Abstract

A simple wide-view circular polarizer comprising of a linear polarizer and two biaxial films is proposed. Over the ±85° viewing cone, the produced polarization is almost circular and the light leakage from the crossed circular polarizers is calculated to be less than 8.23×10-5, provided that the air-interface surface reflections are ignored. The design tolerance within ±5% of the optimal parameters is analyzed.

© 2005 Optical Society of America

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References

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  1. S. T. Wu and D. K. Yang , Reflective Liquid Crystal Displays , ( Wiley, New York , 2001 ).
  2. T. H. Yoon , G. D. Lee , and J. C. Kim , “ Nontwist quarter-wave liquid crystal cell for a high-contrast reflective display ,” Opt. Lett.   25 , 1547 – 1549 ( 2000 ).
    [Crossref]
  3. Y. Iwamoto , Y. Toko , H. Hiramoto , and Y. Iimura , “ Improvement of transmitted light efficiency in SH-LCDs using quarter-wave retardation films ,” Soc. Inf. Display Tech. Digest   31 , 902 – 905 ( 2000 ).
    [Crossref]
  4. T. Ishinabe , T. Miyashita , and T. Uchida , “ Design of a quarter wave plate with wide viewing angle and wide wavelength range for high quality reflective LCDs ,” Soc. Inf. Display Tech. Digest   32 , 906 – 909 ( 2001 ).
    [Crossref]
  5. Q. Hong , T. X. Wu , X. Zhu , R. Lu , and S. T. Wu , “ Designs of wide-view and broadband circular polarizers ,” Opt. Express   13 , 8318 – 8331 ( 2005 ). R. Lu , X. Zhu , S. T. Wu , Q. Hong , and T.X. Wu , “ Ultrawide-view liquid crystal displays ,” J. Display Technology   1 , 3 – 14 ( 2005 ).
    [Crossref] [PubMed]
  6. S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
    [Crossref]
  7. S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
    [Crossref]
  8. K. Ohmuro , S. Kataoka , T. Sasaki , and Y. Koike , Soc. Inf. Display Tech. Digest   33 , 845 – 848 ( 1997 ).
  9. Y. Saitoh , S. Kimura , K. Kusafuka , and H. Shimizu , Jpn. J. Appl. Phys.   37 , 4822 – 4828 ( 1998 ).
    [Crossref]
  10. J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
    [Crossref]
  11. S. Huard , Polarization of Light , ( Wiley, New York , 1997 ).
  12. C. Brosseau , Fundamentals of Polarized Light: A statistical Optics Approach , ( Wiley, New York , 1998 ).
  13. Y. Huang , T. X. Wu , and S. T. Wu , “ Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method ,” J. Appl. Phys.   93 , 2490 – 2495 ( 2003 ).
    [Crossref]
  14. Y. Fujimura , T. Nagatsuka , H. Yoshimi , and T. Shimomura , “ Optical properties of retardation films for STN-LCDs ,” Soc. Inf. Display Tech. Digest ,   22 , 739 – 742 ( 1991 ).
  15. R. L. Haupt and S. E. Haupt , Practical Genetic Algorithms , ( Wiley, Hoboken , 2004 ).
  16. S. Pancharatnam , “ Achromatic combinations of birefringent plates ,” Proc. Ind. Acad. Sci. A   41 , 130 – 144 ( 1956 ).

2005 (1)

2003 (1)

Y. Huang , T. X. Wu , and S. T. Wu , “ Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method ,” J. Appl. Phys.   93 , 2490 – 2495 ( 2003 ).
[Crossref]

2001 (2)

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

T. Ishinabe , T. Miyashita , and T. Uchida , “ Design of a quarter wave plate with wide viewing angle and wide wavelength range for high quality reflective LCDs ,” Soc. Inf. Display Tech. Digest   32 , 906 – 909 ( 2001 ).
[Crossref]

2000 (3)

T. H. Yoon , G. D. Lee , and J. C. Kim , “ Nontwist quarter-wave liquid crystal cell for a high-contrast reflective display ,” Opt. Lett.   25 , 1547 – 1549 ( 2000 ).
[Crossref]

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Y. Iwamoto , Y. Toko , H. Hiramoto , and Y. Iimura , “ Improvement of transmitted light efficiency in SH-LCDs using quarter-wave retardation films ,” Soc. Inf. Display Tech. Digest   31 , 902 – 905 ( 2000 ).
[Crossref]

1998 (2)

Y. Saitoh , S. Kimura , K. Kusafuka , and H. Shimizu , Jpn. J. Appl. Phys.   37 , 4822 – 4828 ( 1998 ).
[Crossref]

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

1997 (1)

K. Ohmuro , S. Kataoka , T. Sasaki , and Y. Koike , Soc. Inf. Display Tech. Digest   33 , 845 – 848 ( 1997 ).

1991 (1)

Y. Fujimura , T. Nagatsuka , H. Yoshimi , and T. Shimomura , “ Optical properties of retardation films for STN-LCDs ,” Soc. Inf. Display Tech. Digest ,   22 , 739 – 742 ( 1991 ).

1956 (1)

S. Pancharatnam , “ Achromatic combinations of birefringent plates ,” Proc. Ind. Acad. Sci. A   41 , 130 – 144 ( 1956 ).

Bos, P. J.

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

Brosseau, C.

C. Brosseau , Fundamentals of Polarized Light: A statistical Optics Approach , ( Wiley, New York , 1998 ).

Chen, J.

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

Cho, H. M.

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Fujikawa, T.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

Fujimura, Y.

Y. Fujimura , T. Nagatsuka , H. Yoshimi , and T. Shimomura , “ Optical properties of retardation films for STN-LCDs ,” Soc. Inf. Display Tech. Digest ,   22 , 739 – 742 ( 1991 ).

Haupt, R. L.

R. L. Haupt and S. E. Haupt , Practical Genetic Algorithms , ( Wiley, Hoboken , 2004 ).

Haupt, S. E.

R. L. Haupt and S. E. Haupt , Practical Genetic Algorithms , ( Wiley, Hoboken , 2004 ).

Hiramoto, H.

Y. Iwamoto , Y. Toko , H. Hiramoto , and Y. Iimura , “ Improvement of transmitted light efficiency in SH-LCDs using quarter-wave retardation films ,” Soc. Inf. Display Tech. Digest   31 , 902 – 905 ( 2000 ).
[Crossref]

Hong, Q.

Hong, S. H.

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Huang, Y.

Y. Huang , T. X. Wu , and S. T. Wu , “ Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method ,” J. Appl. Phys.   93 , 2490 – 2495 ( 2003 ).
[Crossref]

Huard, S.

S. Huard , Polarization of Light , ( Wiley, New York , 1997 ).

Iimura, Y.

Y. Iwamoto , Y. Toko , H. Hiramoto , and Y. Iimura , “ Improvement of transmitted light efficiency in SH-LCDs using quarter-wave retardation films ,” Soc. Inf. Display Tech. Digest   31 , 902 – 905 ( 2000 ).
[Crossref]

Inoue, H.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

Ishinabe, T.

T. Ishinabe , T. Miyashita , and T. Uchida , “ Design of a quarter wave plate with wide viewing angle and wide wavelength range for high quality reflective LCDs ,” Soc. Inf. Display Tech. Digest   32 , 906 – 909 ( 2001 ).
[Crossref]

Iwamoto, Y.

Y. Iwamoto , Y. Toko , H. Hiramoto , and Y. Iimura , “ Improvement of transmitted light efficiency in SH-LCDs using quarter-wave retardation films ,” Soc. Inf. Display Tech. Digest   31 , 902 – 905 ( 2000 ).
[Crossref]

Jeong, Y. H.

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Jyu, J. J.

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

Kataoka, S.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

K. Ohmuro , S. Kataoka , T. Sasaki , and Y. Koike , Soc. Inf. Display Tech. Digest   33 , 845 – 848 ( 1997 ).

Kelly, J. R.

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

Kim, H. Y.

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Kim, J. C.

Kim, K. H.

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

Kimura, S.

Y. Saitoh , S. Kimura , K. Kusafuka , and H. Shimizu , Jpn. J. Appl. Phys.   37 , 4822 – 4828 ( 1998 ).
[Crossref]

Koike, Y.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

K. Ohmuro , S. Kataoka , T. Sasaki , and Y. Koike , Soc. Inf. Display Tech. Digest   33 , 845 – 848 ( 1997 ).

Kusafuka, K.

Y. Saitoh , S. Kimura , K. Kusafuka , and H. Shimizu , Jpn. J. Appl. Phys.   37 , 4822 – 4828 ( 1998 ).
[Crossref]

Lee, G. D.

Lee, W. G.

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Leea, S. H.

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Lu, R.

Miyashita, T.

T. Ishinabe , T. Miyashita , and T. Uchida , “ Design of a quarter wave plate with wide viewing angle and wide wavelength range for high quality reflective LCDs ,” Soc. Inf. Display Tech. Digest   32 , 906 – 909 ( 2001 ).
[Crossref]

Nagatsuka, T.

Y. Fujimura , T. Nagatsuka , H. Yoshimi , and T. Shimomura , “ Optical properties of retardation films for STN-LCDs ,” Soc. Inf. Display Tech. Digest ,   22 , 739 – 742 ( 1991 ).

Ohmuro, K.

K. Ohmuro , S. Kataoka , T. Sasaki , and Y. Koike , Soc. Inf. Display Tech. Digest   33 , 845 – 848 ( 1997 ).

Okamoto, K.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

Pancharatnam, S.

S. Pancharatnam , “ Achromatic combinations of birefringent plates ,” Proc. Ind. Acad. Sci. A   41 , 130 – 144 ( 1956 ).

Saitoh, Y.

Y. Saitoh , S. Kimura , K. Kusafuka , and H. Shimizu , Jpn. J. Appl. Phys.   37 , 4822 – 4828 ( 1998 ).
[Crossref]

Sasabayashi, T.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

Sasaki, T.

K. Ohmuro , S. Kataoka , T. Sasaki , and Y. Koike , Soc. Inf. Display Tech. Digest   33 , 845 – 848 ( 1997 ).

Shimizu, H.

Y. Saitoh , S. Kimura , K. Kusafuka , and H. Shimizu , Jpn. J. Appl. Phys.   37 , 4822 – 4828 ( 1998 ).
[Crossref]

Shimomura, T.

Y. Fujimura , T. Nagatsuka , H. Yoshimi , and T. Shimomura , “ Optical properties of retardation films for STN-LCDs ,” Soc. Inf. Display Tech. Digest ,   22 , 739 – 742 ( 1991 ).

Souk, J. H.

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

Takeda, A.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

Toko, Y.

Y. Iwamoto , Y. Toko , H. Hiramoto , and Y. Iimura , “ Improvement of transmitted light efficiency in SH-LCDs using quarter-wave retardation films ,” Soc. Inf. Display Tech. Digest   31 , 902 – 905 ( 2000 ).
[Crossref]

Tsuda, H.

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

Uchida, T.

T. Ishinabe , T. Miyashita , and T. Uchida , “ Design of a quarter wave plate with wide viewing angle and wide wavelength range for high quality reflective LCDs ,” Soc. Inf. Display Tech. Digest   32 , 906 – 909 ( 2001 ).
[Crossref]

Wu, S. T.

Q. Hong , T. X. Wu , X. Zhu , R. Lu , and S. T. Wu , “ Designs of wide-view and broadband circular polarizers ,” Opt. Express   13 , 8318 – 8331 ( 2005 ). R. Lu , X. Zhu , S. T. Wu , Q. Hong , and T.X. Wu , “ Ultrawide-view liquid crystal displays ,” J. Display Technology   1 , 3 – 14 ( 2005 ).
[Crossref] [PubMed]

Y. Huang , T. X. Wu , and S. T. Wu , “ Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method ,” J. Appl. Phys.   93 , 2490 – 2495 ( 2003 ).
[Crossref]

S. T. Wu and D. K. Yang , Reflective Liquid Crystal Displays , ( Wiley, New York , 2001 ).

Wu, T. X.

Yang, D. K.

S. T. Wu and D. K. Yang , Reflective Liquid Crystal Displays , ( Wiley, New York , 2001 ).

Yoon, T. H.

Yoshimi, H.

Y. Fujimura , T. Nagatsuka , H. Yoshimi , and T. Shimomura , “ Optical properties of retardation films for STN-LCDs ,” Soc. Inf. Display Tech. Digest ,   22 , 739 – 742 ( 1991 ).

Zhu, X.

J. Appl. Phys. (2)

S. H. Hong , Y. H. Jeong , H. Y. Kim , H. M. Cho , W. G. Lee , and S. H. Leea , “ Electro-optic characteristics of 4-domain vertical alignment nematic liquid crystal display with interdigital electrode ,” J. Appl. Phys.   87 , 8259 – 8263 ( 2000 ).
[Crossref]

Y. Huang , T. X. Wu , and S. T. Wu , “ Simulations of liquid-crystal Fabry-Perot etalons by an improved 4×4 matrix method ,” J. Appl. Phys.   93 , 2490 – 2495 ( 2003 ).
[Crossref]

Jpn. J. Appl. Phys. (1)

Y. Saitoh , S. Kimura , K. Kusafuka , and H. Shimizu , Jpn. J. Appl. Phys.   37 , 4822 – 4828 ( 1998 ).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Proc. Ind. Acad. Sci. A (1)

S. Pancharatnam , “ Achromatic combinations of birefringent plates ,” Proc. Ind. Acad. Sci. A   41 , 130 – 144 ( 1956 ).

Soc. Inf. Display Tech. Digest (6)

Y. Fujimura , T. Nagatsuka , H. Yoshimi , and T. Shimomura , “ Optical properties of retardation films for STN-LCDs ,” Soc. Inf. Display Tech. Digest ,   22 , 739 – 742 ( 1991 ).

S. Kataoka , A. Takeda , H. Tsuda , Y. Koike , H. Inoue , T. Fujikawa , T. Sasabayashi , and K. Okamoto , Soc. Inf. Display Tech. Digest   37 , 1066 – 1069 ( 2001 ).
[Crossref]

K. Ohmuro , S. Kataoka , T. Sasaki , and Y. Koike , Soc. Inf. Display Tech. Digest   33 , 845 – 848 ( 1997 ).

Y. Iwamoto , Y. Toko , H. Hiramoto , and Y. Iimura , “ Improvement of transmitted light efficiency in SH-LCDs using quarter-wave retardation films ,” Soc. Inf. Display Tech. Digest   31 , 902 – 905 ( 2000 ).
[Crossref]

T. Ishinabe , T. Miyashita , and T. Uchida , “ Design of a quarter wave plate with wide viewing angle and wide wavelength range for high quality reflective LCDs ,” Soc. Inf. Display Tech. Digest   32 , 906 – 909 ( 2001 ).
[Crossref]

J. Chen , K. H. Kim , J. J. Jyu , J. H. Souk , J. R. Kelly , and P. J. Bos , “ Optimum film compensation modes for TN and VA LCDs ,” Soc. Inf. Display Tech. Digest   29 , 315 – 318 ( 1998 ).
[Crossref]

Other (4)

S. Huard , Polarization of Light , ( Wiley, New York , 1997 ).

C. Brosseau , Fundamentals of Polarized Light: A statistical Optics Approach , ( Wiley, New York , 1998 ).

S. T. Wu and D. K. Yang , Reflective Liquid Crystal Displays , ( Wiley, New York , 2001 ).

R. L. Haupt and S. E. Haupt , Practical Genetic Algorithms , ( Wiley, Hoboken , 2004 ).

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Figures (8)

Fig. 1.
Fig. 1.

Configuration of a wide-view circular polarizer with a linear polarizer and two biaxial films.

Fig. 2.
Fig. 2.

States of polarization inside a wide-view circular polarizer at oblique incidence θ in = 85°. Dotted lines and solid line show the polarization states when the azimuths of incident plane ϕ in are at 30° and 60°, respectively. Red and blue lines show the polarizations inside the first and second biaxial films, respectively.

Fig. 3.
Fig. 3.

State of polarization emerging from a wide-view circular polarizer when θ in = 0° ~ 85° at each fixed ϕ in, where ϕ in = 0° ϕ 360° with 10° interval.

Fig. 4.
Fig. 4.

Device configuration of the crossed wide-view circular polarizers.

Fig. 5.
Fig. 5.

Iso-transmittance contour showing: (a) light leakage of the crossed wide-view circular polarizers, and (b) transmittance of two parallel circular polarizers. λ=550 nm.

Fig. 6.
Fig. 6.

Ten-layer ideal anti-reflection film: (a) refractive indices profile, and (b) transmittance.

Fig. 7.
Fig. 7.

The calculated maximum light leakage of the crossed circular polarizers at different viewing angles as a function of wavelength. The configuration of the crossed circular polarizers is in Fig. 1 and the ten-layer anti-reflection film in Fig. 6 is assumed.

Fig. 8.
Fig. 8.

Design tolerance of the proposed wide-view circular polarizer. The viewing cone is ±85° and λ= 550 nm. Ten-layer anti-reflection film is assumed.

Equations (7)

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

Δ P ( X ) ( RCP ) = P ( X ) P ( RCP )
= ( S 1 _ ( X ) 0 ) 2 + ( S 2 _ ( X ) 0 ) 2 + ( S 3 _ ( X ) ( 1 ) ) 2
= 2 ( S 3 _ ( X ) + 1 ) .
cos t = max { 2 ( S 3 _ ( 2 B ) + 1 ) ( θ in = 0 0 ~ 85 0 , ϕ in = 0 0 ~ 360 0 ) } ,
2 ϕ 1 4 ϕ 2 = 2 × ( 360 + 46.37 ) 4 × ( 180 + 0.68 )
= 90.02 0
90 0

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