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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 4819–4829
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Polarized backlight with constrained angular divergence for enhancement of light extraction efficiency from wire grid polarizer

Po-Hung Yao, Chi-Jui Chung, Chien-Li Wu, and Cheng-Huan Chen  »View Author Affiliations


Optics Express, Vol. 20, Issue 5, pp. 4819-4829 (2012)
http://dx.doi.org/10.1364/OE.20.004819


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Abstract

Efficiency of liquid crystal displays highly depends on the amount of polarized light emerging from the backlight module. In this paper, a backlight architecture using a nanoimprint wire grid polarizer for polarization recycling is proposed and studied, in which the extraction efficiency of polarized light is the major concern. The backlight module is composed of the stack of a wire grid polarizer, a lenticular array and a light guide plate. The light guide plate features interleaving v-groove and trapezoidal ridge coated with aluminum on the top surface, and scattering dot array on the bottom. The angular divergence of emerging light from the light guide plate can be well constrained so as to exploit the angular range with the best transmission of polarized light for the wire grid polarizer. The prototype of a 2.5-inch module has demonstrated an angular divergence of 48°. The overall extraction efficiency of polarized light enhanced by 21% and uniformity of 76% have been achieved.

© 2012 OSA

1. Introduction

Efficiency has been a critical issue for the development of liquid crystal display (LCD). The absorption at the down polarizer is one of the major factors leading to poor transmission of liquid crystal panels. Therefore, several research works have been proposed for increasing the utilization efficiency of polarized light emitting from backlight modules, and the majority are polarization recycling technology using different kind of reflective polarizers, such as multi-layer birefringence film [1

1. G.-J. Park, Y.-G. Kim, J.-H. Yi, J.-H. Kwon, J.-H. Park, S.-H. Kim, B.-K. Kim, J.-K. Shin, and H.-S. Soh, “Enhancement of the optical performance by optimization of optical sheets in direct-illumination LCD backlight,” J. Opt. Soc. Korea 13(1), 152–157 (2009). [CrossRef]

], metal wire grid polarizer (WGP) [2

2. Z. B. Ge and S. T. Wu, “Nanowire grid polarizer for energy efficient and wide-view liquid crystal displays,” Appl. Phys. Lett. 93(12), 121104 (2008). [CrossRef]

4

4. J. J. Wang, L. Chen, X. M. Liu, P. Sciortino, F. Liu, F. Walters, and X. G. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography,” Appl. Phys. Lett. 89(14), 141105 (2006). [CrossRef]

] and cholesteric liquid crystal film [5

5. P. C. Chen and H. L. Kuo, “Color shift improvement in a broadband cholesteric liquid crystal polarizer through computational simulations,” Proc. SPIE 7050, 705015, 705015-8 (2008). [CrossRef]

7

7. Y. Iwamoto and Y. Iimura, “Transmitted light enhancement of electric-field-controlled multidomain vertically aligned liquid crystal displays using circular polarizers and a cholesteric liquid crystal film,” Jpn. J. Appl. Phys. 42, L51–L53 (2003). [CrossRef]

] etc. Among them, metal WGP possesses design parameters from its geometrical feature (as shown in Fig. 1(a)
Fig. 1 (a) Wire grid polarizer and its birefringence property. (b) Schematic diagram of the polarized backlight module with WGP polarizer.
) and therefore becomes to attract more attention with the progress of nanostructure fabrication technology. Transmittance of linearly polarized light of a WGP depends not only on its geometrical feature but also on the light incident angle [8

8. X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003). [CrossRef]

, 9

9. M. Xu, H. P. Urbach, D. de Boer, and H. Cornelissen, “Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon,” Opt. Express 13(7), 2303–2320 (2005). [CrossRef] [PubMed]

]. Manipulation of light incident angle on WGP will then be helpful for the improvement of extraction efficiency of polarized light from the backlight module using WGP as the reflective polarizer for polarization recycling. But normally efficiency is not the only concern, one other major request is the enhancement of on-axis luminance for the best utilization of efficiency. Nevertheless, the corresponding solution normally benefits to both requests because a WGP in most cases shows best transmittance of polarized light at normal incidence. Consequently, a backlight module providing planar illumination with constrained angular divergence becomes a total solution for increasing and best utilization of efficiency. There have been several backlight architectures developed for the enhancement of on-axis luminance. The most widely used for current LCDs is the stack of multiple optical films, including diffuser, microlens film and prism film, on light guide plate. Multi-function optical films which integrate several functionalities into single component are also being developed [10

10. S. H. Baik, S. K. Hwang, Y. G. Kim, G. Park, J. H. Kwon, W.-T. Moon, S.-H. Kim, B.-K. Kim, and S.-H. Kang, “Simulation and fabrication of the cone sheet for LCD backlight application,” J. Opt. Soc. Korea 13(4), 478–483 (2009). [CrossRef]

12

12. J. W. Lee, S. C. Meissner, and R. J. Sudol, “Optical film to enhance cosmetic appearance and brightness in liquid crystal displays,” Opt. Express 15(14), 8609–8618 (2007). [CrossRef] [PubMed]

]. Further integration can be made onto light guide plate to achieve more compact backlight structure [13

13. J. H. Lee, H. S. Lee, B. K. Lee, W. S. Choi, H. Y. Choi, and J. B. Yoon, “Simple liquid crystal display backlight unit comprising only a single-sheet micropatterned polydimethylsiloxane (PDMS) light-guide plate,” Opt. Lett. 32(18), 2665–2667 (2007). [CrossRef] [PubMed]

15

15. K. Käläntär, “A directional backlight with narrow angular luminance distribution for widening viewing angle of a LCD with a front-surface-light-scattering film,” SID 11 Digest. 42(1), 890–893 (2011).

]. Those backlight architecture can be helpful for the transmittance of polarized light from WGP, but with limited improvement because those design do not take the performance of WGP into consideration.

In this paper, a polarized backlight module using a nanoimprint WGP as the reflective polarizer for polarization recycling has been used as the base architecture for improving the efficiency of LCD. The focus is on extracting as most linearly polarized light from the backlight module while maintaining the required uniformity. The angle-dependent transmittance of polarized light from a WGP has been investigated first and an architecture of a divergence-controlled backlight module (DC-BLM) is proposed to provide constrained angular divergence and exploit the best angular range of WGP. DC-BLM is composed of the stack of a lenticular array and a light guide plate, as shown in Fig. 1(b). The light guide plate features interleaving v-groove and trapezoidal ridge coated with aluminum on the top surface and scattering dot array on the bottom. The angular divergence and extraction efficiency of polarized light from WGP have also been evaluated on a 2.5-inch prototype.

2. Angle-dependent transmittance of wire grid polarizer

The total flux of polarized light Φop available for the liquid crystal panel shown in Fig. 1(b) depends on efficiency of optical components Eoc, polarization recycling efficiency Epr and linear polarization transmittance of the down polarizer Tpol. The relationship can be expressed as Eq. (1)
Φop=Φ0×Eoc×Epr×Tpol
(1)
where Φ0 is the input flux and EprEi, Ei refers to the extraction efficiency of polarized light of the ith recycling process.

The spectral transmittance of WGP over visible spectrum at some oblique incident angles was simulated with RCWA and measured with spectrometer. The incident angle is changed from 0° to 40° with an increment of 10° and the results are shown in Fig. 3
Fig. 3 Spectral transmittance of WGP at some specific incident angles (solid line: measured data; dash line: simulation data).
. The gap between simulation and measurement is mainly due to the deviation of nanostructure from an ideal flat top profile. Nevertheless, the percentage of transmittance drop with the increase of incident angle coincides with each other. Both measured and simulated data indicate that the transmission clearly depends on incident angle and it is reduced with the increase of incident angle by a percentage up to 10% with the incident angle increased from 0° to 30°. As a consequence, the narrower the angular divergence of incident light onto WGP, the higher the extraction efficiency of polarized light can be obtained from WGP. This leads to the motivation of facilitating a backlight module giving low divergence illumination for improving Epr while the module should have as less component as possible to avoid too much drop of Eoc upon the improvement of diverging angle, as indicated in Eq. (1).

3. Design and simulation of the backlight module

In conventional LED edge-lit type backlight modules, light emitted from LEDs are scattered and distributed by dot pattern formed on the bottom surface of LGPs for a uniform planar illumination. Normally the emerging light from the top surface needs to be constrained within a specific diverging angle for enhancing on-axis luminance. Therefore, various angle-controlled films were developed [12

12. J. W. Lee, S. C. Meissner, and R. J. Sudol, “Optical film to enhance cosmetic appearance and brightness in liquid crystal displays,” Opt. Express 15(14), 8609–8618 (2007). [CrossRef] [PubMed]

14

14. S. Aoyama, A. Funamoto, and K. Imanaka, “Hybrid normal-reverse prism coupler for light-emitting diode backlight systems,” Appl. Opt. 45(28), 7273–7278 (2006). [CrossRef] [PubMed]

] and stacked with diffuser films to achieve the required on-axis luminance while maintaining uniformity over the whole backlight surface. In order to improve the extraction efficiency when using WGP as the reflective polarizer for polarization recycling, there is a request of reducing the angular divergence from backlight even further to match the angular region with best spectral transmittance of WGP. An aperture-limited light guide plate (AL-LGP) is proposed, as shown in Fig. 4(a)
Fig. 4 (a) Schematic diagram of AL-LGP. (b) Illustration of possible ray path in AL-LGP.
. There are one-dimensional periodic trapezoid stripes on its top surface, where the plateau of each trapezoid stripe is coated with a 200nm thick aluminum layer as a reflective surface. The bottom surface is embossed with scattering dot pattern.

Figure 4(b) shows some possible ray path for the light scattered from the bottom dot pattern. Ray Ii and IIIi are reflected and refracted back into the LGP by the Al layer and the adjacent trapezoid structure respectively. Those oblique rays hitting the side facets of the v-grooves at angles larger than critical angle of total internal reflection are reflected back to the bottom surface, as indicated with IVr in Fig. 4(b). Other rays shown as IIi impinging on the side facets are refracted and deflected toward the normal of top surface (z axis), i.e. emerging from the top surface with a reduced oblique angle from the surface normal. The overall diverging angle of emerging light is dependent of refractive index of the LGP material and the slanted angle β of the side facet of trapezoid structure. For a specified material of PMMA, the major design parameter becomes angle β. With the criteria of highest on-axis intensity while suppressing side-lobe as possible for the best transmittance of Pλ polarization for WGP, optimized value of β = 45° was obtained, which in turn makes the angle of V-groove α = 90°. In addition to the issue of diverging angle, the ratio of Al-coated area has significant influence on the efficiency and uniformity. Simulation shows efficiency drop and bar pattern when the ratio get too high. On the contrary, the emerging rays with small oblique angle are likely to be diverted away from the surface normal if the ratio gets too small, which in turn increases the diverging angle. Optimized ratio has been found between 30 and 40% so that the efficiency can be maintained above 70% and the uniformity above 65% without bar pattern mura. The optimized pitch and tip width of the trapezoid array becomes PT = 60 μm and w = 20 μm. Figure 5
Fig. 5 Angular profile of emerging light from AL-LGP compared with Lambertian profile.
shows the normally angular profile of the emerging light from the proposed AL-LGP with the Lambertian profile as the reference for comparison. The half angle is 84° compared to the 120° of Lambertian profile.

With the exit of emerging ray being localized at the area of V-groove, a dedicated lenticular array, as shown in Fig. 6(a)
Fig. 6 (a) Lenticular array with feature parameters. (b) Configuration of AL-LGP covered with lenticular array.
, is stacked onto the LGP with the lenslet facing downward and aligned with the V-groove for further reducing the diverging angle, as shown in Fig. 6(b), where PL is pitch of the lens; r is curvature radius of the lenslet; Ds and DL refer to thickness of PET substrate and sag of the lenticular lens respectively.

In order to concentrate emerging rays within small diverging angle (i.e. narrower FWHM) corresponding to the efficient angular conditions of the WGP, parameters of the lenticular array were adjusted with the field distribution of AL-LGP by ray tracing principles. The ray path with associated denotation for the lenslet is shown in Fig. 7
Fig. 7 Geometry of optical ray tracing for the lenticular lenslet and the optical parameters for determining the optical matrices.
. Optical matrices have been employed as the paraxial ray tracing tool for determining the radius of curvature r of the lenslet.

As shown in Fig. 7, Ri=(1ϕi01), i = 1-3 is the refractive matrix of each refractive interface and φi=Ci(ni1) is the refractive power of each refractive interface and Ci is the curvature of each interface and n is refractive index; Tj=(10tjnj1), j = 1,2 is the translation matrix between two interfaces and tj is the corresponding thickness and nj is the corresponding refractive index. The radius of curvature r can be derived from Eq. (2) after the focal length f is determined with the thickness parameters of lenticular array and WGP.
r=(ƒ+Γ)(n1)
(2)
where Γ=Ds+DLn, nUV = nPET = n and f refers to effective focal length.

The parameters of the lenslet used in this case are listed in Table 1

Table 1. Parameters of Lenticular Lenslet

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.

Two criteria are considered to determine r of the lenticular lens, one is on-axis luminance gain for brightness performance of LCD panels and the other is FWHM for preserving the decay of angular transmission from WGP as lowest. Thus, combining the emission field of the optimized AL-LGP, radius of curvature r is optimized to be 55 μm with f = 100μm while the ray tracing simulation indicates that the FWHM diverging angle of the emerging light from DC-BLM has been reduced to 48° with an on-axis gain of 2.2x, as shown in Fig. 8
Fig. 8 Comparison of normalized intensity distribution of different backlight structures from simulation.
. The corresponding performance of conventional backlight modules has also been simulated for comparison. The normalized angular profile of three other film combination, including diffuser only, diffuser plus one prism sheet and diffuser plus two prism sheets, are shown together in Fig. 8. It clearly shows that the proposed DC-BLM exhibits the narrowest angular divergence and the highest on-axis enhancement with the lowest side-lobe. Those performance indices for four cases are listed in Table 2

Table 2. Comparison of Different Backlight Architectures Basing on the Same LED Input; Df: Diffuser Sheet, Pr: Prism Sheet.

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. In addition, the tolerance for alignment between lenticular array and LGP has also been investigated and it indicates a drop of on-axis luminous intensity by 4% with a misalignment by one half pitch of lenticular lens.

Figure 9
Fig. 9 Illuminance distribution of DC-BLM with stack of AL-LGP and the lenticular array by simulation.
shows the simulated illuminance distribution over a 2.5” backlight module using the proposed DC-BLM configuration, and the uniformity is estimated to be 73%.

4. Performance evaluation of DC-BLM with WGP

The AL-LGP and lenticular array have been fabricated with the process shown in Fig. 10(a)
Fig. 10 (a) Diamond tooling process for AL-LGP. (b) Fabrication process for the lenticular sheet.
and 10(b) respectively. AL-LGP is made of PMMA and lenticular array is made of acrylic resin on a PET substrate by UV-curing process. The prototypes are shown in Fig. 11(a)
Fig. 11 (a) 2.5-inch PMMA AL-LGP. (b) 2.5-inch PET lenticular array film replicated by UV imprint process with a grooved master mold.
and 11(b) respectively.

5-point on-axis luminance of the 2.5-inch DC-BLM was taken by a luminance meter and the result is shown in Fig. 12(a)
Fig. 12 (a) 5 points on-axis luminance of the 2.5-inch DC-BLM. (b) Measured angular intensity of the proposed DC-BLM and a diffuser-stacked module.
. Additionally, the angular intensity distribution was also measured with the IS-VA system from Radiant Image and the result is shown in Fig. 12(b). In good agreement with the simulation result, the FWHM angular divergence of 48° is achieved and the on-axis brightness is enhanced by 120% with uniformity of 76%.

Enhancement of extraction efficiency for polarized light from WGP has been evaluated by using an additional absorptive polarizer and an integrating sphere detector was used to measure the total output flux of the whole assembly, including DC-BLM, WGP and absorptive polarizer. The result is compared with that of the case where DC-BLM is replaced with a cross-prism-stacked backlight module (CPS-BLM) in where one diffuser and two cross-oriented prism sheets are stacked, as listed in Table 3

Table 3. Optical Performance of the DC-BLM and Cross-Prism-Stacked BLM (CPS-BLM)

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. The DC-BLM has lower optical component efficiency Eoc, reasonably due to aperture limited configuration with Al coating. However, the overall extraction efficiency of polarized light gets higher due to higher polarization recycling efficiency, which attributes to the lower divergence angle of emerging light. As a result, the polarized output flux and the on-axis brightness are enhanced by 21% and 5% respectively with the case of CPS-BLM as reference.

5. Conclusions

For the backlight illumination of liquid crystal displays, only the part of linearly polarized light contributes to the effective total lumen and efficiency. Based on the scheme of polarization recycling with wire grid polarizer, the proposed backlight module provides illumination source with low angular divergence and highly suppressed side lobe component, which has been demonstrated as an effective approach for enhancing the overall extraction efficiency of polarized light. The general requirement of on-axis luminance enhancement is naturally fulfilled in the mean time, and the uniformity performance can also be met with proper design on the available parameters in the proposed architecture. This indicates that the proposed architecture can be a feasible total solution from all performance aspects of LCD backlight module with the emphasis on efficiency enhancement. Number of the components in the whole module is relatively few, which could be considered as an additional advantage for the potential of slim backlights.

Acknowledgments

References and links

1.

G.-J. Park, Y.-G. Kim, J.-H. Yi, J.-H. Kwon, J.-H. Park, S.-H. Kim, B.-K. Kim, J.-K. Shin, and H.-S. Soh, “Enhancement of the optical performance by optimization of optical sheets in direct-illumination LCD backlight,” J. Opt. Soc. Korea 13(1), 152–157 (2009). [CrossRef]

2.

Z. B. Ge and S. T. Wu, “Nanowire grid polarizer for energy efficient and wide-view liquid crystal displays,” Appl. Phys. Lett. 93(12), 121104 (2008). [CrossRef]

3.

T. Sergan, M. Lavrentovich, J. Kelly, E. Gardner, and D. Hansen, “Measurement and modeling of optical performance of wire grids and liquid-crystal displays utilizing grid polarizers,” J. Opt. Soc. Am. A 19(9), 1872–1885 (2002). [CrossRef] [PubMed]

4.

J. J. Wang, L. Chen, X. M. Liu, P. Sciortino, F. Liu, F. Walters, and X. G. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography,” Appl. Phys. Lett. 89(14), 141105 (2006). [CrossRef]

5.

P. C. Chen and H. L. Kuo, “Color shift improvement in a broadband cholesteric liquid crystal polarizer through computational simulations,” Proc. SPIE 7050, 705015, 705015-8 (2008). [CrossRef]

6.

L. Li, J. F. Li, B. S. Fan, Y. Q. Jiang, and S. M. Faris, “Reflective cholesteric liquid crystal polarizers and their applications,” Proc. SPIE 3560, 33–40 (1998). [CrossRef]

7.

Y. Iwamoto and Y. Iimura, “Transmitted light enhancement of electric-field-controlled multidomain vertically aligned liquid crystal displays using circular polarizers and a cholesteric liquid crystal film,” Jpn. J. Appl. Phys. 42, L51–L53 (2003). [CrossRef]

8.

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003). [CrossRef]

9.

M. Xu, H. P. Urbach, D. de Boer, and H. Cornelissen, “Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon,” Opt. Express 13(7), 2303–2320 (2005). [CrossRef] [PubMed]

10.

S. H. Baik, S. K. Hwang, Y. G. Kim, G. Park, J. H. Kwon, W.-T. Moon, S.-H. Kim, B.-K. Kim, and S.-H. Kang, “Simulation and fabrication of the cone sheet for LCD backlight application,” J. Opt. Soc. Korea 13(4), 478–483 (2009). [CrossRef]

11.

C. F. Lin, Y. B. Fang, and P. H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol. 7(1), 3–9 (2011). [CrossRef]

12.

J. W. Lee, S. C. Meissner, and R. J. Sudol, “Optical film to enhance cosmetic appearance and brightness in liquid crystal displays,” Opt. Express 15(14), 8609–8618 (2007). [CrossRef] [PubMed]

13.

J. H. Lee, H. S. Lee, B. K. Lee, W. S. Choi, H. Y. Choi, and J. B. Yoon, “Simple liquid crystal display backlight unit comprising only a single-sheet micropatterned polydimethylsiloxane (PDMS) light-guide plate,” Opt. Lett. 32(18), 2665–2667 (2007). [CrossRef] [PubMed]

14.

S. Aoyama, A. Funamoto, and K. Imanaka, “Hybrid normal-reverse prism coupler for light-emitting diode backlight systems,” Appl. Opt. 45(28), 7273–7278 (2006). [CrossRef] [PubMed]

15.

K. Käläntär, “A directional backlight with narrow angular luminance distribution for widening viewing angle of a LCD with a front-surface-light-scattering film,” SID 11 Digest. 42(1), 890–893 (2011).

16.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

17.

V. C. Ballenegger and T. A. Weber, “The Ewald–Oseen extinction theorem and extinction lengths,” Am. J. Phys. 67(7), 599–605 (1999). [CrossRef]

18.

K. Takano, H. Yokoyama, A. Ichii, I. Morimoto, and M. Hangyo, “Wire-grid polarizer sheet in the terahertz region fabricated by nanoimprint technology,” Opt. Lett. 36(14), 2665–2667 (2011). [CrossRef] [PubMed]

OCIS Codes
(120.2040) Instrumentation, measurement, and metrology : Displays
(220.4000) Optical design and fabrication : Microstructure fabrication
(110.2945) Imaging systems : Illumination design

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: November 11, 2011
Revised Manuscript: January 20, 2012
Manuscript Accepted: January 21, 2012
Published: February 13, 2012

Citation
Po-Hung Yao, Chi-Jui Chung, Chien-Li Wu, and Cheng-Huan Chen, "Polarized backlight with constrained angular divergence for enhancement of light extraction efficiency from wire grid polarizer," Opt. Express 20, 4819-4829 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-4819


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References

  1. G.-J. Park, Y.-G. Kim, J.-H. Yi, J.-H. Kwon, J.-H. Park, S.-H. Kim, B.-K. Kim, J.-K. Shin, and H.-S. Soh, “Enhancement of the optical performance by optimization of optical sheets in direct-illumination LCD backlight,” J. Opt. Soc. Korea13(1), 152–157 (2009). [CrossRef]
  2. Z. B. Ge and S. T. Wu, “Nanowire grid polarizer for energy efficient and wide-view liquid crystal displays,” Appl. Phys. Lett.93(12), 121104 (2008). [CrossRef]
  3. T. Sergan, M. Lavrentovich, J. Kelly, E. Gardner, and D. Hansen, “Measurement and modeling of optical performance of wire grids and liquid-crystal displays utilizing grid polarizers,” J. Opt. Soc. Am. A19(9), 1872–1885 (2002). [CrossRef] [PubMed]
  4. J. J. Wang, L. Chen, X. M. Liu, P. Sciortino, F. Liu, F. Walters, and X. G. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography,” Appl. Phys. Lett.89(14), 141105 (2006). [CrossRef]
  5. P. C. Chen and H. L. Kuo, “Color shift improvement in a broadband cholesteric liquid crystal polarizer through computational simulations,” Proc. SPIE7050, 705015, 705015-8 (2008). [CrossRef]
  6. L. Li, J. F. Li, B. S. Fan, Y. Q. Jiang, and S. M. Faris, “Reflective cholesteric liquid crystal polarizers and their applications,” Proc. SPIE3560, 33–40 (1998). [CrossRef]
  7. Y. Iwamoto and Y. Iimura, “Transmitted light enhancement of electric-field-controlled multidomain vertically aligned liquid crystal displays using circular polarizers and a cholesteric liquid crystal film,” Jpn. J. Appl. Phys.42, L51–L53 (2003). [CrossRef]
  8. X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys.93(8), 4407–4412 (2003). [CrossRef]
  9. M. Xu, H. P. Urbach, D. de Boer, and H. Cornelissen, “Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon,” Opt. Express13(7), 2303–2320 (2005). [CrossRef] [PubMed]
  10. S. H. Baik, S. K. Hwang, Y. G. Kim, G. Park, J. H. Kwon, W.-T. Moon, S.-H. Kim, B.-K. Kim, and S.-H. Kang, “Simulation and fabrication of the cone sheet for LCD backlight application,” J. Opt. Soc. Korea13(4), 478–483 (2009). [CrossRef]
  11. C. F. Lin, Y. B. Fang, and P. H. Yang, “Optimized micro-prism diffusion film for slim-type bottom-lit backlight units,” J. Disp. Technol.7(1), 3–9 (2011). [CrossRef]
  12. J. W. Lee, S. C. Meissner, and R. J. Sudol, “Optical film to enhance cosmetic appearance and brightness in liquid crystal displays,” Opt. Express15(14), 8609–8618 (2007). [CrossRef] [PubMed]
  13. J. H. Lee, H. S. Lee, B. K. Lee, W. S. Choi, H. Y. Choi, and J. B. Yoon, “Simple liquid crystal display backlight unit comprising only a single-sheet micropatterned polydimethylsiloxane (PDMS) light-guide plate,” Opt. Lett.32(18), 2665–2667 (2007). [CrossRef] [PubMed]
  14. S. Aoyama, A. Funamoto, and K. Imanaka, “Hybrid normal-reverse prism coupler for light-emitting diode backlight systems,” Appl. Opt.45(28), 7273–7278 (2006). [CrossRef] [PubMed]
  15. K. Käläntär, “A directional backlight with narrow angular luminance distribution for widening viewing angle of a LCD with a front-surface-light-scattering film,” SID 11 Digest.42(1), 890–893 (2011).
  16. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).
  17. V. C. Ballenegger and T. A. Weber, “The Ewald–Oseen extinction theorem and extinction lengths,” Am. J. Phys.67(7), 599–605 (1999). [CrossRef]
  18. K. Takano, H. Yokoyama, A. Ichii, I. Morimoto, and M. Hangyo, “Wire-grid polarizer sheet in the terahertz region fabricated by nanoimprint technology,” Opt. Lett.36(14), 2665–2667 (2011). [CrossRef] [PubMed]

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