 5205–5211 (2010).
[CrossRef] [PubMed]

H. Ono, T. Sekiguchi, A. Emoto, T. Shioda, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

H. Ono, T. Sasaki, A. Emoto, N. Kawatsuki, and E. Uchida, “Polarization gratings in twisted-nematic liquid-crystal composites doped with azobenzene dye,” Opt. Lett. 30, 1950–1952 (2005).
[CrossRef] [PubMed]

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

Escuti, M. J.

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

Francescangeli, O.

Fuh, A. Y.-G.

Galstian, T. V.

Gedne, S. C.

A. Taflove and S. C. Gedne, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).

Gorkhali, S. P.

S. P. Gorkhali, S. G. Cloutier, G. P. Crawford, and R. A. Pelcovits, “Stable polarization gratings recorded in azo-dye-doped liquid crystals,” Appl. Phys. Lett. 88, 251113 (2006).
[CrossRef]

Gu, G.

P. Yeh and G. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

Hanaizumi, O.

Hasegawa, T.

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

Huang, T.

Hvilsted, S.

Ivanov, M.

Kawatsuki, N.

H. Ono, T. Sekiguchi, A. Emoto, T. Shioda, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

T. Sasaki, H. Ono, and N. Kawatsuki, “Three-dimensional vector holograms in anisotropic photoreactive liquid-crystal composites,” Appl. Opt. 47, 2192–2200 (2008).
[CrossRef] [PubMed]

H. Ono, T. Sasaki, A. Emoto, N. Kawatsuki, and E. Uchida, “Polarization gratings in twisted-nematic liquid-crystal composites doped with azobenzene dye,” Opt. Lett. 30, 1950–1952 (2005).
[CrossRef] [PubMed]

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

Khoo, I. C.

I. C. Khoo, H. Li, and Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447(1993).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Labarthet, F.-L.

F.-L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Li, H.

I. C. Khoo, H. Li, and Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447(1993).
[CrossRef]

Liang, Y.

I. C. Khoo, H. Li, and Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447(1993).
[CrossRef]

Lien, A.

A. Lien, “Extended Jones matrix method representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767–2769 (1990).
[CrossRef]

Mazzulla, A.

McManamon, P. F.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Miranda, F. A.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Miura, K.

Mo, T.-S.

Nikolova, L.

Oh, C.

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

Ono, H.

Pelcovits, R. A.

S. P. Gorkhali, S. G. Cloutier, G. P. Crawford, and R. A. Pelcovits, “Stable polarization gratings recorded in azo-dye-doped liquid crystals,” Appl. Phys. Lett. 88, 251113 (2006).
[CrossRef]

Pouch, J. J.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Ramanujam, P. S.

Reznikov, Y.

Sarkissian, H.

Sasaki, T.

Scharf, T.

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

Sekiguchi, T.

H. Ono, T. Sekiguchi, A. Emoto, T. Shioda, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

Shioda, T.

H. Ono, T. Sekiguchi, A. Emoto, T. Shioda, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

Simoni, F.

Slussarenko, S.

Sourisseau, C.

F.-L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Southwell, W. H.

Tabriyan, N. V.

Taflove, A.

A. Taflove and S. C. Gedne, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).

Todorov, T.

Uchida, E.

Wagner, K. H.

Wang, B.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Wang, X.

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Wu, W.-Y.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Yeh, P.

P. Yeh and G. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

Zeldovich, B. Ya

Appl. Opt. (3)

Appl. Phys. B (1)

F.-L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Appl. Phys. Lett. (3)

S. P. Gorkhali, S. G. Cloutier, G. P. Crawford, and R. A. Pelcovits, “Stable polarization gratings recorded in azo-dye-doped liquid crystals,” Appl. Phys. Lett. 88, 251113 (2006).
[CrossRef]

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

A. Lien, “Extended Jones matrix method representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767–2769 (1990).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

IEEE J. Quantum Electron. (1)

I. C. Khoo, H. Li, and Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447(1993).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

J. Appl. Phys. (1)

X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phase array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (4)

Jpn. J. Appl. Phys. (1)

H. Ono, T. Sekiguchi, A. Emoto, T. Shioda, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

Opt. Acta (1)

L. Nikolova and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579–588 (1984).
[CrossRef]

Opt. Lett. (4)

Opt. Spectrosk. (1)

T. D. Ebralidze, “Model of an anisotropic diffraction grating,” Opt. Spectrosk. 53, 944–946 (1982).

Phys. Rev. A (1)

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

Other (3)

A. Taflove and S. C. Gedne, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2005).

P. Yeh and G. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

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Figures (7)

Fig. 1
Fig. 1

Schematic illustration of the principle of 3DVH.

Fig. 2
Fig. 2

Schematic illustration of a photoinduced reflective grating. Ellipsoids represent the refractive index ellipsoid.

Fig. 3
Fig. 3

Polarization states of incident and diffracted light. Red and blue lines are the polarization states of diffracted light as calculated by CWA and the 4 × 4 matrix method.

Fig. 4
Fig. 4

Ellipticity of diffracted light for right-handed circularly polarized incident light. The red line represents the result calculated by CWA. Other curves represent the results calculated by the 4 × 4 matrix method for different values of ϕ 0 .

Fig. 5
Fig. 5

Wavelength dispersion of the diffraction efficiency. The red curve is the result calculated by CWA. The blue and green curves are the results calculated by the 4 × 4 matrix method for right-handed circularly polarized (CP) light and linearly polarized (LP) light with parallel to the x axis.

Fig. 6
Fig. 6

Dependence of the diffraction properties on ϕ 0 . (a) Diffraction efficiency at the Bragg wavelength. (b) Bandwidth Δ λ . Red and blue curves represent the results calculated by CWA and the 4 × 4 matrix method.

Fig. 7
Fig. 7

Dependence of the diffraction efficiency at the Bragg wavelength on the thickness for (a) 0 d 50 Λ z and (b) 0 d 5 Λ z . Red and blue curves represent the results calculated by CWA and the 4 × 4 matrix method.

Equations (21)

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

E ( x , z ) = J 1 ( z ) E 1 exp ( i k 1 x ) + J 2 ( z ) E 2 exp ( i k 2 x ) ,
J m = [ exp ( i k z 1 z ) 0 0 exp ( i k z 2 z ) ] ,
k z 1 = k 0 n o 2 ( k m / k ) 2 ,
k z 2 = k 0 n e n o n o 2 ( k m / k ) 2 ,
c = ( cos ϕ , sin ϕ , 0 ) ,
ϕ = ϕ 0 sin [ 2 π ( x Λ x + z Λ z ) ] ,
ϕ ( z ) = ϕ 0 sin ( 2 π z Λ z ) ϕ 0 sin ( q z ) .
ε ( z ) = ε 0 [ n o 2 + ( n e 2 n o 2 ) cos 2 ϕ ( n e 2 n o 2 ) sin ϕ cos ϕ 0 ( n e 2 n o 2 ) sin ϕ cos ϕ n o 2 + ( n e 2 n o 2 ) sin 2 ϕ 0 0 0 n o 2 ] ,
ε ( z ) = ε 0 [ α 0 0 0 α 0 0 0 n o 2 ] + ε 0 β [ cos ( 2 ϕ ) sin ( 2 ϕ ) 0 sin ( 2 ϕ ) cos ( 2 ϕ ) 0 0 0 0 ] ,
Δ ε ( z ) = ε 0 β 2 { [ 1 i i 1 ] exp ( i 2 ϕ ) + [ 1 i i 1 ] exp ( i 2 ϕ ) } .
Δ P = Δ ε E i ,
E i = J i exp ( i k z ) [ A x A y ] exp ( i k z ) ,
exp ( ± i 2 ϕ ) = h = 0 [ ± i 2 ϕ 0 sin ( q z ) ] h h ! .
exp ( ± i 2 ϕ ) 1 ± ϕ 0 [ exp ( i q z ) exp ( i q z ) ] .
J d = [ A y A x ] .
η = | i κ * sinh ( μ d ) μ cosh ( μ d ) i γ sinh ( μ d ) | 2 ,
κ = i 2 π 2 β λ 2 J 1 ( 2 ϕ 0 ) ( k + k ) 1 / 2 ,
γ = 1 2 ( k + + k q ) ,
μ = | κ | 2 γ 2 ,
k ± = 2 π λ α ± J 0 ( 2 ϕ 0 ) β .
Q = 4 π d Λ z ,

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