Abstract

A color and polarization separating backlight can be obtained by using a surface-relief grating made of birefringent material as an outcoupling structure on top of the lightguide. A rigorous finite element diffraction model was applied to study the polarization effect of such a grating. The diffraction of plane waves by the anisotropic grating was studied for general conical incidence.

© 2007 Optical Society of America

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References

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  1. Y. Taira, D. Nakano, H. Numata, A. Nishikai, S. Ono, F. Yamada, M. Suzuki, M. Noguchi, R. Singh, and E. G. Colgan, "Low-power LCD using a novel optical system," SID 02 Digest, 1313-1315 (2002).
    [CrossRef]
  2. F. Yamada, S. Ono, and Y. Taira, "Dual layered very thin flat surface micro prism array directly molded in an LCD cell," Euro display 2002, 339-342 (2002).
  3. D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).
  4. www.gsolver.com
  5. X. Wei, H. P. Urbach, and A. J. H. Wachters, "Finite element model for three-dimensional optical scattering problems," J. Opt. Soc. Am. A 24, 866 (2007).
    [CrossRef]
  6. M. Born and E. Wolf, "Rigorous diffraction theory," in Principles of Optics, (The University Press, Cambridge, 2005), pp. 633-673.
  7. K. Rokushima and J. Yamakita, "Analysis of anisotropic dielectric gratings," J. Opt. Soc. Am. A 73, 901 (1983).
    [CrossRef]
  8. E. N. Glytsis and T. K. Gaylord, "Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings," J. Opt. Soc. Am. A 4, 2061 (1987).
    [CrossRef]
  9. S. Mori, K. Mukai, J. Yamakita, and K. Rokushima, "Analysis of dielectric lamellar gratings coated with anisotropic layers," J. Opt. Soc. Am. A 7, 1661 (1990).
    [CrossRef]
  10. J. B. Harris, T. W. Preist, E. L. Wood, and J. R. Sambles, "Conical diffraction from multicoated gratings containing uniaxial materials," J. Opt. Soc. Am. A 13, 803 (1996).
    [CrossRef]
  11. L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
    [CrossRef]
  12. X. Wei, Three dimensional rigorous model for optical scattering problems, PhD thesis, Optics Research Group, Delft University of Technology, August 2006.
  13. J. P. Berenger, "Perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics 114, 185-200 (1994).
    [CrossRef]
  14. R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

2007

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

X. Wei, H. P. Urbach, and A. J. H. Wachters, "Finite element model for three-dimensional optical scattering problems," J. Opt. Soc. Am. A 24, 866 (2007).
[CrossRef]

2006

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

2002

F. Yamada, S. Ono, and Y. Taira, "Dual layered very thin flat surface micro prism array directly molded in an LCD cell," Euro display 2002, 339-342 (2002).

1998

L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
[CrossRef]

1996

1994

J. P. Berenger, "Perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics 114, 185-200 (1994).
[CrossRef]

1990

1987

1983

K. Rokushima and J. Yamakita, "Analysis of anisotropic dielectric gratings," J. Opt. Soc. Am. A 73, 901 (1983).
[CrossRef]

Berenger, J. P.

J. P. Berenger, "Perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics 114, 185-200 (1994).
[CrossRef]

Caputo, R.

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

Cornelissen, H. J.

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

de Boer, D. K. G.

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

De Sio, L.

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

Gaylord, T. K.

Glytsis, E. N.

Harris, J. B.

Hornix, E. J.

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

Jak, M. J. J.

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

Krijn, M. P. C.

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

Li, L.

L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
[CrossRef]

Mori, S.

Mukai, K.

Ono, S.

F. Yamada, S. Ono, and Y. Taira, "Dual layered very thin flat surface micro prism array directly molded in an LCD cell," Euro display 2002, 339-342 (2002).

Preist, T. W.

Rokushima, K.

Sambles, J. R.

Taira, Y.

F. Yamada, S. Ono, and Y. Taira, "Dual layered very thin flat surface micro prism array directly molded in an LCD cell," Euro display 2002, 339-342 (2002).

Urbach, H. P.

van Heesch, C. M.

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

Wachters, A. J. H.

Wei, X.

Wood, E. L.

Yamada, F.

F. Yamada, S. Ono, and Y. Taira, "Dual layered very thin flat surface micro prism array directly molded in an LCD cell," Euro display 2002, 339-342 (2002).

Yamakita, J.

Asia Display

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, H. J. Cornelissen, and M. P. C. Krijn, "New system concept for colour separating backlights," Asia Display 2007, in press.

Euro display

F. Yamada, S. Ono, and Y. Taira, "Dual layered very thin flat surface micro prism array directly molded in an LCD cell," Euro display 2002, 339-342 (2002).

J. Mod. Opt.

L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Journal of Computational Physics

J. P. Berenger, "Perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics 114, 185-200 (1994).
[CrossRef]

Proc. SPIE

D. K. G. de Boer, R. Caputo, H. J. Cornelissen, C. M. van Heesch, E. J. Hornix, and M. J. J. Jak, "Diffractive grating structures for colour-separating backlights," Proc. SPIE 6196, 61960R (2006).

Other

www.gsolver.com

M. Born and E. Wolf, "Rigorous diffraction theory," in Principles of Optics, (The University Press, Cambridge, 2005), pp. 633-673.

Y. Taira, D. Nakano, H. Numata, A. Nishikai, S. Ono, F. Yamada, M. Suzuki, M. Noguchi, R. Singh, and E. G. Colgan, "Low-power LCD using a novel optical system," SID 02 Digest, 1313-1315 (2002).
[CrossRef]

X. Wei, Three dimensional rigorous model for optical scattering problems, PhD thesis, Optics Research Group, Delft University of Technology, August 2006.

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Figures (8)

Fig. 1.
Fig. 1.

Configuration of the polarized color-separating backlight.

Fig. 2.
Fig. 2.

Configuration of the grating with the computational domain Ω.

Fig. 3.
Fig. 3.

Relative intensity of the -1 st diffracted transmitted order as function of θi for ϕ i = 0 and for three wavelengths namely 450, 535 and 632 nm for (a) s-polarization and (b) p-polarization.

Fig. 4.
Fig. 4.

Relative intensity of the -1 st diffracted transmitted order as function of incident angle ϕ i for incident angle ϕ i = 67° and for the three wavelengths 450, 535 and 632 nm. RI in the titles is an abbreviation of relative intensity, and the first subscript denotes the polarization of the diffracted transmitted order whereas the second subscript indicates the polarization of the incident field.

Fig. 5.
Fig. 5.

Angular distribution (θd , ϕ d ) of the -1 st diffracted order for different colors, blue (450 nm), green (535 nm) and red (632 nm) for θi = 67° and for varying ϕ i (-90° ≤ϕ i ≤90°).

Fig. 6.
Fig. 6.

Relative intensity of the -1st diffracted transmitted order as function of diffraction angle θd , for incident angle θi = 67°, and for varying 0° ≤ ϕ i ≤ 90°, for the three wavelengths 450, 535 and 632 nm. RI in the titles is an abbreviation for relative intensity, and the first subscript denotes the polarization of the transmitted field whereas the second subscript indicates the polarization of the incident field.

Fig. 7.
Fig. 7.

Contrast ratio between calculated intensities of the s- and p-polarized components of the -1 st transmitted order as function of diffraction angle θd for ϕ i = 67°, and for varying 0° ≤ ϕ i ≤ 90°, (a) for s-polarization incidence, and (b) for unpolarized incident field.

Fig. 8.
Fig. 8.

Measured angular distribution of color-separated luminance for s-polarized (left) and p-polarized (center) light and angular distribution of s/p contrast ratio (right) for color-separating polarized backlight structure with TL 213 (refractive indices of Table 1) as birefringent material. (Note that the azimuthal angles are shifted by 90° with respect to those used before.)

Tables (1)

Tables Icon

Table 1. The refractive indices of polycarbonate and of liquid crystal for three colors.

Equations (38)

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

× E = μ 0 H ,
× H = ε 0 ε͇ E ,
ε͇ = ( ε xx ε xy ε xz ε yx ε yy ε yz ε zx ε zy ε zz ) ,
ε ij = ε ij + ij , ( i , j = x , y , z )
ε′ ε″ v = ε″ ε′v .
y E = ik y E ,
y H = ik y H ,
E x E z = ω 2 ε 0 μ 0 D 𝒩 ε xy ε zy E y + i D 𝒩 x k y E y ωμ 0 H y + i D 𝒬 z k y E y ωμ 0 H y
H z H x = k y ωμ 0 E x E z + i ωμ 0 x z E y
= ω 2 ε 0 μ 0 D k y ωμ 0 𝒩 ε xy ε zy E y + i D k y ω μ 0 𝒩 x k y E y ωμ 0 H y + i D k y ω μ 0 𝒬 z k y E y ω μ 0 H y + i ω μ 0 x y E y ,
D = ( ω 2 ε 0 μ 0 ε xx k y 2 ) ( ω 2 ε 0 μ 0 ε zz k y 2 ) ( ω 2 ε 0 μ 0 ) 2 ε xz ε zx
= ( ω 2 ε 0 μ 0 ) 2 ( ε xx ε zz ε xz ε zx ) ω 2 ε 0 μ 0 k y 2 ( ε xx + ε zz ) + k y 4 .
𝒩 = ( ω 2 ε 0 μ 0 ε zz k y 2 ω 2 ε 0 μ 0 ε xz ω 2 ε 0 μ 0 ε zx ω 2 ε 0 μ 0 ε xx k y 2 ) ,
𝒬 = 𝒩 ( 0 1 1 0 ) = ( ω 2 ε 0 μ 0 ε xz ( ω 2 ε 0 μ 0 ε zz k y 2 ) ω 2 ε 0 μ 0 ε xx k y 2 ω 2 ε 0 μ 0 ε zx ) ,
μ 0 H y = ͂ ( 0 1 1 0 ) E x E z ,
ε 0 ε yy E y = ε 0 ( ε yx ε yz ) E x E z ͂ H z H x ,
͂ = x z .
μ 0 H y = ω 2 ε 0 μ o ͂ [ 1 D 𝒬 T ε xy ε zy E y ] + i ͂ [ 1 D 𝒬 T x k y E y ω 0 μ 0 H y ] + i ͂ [ 1 D z k y E y ω μ 0 H y ] ,
i ω ε 0 ε yy E y = i ω 2 ε 0 μ 0 D ω ε 0 ( ε yx ε yz ) 𝒩 ε xy ε zy E y + ω ε 0 D ( ε yx ε yz ) 𝒩 x k y E y ω μ 0 H y
+ ω ε 0 D ( ε yx ε yz ) 𝒬 z k y E y ω μ 0 H y + k y ω μ 0 ω 2 ε 0 μ 0 ͂ [ 1 D 𝒩 ε xy ε zy E y ]
i k y ω μ 0 ͂ [ 1 D 𝒩 x k y E y ω μ 0 H y ] i k y ω μ 0 ͂ [ 1 D 𝒬 z k y E y ω μ 0 H y ] i ω μ 0 Δ E y ,
= ( ω 2 ε 0 μ 0 ε xx k y 2 ω 2 ε 0 μ 0 ε xz ω 2 ε 0 μ 0 ε zx ω 2 ε 0 μ 0 ε zz k y 2 ) .
ε͇ = ( ε xx 0 ε xz 0 ε yy 0 ε zx 0 ε zz ) ,
i ω μ 0 H y = i ͂ [ 1 D 𝒬 T x k y E y ω 0 μ 0 H y ] + i ͂ [ 1 D z k y E y ω μ 0 H y ] ,
i ω ε 0 ε yy E y = i k y ω μ 0 ͂ [ 1 D 𝒩 x k y E y ω μ 0 H y ] i k y ω μ 0 ͂ [ 1 D 𝒬 z k y E y ω μ 0 H y ] i ω μ 0 Δ E y ,
E x E z = i D 𝒩 x k y E y ω μ 0 H y + i D 𝒬 z k y E y ω μ 0 H y
H z H x = i D k y ω μ 0 𝒩 x k y E y ω μ 0 H y + i D k y ω μ 0 𝒬 z k y E y ω μ 0 H y + i ω μ 0 x z E y ,
ω 2 μ 0 ε 0 H y + x ( ε xx ε xx ε zz ε xz ε zx H y x + ε zx ε xx ε zz ε xz ε zx H y z ) + z ( ε xz ε xx ε zz ε xz ε zx H y x + ε zz ε xx ε zz ε xz ε zx H y z ) = 0 ,
ω 2 ε 0 μ 0 ε yy E y + 2 E y z 2 + 2 E y x 2 = 0 .
ε͇ = ( ε xx 0 0 0 ε yy 0 0 0 ε zz ) ,
k x i = k 0 n i cos ϕ i sin θ i ,
k y i = k 0 n i sin ϕ i sin θ i ,
k x d = k 0 n d cos ϕ d sin θ d ,
k y d = k 0 n d sin ϕ d sin θ d ,
k x d = k x i + 2 π m p ,
k y d = k y i ,
n d cos ϕ d sin θ d = n i cos ϕ i sin θ i + p ,
n d sin ϕ d sin θ d = n i sin ϕ i sin θ i .

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