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

Full Article  |  PDF Article
OSA Recommended Articles
Polarized backlight based on selective total internal reflection at microgrooves

Ko-Wei Chien, Han-Ping D. Shieh, and Hugo Cornelissen
Appl. Opt. 43(24) 4672-4676 (2004)

Polarizing grating color filters with large acceptance angle and high transmittance

Zhenyue Luo, Guiju Zhang, Ruidong Zhu, Yating Gao, and Shin-Tson Wu
Appl. Opt. 55(1) 70-76 (2016)

Time-sequential autostereoscopic 3-D display with a novel directional backlight system based on volume-holographic optical elements

Yong Seok Hwang, Friedrich-Karl Bruder, Thomas Fäcke, Seung-Cheol Kim, Günther Walze, Rainer Hagen, and Eun-Soo Kim
Opt. Express 22(8) 9820-9838 (2014)

References

  • View by:
  • |
  • |
  • |

  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,” Eurodisplay 2002 , 339–342 (2002).
  3. Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (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. Max Born and Emil 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. Xiuhong 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(2), 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 Display2007, in press.

2007 (2)

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]

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 Display2007, in press.

2006 (1)

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (2006).

2002 (2)

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]

F. Yamada, S. Ono, and Y. Taira, “Dual layered very thin flat surface micro prism array directly molded in an LCD cell,” Eurodisplay 2002 , 339–342 (2002).

1998 (1)

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

1996 (1)

1994 (1)

J.P. Berenger, “Perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics,  114(2), 185–200 (1994).
[Crossref]

1990 (1)

1987 (1)

1983 (1)

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(2), 185–200 (1994).
[Crossref]

Boer, D.K.G. de

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 Display2007, in press.

Boer, Dick K. G. de

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (2006).

Born, Max

Max Born and Emil Wolf, “Rigorous diffraction theory,” in Principles of Optics, (The University Press, Cambridge, 2005), pp.633–673.

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 Display2007, in press.

Caputo, Roberto

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (2006).

Colgan, E.G.

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]

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 Display2007, in press.

Cornelissen, Hugo J.

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (2006).

Gaylord, T.K.

Glytsis, E.N.

Harris, J.B.

Heesch, Chris M. van

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (2006).

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 Display2007, in press.

Hornix, Eefje J.

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (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 Display2007, in press.

Jak, Martin J.J.

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (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 Display2007, 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.

Nakano, D.

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]

Nishikai, A.

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]

Noguchi, M.

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]

Numata, H.

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]

Ono, S.

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]

F. Yamada, S. Ono, and Y. Taira, “Dual layered very thin flat surface micro prism array directly molded in an LCD cell,” Eurodisplay 2002 , 339–342 (2002).

Preist, T.W.

Rokushima, K.

Sambles, J.R.

Singh, R.

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]

Sio, L. De

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 Display2007, in press.

Suzuki, M.

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]

Taira, Y.

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]

F. Yamada, S. Ono, and Y. Taira, “Dual layered very thin flat surface micro prism array directly molded in an LCD cell,” Eurodisplay 2002 , 339–342 (2002).

Urbach, H.P.

Wachters, A.J.H.

Wei, X.

Wei, Xiuhong

Xiuhong Wei , Three Dimensional Rigorous Model for Optical Scattering Problems, PhD thesis, Optics Research Group, Delft University of Technology, August 2006.

Wolf, Emil

Max Born and Emil Wolf, “Rigorous diffraction theory,” in Principles of Optics, (The University Press, Cambridge, 2005), pp.633–673.

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,” Eurodisplay 2002 , 339–342 (2002).

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]

Yamakita, J.

Asia Display (1)

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 Display2007, in press.

Eurodisplay 2002 (1)

F. Yamada, S. Ono, and Y. Taira, “Dual layered very thin flat surface micro prism array directly molded in an LCD cell,” Eurodisplay 2002 , 339–342 (2002).

J. Mod. Opt. (1)

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 (5)

Journal of Computational Physics (1)

J.P. Berenger, “Perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics,  114(2), 185–200 (1994).
[Crossref]

Photonics in Multimedia, Proc. SPIE (1)

Dick K. G. de Boer, Roberto Caputo, Hugo J. Cornelissen, Chris M. van Heesch, Eefje J. Hornix, and Martin J.J. Jak, “Diffractive grating structures for colour-separating backlights,” Photonics in Multimedia, Proc. SPIE 6196, (2006).

SID 02 Digest (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]

Other (3)

Xiuhong Wei , Three Dimensional Rigorous Model for Optical Scattering Problems, PhD thesis, Optics Research Group, Delft University of Technology, August 2006.

www.gsolver.com

Max Born and Emil Wolf, “Rigorous diffraction theory,” in Principles of Optics, (The University Press, Cambridge, 2005), pp.633–673.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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 .

Metrics