Abstract

The anisotropically intrinsic scattering and reflection of a sole cell of polymer network-90° twisted nematic liquid crystals (PN-90° TNLCs) without any polarizer are proposed. Light with specifically linear polarizations, incident from one direction, can penetrate the PN-90° TNLCs with applied voltage. The polarization direction of the output beam will be rotated 90°. The same linearly polarized light, incident from the other direction, will be scattered because it encounters the refractive indices mismatch of various LC domains. The reflection, resulting from the boundaries of LCs and polymers, also shows optical anisotropy. Such LC devices can be applied as scattering-type linear polarizers.

© 2017 Optical Society of America

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2016 (1)

R. Yamaguchi, K. Inoue, and R. Kurosawa, “Effect of Liquid Crystal Material on Polymer Network Structure in Polymer Stabilized Liquid Crystal Cell,” J. Photopolym. Sci. Technol. 29(2), 289–292 (2016).
[Crossref]

2015 (3)

R. Yamaguchi, K. Goto, S. Sakurai, L. Xiong, and T. Tomono, “Normal and reverse mode light scattering properties in nematic liquid crystal cell using polymer stabilized effect,” J. Photopolym. Sci. Technol. 28(3), 319–323 (2015).
[Crossref]

A. Y. G. Fuh, W. K. Chen, K. T. Cheng, Y. C. Liu, C. K. Liu, and Y. D. Chen, “Formation of holographic gratings in polymer dispersed liquid crystals using off-resonant light,” Opt. Mater. Express 5(4), 774–780 (2015).
[Crossref]

R. Yamaguchi and T. Takasu, “Hybrid aligned nematic liquid crystal smart glass with asymmetrical daylight controls,” J. Soc. Inf. Disp. 23(8), 365–370 (2015).
[Crossref]

2014 (3)

D. Xu, J. Yuan, M. Schadt, and S. T. Wu, “Blue phase liquid crystals stabilized by linear photo-polymerization,” Appl. Phys. Lett. 105(8), 081114 (2014).
[Crossref]

J. Sun and S. T. Wu, “Recent advances in polymer network liquid crystal spatial light modulators,” J. Polym. Sci. Part B Polym. Phys. 52, 183–192 (2014).

J. Sun, S. T. Wu, and Y. Haseba, “Submillisecond-Response Polymer Network Liquid Crystal for Next-Generation Spatial Light Modulators,” Dig. Tech. Pap. 45(1), 1449–1452 (2014).
[Crossref]

2013 (1)

J. Sun, S. Xu, H. Ren, and S. T. Wu, “Reconfigurable fabrication of scattering-free polymer network liquid crystal prism/grating/lens,” Appl. Phys. Lett. 102(16), 161106 (2013).
[Crossref]

2012 (4)

K. Takatoha, A. Harimaa, Y. Kanamea, K. Shinoharaa, and M. Akimotoa, “Fast-response twisted nematic liquid crystal displays with ultrashort pitch liquid crystalline materials,” Liq. Cryst. 39(6), 715–720 (2012).
[Crossref]

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Electro-optical properties and morphology of reverse scattering mode TN LCD,” J. Photopolym. Sci. Technol. 25(3), 313–316 (2012).
[Crossref]

J. Sun, Y. Chen, and S. T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012).
[Crossref] [PubMed]

E. Kallos, V. Yannopapas, and D. J. Photinos, “Enhanced light absorption using optical diodes based on cholesteric liquid crystals,” Opt. Express 2(10), 1449–1461 (2012).
[Crossref]

2011 (2)

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Polarizer free reverse-mode liquid crystal gels with super twisted orientation,” IMID digest 12, 86– 87 (2011).

C. K. Liu, K. T. Cheng, and A. Y. G. Fuh, “Observation of anisotropically reflected colors in chiral monomer-doped cholesteric liquid crystals,” Appl. Phys. Lett. 98(4), 041106 (2011).
[Crossref]

2010 (1)

R. Yamaguchi and L. Xiong, “Reverse-mode liquid crystal gels with twisted orientation,” Jpn. J. Appl. Phys. 49(6), 060203 (2010).
[Crossref]

2007 (1)

S. Y. Lu and L. C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[Crossref]

2006 (1)

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

2005 (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

2004 (3)

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Y. T. O, J. B. Koo, K. J. Hong, J. S. Park, and D. C. Shin, “Effect of grain size on transmittance and mechanical strength of sintered alumina,” Mater. Sci. Eng. A 374(1-2), 191–195 (2004).
[Crossref]

Y. Q. Lu, F. Du, Y. H. Lin, and S. T. Wu, “Variable optical attenuator based on polymer stabilized twisted nematic liquid crystal,” Opt. Express 12(7), 1221–1227 (2004).
[Crossref] [PubMed]

2003 (3)

R. Apetz and M. P. B. van Bruggen, “Transparent alumina: a light-scattering model,” J. Am. Ceram. Soc. 86(3), 480–486 (2003).
[Crossref]

N. Kawatsuki, E. Uchida, and H. Ono, “Formation of pure polarization gratings in 4-methoxyazobenzene containing polymer films using off-resonant laser light,” Appl. Phys. Lett. 83(22), 4544–4546 (2003).
[Crossref]

R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino, “Electrically color-tunable defect mode lasing in one-dimensional photonic-band-gap system containing liquid crystal,” Appl. Phys. Lett. 82(21), 3593–3595 (2003).
[Crossref]

2002 (1)

2000 (1)

I. Dierking, “Polymer Network Stabilized Liquid Crystals,” Adv. Mater. 12(3), 167–181 (2000).
[Crossref]

1996 (1)

A. Y. G. Fuh, M. S. Tsai, and C. Y. Huang, “Polymer-Network Formed in Liquid Crystals: Polymer Network Induced Birefringence in Liquid Crystals,” Jpn. J. Appl. Phys. 35(1), 3960–3963 (1996).
[Crossref]

1995 (2)

R. A. M. Hikmet and H. M. J. Boots, “Domain structure and switching behavior of anisotropic gels,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5824–5831 (1995).
[Crossref] [PubMed]

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

1994 (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

1993 (1)

P. Bos, J. Rahman, and J. W. Doane, “A low-threshold-voltage polymer network TN device,” Dig. Tech. Pap. 24, 877–880 (1993).

1992 (1)

R. A. M. Hikmet, “Electrically induced light scattering from anisotropic gels with negative dielectric anisotropic,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 213(1), 117–131 (1992).
[Crossref]

1991 (1)

R. A. M. Hikmet, “Anisotropic gels and plasticized networks formed by liquid crystal molecules,” Liq. Cryst. 9(3), 405–416 (1991).
[Crossref]

1990 (1)

R. A. M. Hikmet, “Electrically induced light scattering from anisotropic gels,” J. Appl. Phys. 68(9), 4406–4412 (1990).
[Crossref]

Akimotoa, M.

K. Takatoha, A. Harimaa, Y. Kanamea, K. Shinoharaa, and M. Akimotoa, “Fast-response twisted nematic liquid crystal displays with ultrashort pitch liquid crystalline materials,” Liq. Cryst. 39(6), 715–720 (2012).
[Crossref]

Apetz, R.

R. Apetz and M. P. B. van Bruggen, “Transparent alumina: a light-scattering model,” J. Am. Ceram. Soc. 86(3), 480–486 (2003).
[Crossref]

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Boots, H. M. J.

R. A. M. Hikmet and H. M. J. Boots, “Domain structure and switching behavior of anisotropic gels,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5824–5831 (1995).
[Crossref] [PubMed]

Bos, P.

P. Bos, J. Rahman, and J. W. Doane, “A low-threshold-voltage polymer network TN device,” Dig. Tech. Pap. 24, 877–880 (1993).

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Chen, W. K.

Chen, Y.

Chen, Y. D.

Cheng, K. T.

A. Y. G. Fuh, W. K. Chen, K. T. Cheng, Y. C. Liu, C. K. Liu, and Y. D. Chen, “Formation of holographic gratings in polymer dispersed liquid crystals using off-resonant light,” Opt. Mater. Express 5(4), 774–780 (2015).
[Crossref]

C. K. Liu, K. T. Cheng, and A. Y. G. Fuh, “Observation of anisotropically reflected colors in chiral monomer-doped cholesteric liquid crystals,” Appl. Phys. Lett. 98(4), 041106 (2011).
[Crossref]

Chien, L. C.

S. Y. Lu and L. C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[Crossref]

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

Dierking, I.

I. Dierking, “Polymer Network Stabilized Liquid Crystals,” Adv. Mater. 12(3), 167–181 (2000).
[Crossref]

Doane, J. W.

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

P. Bos, J. Rahman, and J. W. Doane, “A low-threshold-voltage polymer network TN device,” Dig. Tech. Pap. 24, 877–880 (1993).

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Du, F.

Fan, Y. H.

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Fuh, A. Y. G.

A. Y. G. Fuh, W. K. Chen, K. T. Cheng, Y. C. Liu, C. K. Liu, and Y. D. Chen, “Formation of holographic gratings in polymer dispersed liquid crystals using off-resonant light,” Opt. Mater. Express 5(4), 774–780 (2015).
[Crossref]

C. K. Liu, K. T. Cheng, and A. Y. G. Fuh, “Observation of anisotropically reflected colors in chiral monomer-doped cholesteric liquid crystals,” Appl. Phys. Lett. 98(4), 041106 (2011).
[Crossref]

A. Y. G. Fuh, M. S. Tsai, and C. Y. Huang, “Polymer-Network Formed in Liquid Crystals: Polymer Network Induced Birefringence in Liquid Crystals,” Jpn. J. Appl. Phys. 35(1), 3960–3963 (1996).
[Crossref]

Fung, Y. K.

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

Gauza, S.

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Goto, K.

R. Yamaguchi, K. Goto, S. Sakurai, L. Xiong, and T. Tomono, “Normal and reverse mode light scattering properties in nematic liquid crystal cell using polymer stabilized effect,” J. Photopolym. Sci. Technol. 28(3), 319–323 (2015).
[Crossref]

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Electro-optical properties and morphology of reverse scattering mode TN LCD,” J. Photopolym. Sci. Technol. 25(3), 313–316 (2012).
[Crossref]

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Polarizer free reverse-mode liquid crystal gels with super twisted orientation,” IMID digest 12, 86– 87 (2011).

Harimaa, A.

K. Takatoha, A. Harimaa, Y. Kanamea, K. Shinoharaa, and M. Akimotoa, “Fast-response twisted nematic liquid crystal displays with ultrashort pitch liquid crystalline materials,” Liq. Cryst. 39(6), 715–720 (2012).
[Crossref]

Haseba, Y.

J. Sun, S. T. Wu, and Y. Haseba, “Submillisecond-Response Polymer Network Liquid Crystal for Next-Generation Spatial Light Modulators,” Dig. Tech. Pap. 45(1), 1449–1452 (2014).
[Crossref]

Hikmet, R. A. M.

R. A. M. Hikmet and H. M. J. Boots, “Domain structure and switching behavior of anisotropic gels,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5824–5831 (1995).
[Crossref] [PubMed]

R. A. M. Hikmet, “Electrically induced light scattering from anisotropic gels with negative dielectric anisotropic,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 213(1), 117–131 (1992).
[Crossref]

R. A. M. Hikmet, “Anisotropic gels and plasticized networks formed by liquid crystal molecules,” Liq. Cryst. 9(3), 405–416 (1991).
[Crossref]

R. A. M. Hikmet, “Electrically induced light scattering from anisotropic gels,” J. Appl. Phys. 68(9), 4406–4412 (1990).
[Crossref]

Hong, K. J.

Y. T. O, J. B. Koo, K. J. Hong, J. S. Park, and D. C. Shin, “Effect of grain size on transmittance and mechanical strength of sintered alumina,” Mater. Sci. Eng. A 374(1-2), 191–195 (2004).
[Crossref]

Huang, C. Y.

A. Y. G. Fuh, M. S. Tsai, and C. Y. Huang, “Polymer-Network Formed in Liquid Crystals: Polymer Network Induced Birefringence in Liquid Crystals,” Jpn. J. Appl. Phys. 35(1), 3960–3963 (1996).
[Crossref]

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Inoue, K.

R. Yamaguchi, K. Inoue, and R. Kurosawa, “Effect of Liquid Crystal Material on Polymer Network Structure in Polymer Stabilized Liquid Crystal Cell,” J. Photopolym. Sci. Technol. 29(2), 289–292 (2016).
[Crossref]

Ishikawa, K.

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Kallos, E.

E. Kallos, V. Yannopapas, and D. J. Photinos, “Enhanced light absorption using optical diodes based on cholesteric liquid crystals,” Opt. Express 2(10), 1449–1461 (2012).
[Crossref]

Kanamea, Y.

K. Takatoha, A. Harimaa, Y. Kanamea, K. Shinoharaa, and M. Akimotoa, “Fast-response twisted nematic liquid crystal displays with ultrashort pitch liquid crystalline materials,” Liq. Cryst. 39(6), 715–720 (2012).
[Crossref]

Kawatsuki, N.

N. Kawatsuki, E. Uchida, and H. Ono, “Formation of pure polarization gratings in 4-methoxyazobenzene containing polymer films using off-resonant laser light,” Appl. Phys. Lett. 83(22), 4544–4546 (2003).
[Crossref]

Kivshar, Y. S.

Koo, J. B.

Y. T. O, J. B. Koo, K. J. Hong, J. S. Park, and D. C. Shin, “Effect of grain size on transmittance and mechanical strength of sintered alumina,” Mater. Sci. Eng. A 374(1-2), 191–195 (2004).
[Crossref]

Kurosawa, R.

R. Yamaguchi, K. Inoue, and R. Kurosawa, “Effect of Liquid Crystal Material on Polymer Network Structure in Polymer Stabilized Liquid Crystal Cell,” J. Photopolym. Sci. Technol. 29(2), 289–292 (2016).
[Crossref]

Lin, Y. H.

Y. Q. Lu, F. Du, Y. H. Lin, and S. T. Wu, “Variable optical attenuator based on polymer stabilized twisted nematic liquid crystal,” Opt. Express 12(7), 1221–1227 (2004).
[Crossref] [PubMed]

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Liu, C. K.

A. Y. G. Fuh, W. K. Chen, K. T. Cheng, Y. C. Liu, C. K. Liu, and Y. D. Chen, “Formation of holographic gratings in polymer dispersed liquid crystals using off-resonant light,” Opt. Mater. Express 5(4), 774–780 (2015).
[Crossref]

C. K. Liu, K. T. Cheng, and A. Y. G. Fuh, “Observation of anisotropically reflected colors in chiral monomer-doped cholesteric liquid crystals,” Appl. Phys. Lett. 98(4), 041106 (2011).
[Crossref]

Liu, Y. C.

Lu, S. Y.

S. Y. Lu and L. C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[Crossref]

Lu, Y. Q.

Matsui, T.

R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino, “Electrically color-tunable defect mode lasing in one-dimensional photonic-band-gap system containing liquid crystal,” Appl. Phys. Lett. 82(21), 3593–3595 (2003).
[Crossref]

Mingaleev, S. F.

Nishimura, S.

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

O, Y. T.

Y. T. O, J. B. Koo, K. J. Hong, J. S. Park, and D. C. Shin, “Effect of grain size on transmittance and mechanical strength of sintered alumina,” Mater. Sci. Eng. A 374(1-2), 191–195 (2004).
[Crossref]

Ono, H.

N. Kawatsuki, E. Uchida, and H. Ono, “Formation of pure polarization gratings in 4-methoxyazobenzene containing polymer films using off-resonant laser light,” Appl. Phys. Lett. 83(22), 4544–4546 (2003).
[Crossref]

Ozaki, M.

R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino, “Electrically color-tunable defect mode lasing in one-dimensional photonic-band-gap system containing liquid crystal,” Appl. Phys. Lett. 82(21), 3593–3595 (2003).
[Crossref]

Ozaki, R.

R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino, “Electrically color-tunable defect mode lasing in one-dimensional photonic-band-gap system containing liquid crystal,” Appl. Phys. Lett. 82(21), 3593–3595 (2003).
[Crossref]

Park, B.

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Park, J. S.

Y. T. O, J. B. Koo, K. J. Hong, J. S. Park, and D. C. Shin, “Effect of grain size on transmittance and mechanical strength of sintered alumina,” Mater. Sci. Eng. A 374(1-2), 191–195 (2004).
[Crossref]

Photinos, D. J.

E. Kallos, V. Yannopapas, and D. J. Photinos, “Enhanced light absorption using optical diodes based on cholesteric liquid crystals,” Opt. Express 2(10), 1449–1461 (2012).
[Crossref]

Rahman, J.

P. Bos, J. Rahman, and J. W. Doane, “A low-threshold-voltage polymer network TN device,” Dig. Tech. Pap. 24, 877–880 (1993).

Ren, H.

J. Sun, S. Xu, H. Ren, and S. T. Wu, “Reconfigurable fabrication of scattering-free polymer network liquid crystal prism/grating/lens,” Appl. Phys. Lett. 102(16), 161106 (2013).
[Crossref]

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Sakurai, S.

R. Yamaguchi, K. Goto, S. Sakurai, L. Xiong, and T. Tomono, “Normal and reverse mode light scattering properties in nematic liquid crystal cell using polymer stabilized effect,” J. Photopolym. Sci. Technol. 28(3), 319–323 (2015).
[Crossref]

Scalora, M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Schadt, M.

D. Xu, J. Yuan, M. Schadt, and S. T. Wu, “Blue phase liquid crystals stabilized by linear photo-polymerization,” Appl. Phys. Lett. 105(8), 081114 (2014).
[Crossref]

Shin, D. C.

Y. T. O, J. B. Koo, K. J. Hong, J. S. Park, and D. C. Shin, “Effect of grain size on transmittance and mechanical strength of sintered alumina,” Mater. Sci. Eng. A 374(1-2), 191–195 (2004).
[Crossref]

Shinoharaa, K.

K. Takatoha, A. Harimaa, Y. Kanamea, K. Shinoharaa, and M. Akimotoa, “Fast-response twisted nematic liquid crystal displays with ultrashort pitch liquid crystalline materials,” Liq. Cryst. 39(6), 715–720 (2012).
[Crossref]

Song, M. H.

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Sun, J.

J. Sun and S. T. Wu, “Recent advances in polymer network liquid crystal spatial light modulators,” J. Polym. Sci. Part B Polym. Phys. 52, 183–192 (2014).

J. Sun, S. T. Wu, and Y. Haseba, “Submillisecond-Response Polymer Network Liquid Crystal for Next-Generation Spatial Light Modulators,” Dig. Tech. Pap. 45(1), 1449–1452 (2014).
[Crossref]

J. Sun, S. Xu, H. Ren, and S. T. Wu, “Reconfigurable fabrication of scattering-free polymer network liquid crystal prism/grating/lens,” Appl. Phys. Lett. 102(16), 161106 (2013).
[Crossref]

J. Sun, Y. Chen, and S. T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012).
[Crossref] [PubMed]

Takanishi, Y.

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Takasu, T.

R. Yamaguchi and T. Takasu, “Hybrid aligned nematic liquid crystal smart glass with asymmetrical daylight controls,” J. Soc. Inf. Disp. 23(8), 365–370 (2015).
[Crossref]

Takatoha, K.

K. Takatoha, A. Harimaa, Y. Kanamea, K. Shinoharaa, and M. Akimotoa, “Fast-response twisted nematic liquid crystal displays with ultrashort pitch liquid crystalline materials,” Liq. Cryst. 39(6), 715–720 (2012).
[Crossref]

Takezoe, H.

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Tomono, T.

R. Yamaguchi, K. Goto, S. Sakurai, L. Xiong, and T. Tomono, “Normal and reverse mode light scattering properties in nematic liquid crystal cell using polymer stabilized effect,” J. Photopolym. Sci. Technol. 28(3), 319–323 (2015).
[Crossref]

Toyooka, T.

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Tsai, M. S.

A. Y. G. Fuh, M. S. Tsai, and C. Y. Huang, “Polymer-Network Formed in Liquid Crystals: Polymer Network Induced Birefringence in Liquid Crystals,” Jpn. J. Appl. Phys. 35(1), 3960–3963 (1996).
[Crossref]

Uchida, E.

N. Kawatsuki, E. Uchida, and H. Ono, “Formation of pure polarization gratings in 4-methoxyazobenzene containing polymer films using off-resonant laser light,” Appl. Phys. Lett. 83(22), 4544–4546 (2003).
[Crossref]

van Bruggen, M. P. B.

R. Apetz and M. P. B. van Bruggen, “Transparent alumina: a light-scattering model,” J. Am. Ceram. Soc. 86(3), 480–486 (2003).
[Crossref]

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Wu, S. T.

D. Xu, J. Yuan, M. Schadt, and S. T. Wu, “Blue phase liquid crystals stabilized by linear photo-polymerization,” Appl. Phys. Lett. 105(8), 081114 (2014).
[Crossref]

J. Sun and S. T. Wu, “Recent advances in polymer network liquid crystal spatial light modulators,” J. Polym. Sci. Part B Polym. Phys. 52, 183–192 (2014).

J. Sun, S. T. Wu, and Y. Haseba, “Submillisecond-Response Polymer Network Liquid Crystal for Next-Generation Spatial Light Modulators,” Dig. Tech. Pap. 45(1), 1449–1452 (2014).
[Crossref]

J. Sun, S. Xu, H. Ren, and S. T. Wu, “Reconfigurable fabrication of scattering-free polymer network liquid crystal prism/grating/lens,” Appl. Phys. Lett. 102(16), 161106 (2013).
[Crossref]

J. Sun, Y. Chen, and S. T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012).
[Crossref] [PubMed]

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

Y. Q. Lu, F. Du, Y. H. Lin, and S. T. Wu, “Variable optical attenuator based on polymer stabilized twisted nematic liquid crystal,” Opt. Express 12(7), 1221–1227 (2004).
[Crossref] [PubMed]

Xiong, L.

R. Yamaguchi, K. Goto, S. Sakurai, L. Xiong, and T. Tomono, “Normal and reverse mode light scattering properties in nematic liquid crystal cell using polymer stabilized effect,” J. Photopolym. Sci. Technol. 28(3), 319–323 (2015).
[Crossref]

R. Yamaguchi and L. Xiong, “Reverse-mode liquid crystal gels with twisted orientation,” Jpn. J. Appl. Phys. 49(6), 060203 (2010).
[Crossref]

Xu, D.

D. Xu, J. Yuan, M. Schadt, and S. T. Wu, “Blue phase liquid crystals stabilized by linear photo-polymerization,” Appl. Phys. Lett. 105(8), 081114 (2014).
[Crossref]

Xu, S.

J. Sun, S. Xu, H. Ren, and S. T. Wu, “Reconfigurable fabrication of scattering-free polymer network liquid crystal prism/grating/lens,” Appl. Phys. Lett. 102(16), 161106 (2013).
[Crossref]

Yamaguchi, R.

R. Yamaguchi, K. Inoue, and R. Kurosawa, “Effect of Liquid Crystal Material on Polymer Network Structure in Polymer Stabilized Liquid Crystal Cell,” J. Photopolym. Sci. Technol. 29(2), 289–292 (2016).
[Crossref]

R. Yamaguchi, K. Goto, S. Sakurai, L. Xiong, and T. Tomono, “Normal and reverse mode light scattering properties in nematic liquid crystal cell using polymer stabilized effect,” J. Photopolym. Sci. Technol. 28(3), 319–323 (2015).
[Crossref]

R. Yamaguchi and T. Takasu, “Hybrid aligned nematic liquid crystal smart glass with asymmetrical daylight controls,” J. Soc. Inf. Disp. 23(8), 365–370 (2015).
[Crossref]

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Electro-optical properties and morphology of reverse scattering mode TN LCD,” J. Photopolym. Sci. Technol. 25(3), 313–316 (2012).
[Crossref]

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Polarizer free reverse-mode liquid crystal gels with super twisted orientation,” IMID digest 12, 86– 87 (2011).

R. Yamaguchi and L. Xiong, “Reverse-mode liquid crystal gels with twisted orientation,” Jpn. J. Appl. Phys. 49(6), 060203 (2010).
[Crossref]

Yang, D. K.

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

Yannopapas, V.

E. Kallos, V. Yannopapas, and D. J. Photinos, “Enhanced light absorption using optical diodes based on cholesteric liquid crystals,” Opt. Express 2(10), 1449–1461 (2012).
[Crossref]

Yaroshchuk, O.

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Electro-optical properties and morphology of reverse scattering mode TN LCD,” J. Photopolym. Sci. Technol. 25(3), 313–316 (2012).
[Crossref]

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Polarizer free reverse-mode liquid crystal gels with super twisted orientation,” IMID digest 12, 86– 87 (2011).

Ying, S.

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

Yoshino, K.

R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino, “Electrically color-tunable defect mode lasing in one-dimensional photonic-band-gap system containing liquid crystal,” Appl. Phys. Lett. 82(21), 3593–3595 (2003).
[Crossref]

Yuan, J.

D. Xu, J. Yuan, M. Schadt, and S. T. Wu, “Blue phase liquid crystals stabilized by linear photo-polymerization,” Appl. Phys. Lett. 105(8), 081114 (2014).
[Crossref]

Zumer, S.

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

Adv. Mater. (1)

I. Dierking, “Polymer Network Stabilized Liquid Crystals,” Adv. Mater. 12(3), 167–181 (2000).
[Crossref]

Appl. Phys. Lett. (7)

R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino, “Electrically color-tunable defect mode lasing in one-dimensional photonic-band-gap system containing liquid crystal,” Appl. Phys. Lett. 82(21), 3593–3595 (2003).
[Crossref]

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[Crossref]

J. Sun, S. Xu, H. Ren, and S. T. Wu, “Reconfigurable fabrication of scattering-free polymer network liquid crystal prism/grating/lens,” Appl. Phys. Lett. 102(16), 161106 (2013).
[Crossref]

S. Y. Lu and L. C. Chien, “A polymer-stabilized single-layer color cholesteric liquid crystal display with anisotropic reflection,” Appl. Phys. Lett. 91(13), 131119 (2007).
[Crossref]

C. K. Liu, K. T. Cheng, and A. Y. G. Fuh, “Observation of anisotropically reflected colors in chiral monomer-doped cholesteric liquid crystals,” Appl. Phys. Lett. 98(4), 041106 (2011).
[Crossref]

D. Xu, J. Yuan, M. Schadt, and S. T. Wu, “Blue phase liquid crystals stabilized by linear photo-polymerization,” Appl. Phys. Lett. 105(8), 081114 (2014).
[Crossref]

N. Kawatsuki, E. Uchida, and H. Ono, “Formation of pure polarization gratings in 4-methoxyazobenzene containing polymer films using off-resonant laser light,” Appl. Phys. Lett. 83(22), 4544–4546 (2003).
[Crossref]

Dig. Tech. Pap. (2)

P. Bos, J. Rahman, and J. W. Doane, “A low-threshold-voltage polymer network TN device,” Dig. Tech. Pap. 24, 877–880 (1993).

J. Sun, S. T. Wu, and Y. Haseba, “Submillisecond-Response Polymer Network Liquid Crystal for Next-Generation Spatial Light Modulators,” Dig. Tech. Pap. 45(1), 1449–1452 (2014).
[Crossref]

IMID digest (1)

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Polarizer free reverse-mode liquid crystal gels with super twisted orientation,” IMID digest 12, 86– 87 (2011).

J. Am. Ceram. Soc. (1)

R. Apetz and M. P. B. van Bruggen, “Transparent alumina: a light-scattering model,” J. Am. Ceram. Soc. 86(3), 480–486 (2003).
[Crossref]

J. Appl. Phys. (2)

R. A. M. Hikmet, “Electrically induced light scattering from anisotropic gels,” J. Appl. Phys. 68(9), 4406–4412 (1990).
[Crossref]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

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

J. Photopolym. Sci. Technol. (3)

R. Yamaguchi, K. Goto, and O. Yaroshchuk, “Electro-optical properties and morphology of reverse scattering mode TN LCD,” J. Photopolym. Sci. Technol. 25(3), 313–316 (2012).
[Crossref]

R. Yamaguchi, K. Goto, S. Sakurai, L. Xiong, and T. Tomono, “Normal and reverse mode light scattering properties in nematic liquid crystal cell using polymer stabilized effect,” J. Photopolym. Sci. Technol. 28(3), 319–323 (2015).
[Crossref]

R. Yamaguchi, K. Inoue, and R. Kurosawa, “Effect of Liquid Crystal Material on Polymer Network Structure in Polymer Stabilized Liquid Crystal Cell,” J. Photopolym. Sci. Technol. 29(2), 289–292 (2016).
[Crossref]

J. Polym. Sci. Part B Polym. Phys. (1)

J. Sun and S. T. Wu, “Recent advances in polymer network liquid crystal spatial light modulators,” J. Polym. Sci. Part B Polym. Phys. 52, 183–192 (2014).

J. Soc. Inf. Disp. (1)

R. Yamaguchi and T. Takasu, “Hybrid aligned nematic liquid crystal smart glass with asymmetrical daylight controls,” J. Soc. Inf. Disp. 23(8), 365–370 (2015).
[Crossref]

Jpn. J. Appl. Phys. (2)

A. Y. G. Fuh, M. S. Tsai, and C. Y. Huang, “Polymer-Network Formed in Liquid Crystals: Polymer Network Induced Birefringence in Liquid Crystals,” Jpn. J. Appl. Phys. 35(1), 3960–3963 (1996).
[Crossref]

R. Yamaguchi and L. Xiong, “Reverse-mode liquid crystal gels with twisted orientation,” Jpn. J. Appl. Phys. 49(6), 060203 (2010).
[Crossref]

Liq. Cryst. (3)

K. Takatoha, A. Harimaa, Y. Kanamea, K. Shinoharaa, and M. Akimotoa, “Fast-response twisted nematic liquid crystal displays with ultrashort pitch liquid crystalline materials,” Liq. Cryst. 39(6), 715–720 (2012).
[Crossref]

R. A. M. Hikmet, “Anisotropic gels and plasticized networks formed by liquid crystal molecules,” Liq. Cryst. 9(3), 405–416 (1991).
[Crossref]

Y. K. Fung, D. K. Yang, S. Ying, L. C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995).
[Crossref]

Mater. Sci. Eng. A (1)

Y. T. O, J. B. Koo, K. J. Hong, J. S. Park, and D. C. Shin, “Effect of grain size on transmittance and mechanical strength of sintered alumina,” Mater. Sci. Eng. A 374(1-2), 191–195 (2004).
[Crossref]

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (1)

R. A. M. Hikmet, “Electrically induced light scattering from anisotropic gels with negative dielectric anisotropic,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 213(1), 117–131 (1992).
[Crossref]

Nat. Mater. (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Mater. Express (1)

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

R. A. M. Hikmet and H. M. J. Boots, “Domain structure and switching behavior of anisotropic gels,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(6), 5824–5831 (1995).
[Crossref] [PubMed]

Thin Solid Films (1)

M. H. Song, B. Park, Y. Takanishi, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Simple electro-tunable optical diode using photonic and anisotropic liquid crystal films,” Thin Solid Films 509(1-2), 49–52 (2006).
[Crossref]

Other (7)

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

S. T. Wu and D. K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

E. Hecht, Optics (Addison Wesley, 4th edition).

Y. Huang, H. Ren, X. Zhu, and S. T. Wu, “Electrically tunable polarization-independent micro lens using polymer network twisted nematic liquid crystal,” United States patent 7079203 B1, Jul. 18 (2006).

J. Li, P. J. Bos, and J. Chen, “Polymer stabilized four domain twisted nematic liquid crystal display,” United States patent 5831700 A, Nov. 3 (1998).

Y. Huang, H. Ren, X. Zhu, and S. T. Wu, “Electronically tunable polarization-independent micro lens using polymer network twisted nematic liquid crystal,” United States patent 7408601 B1, Aug. 5 (2008).

P. Yeh and C. Gu, Optics of Liquid Crystals Displays (Wiley, 1999).

Supplementary Material (1)

NameDescription
» Visualization 1       The video (Visualization 1) clearly demonstrates the asymmetrical polarization-dependent transmission using a single liquid crystal cell of polymer network-90° twisted nematic liquid crystals.

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Figures (10)

Fig. 1
Fig. 1 Schematics of (a) PN-90° TNLCs structures under UV illumination (365 nm) and (b) structures of PN-90° TNLCs with an application of external voltage after the photo-polymerization processes are completed. S1 and S2 represent command and reference surfaces, respectively.
Fig. 2
Fig. 2 Schematics polarization states variations of incident light in the bulks of LC cell. The orange rods represent the orientation of p-RM257/LC molecules on the xy-plane at 11 positions, marked as 0, d 10 , 2d 10 8d 10 , 9d 10 , and d. (a) L1in and L2in travel along the + z-axis from z = 0, and (b) L3in and L4in travel along the −z-axis from z = d.
Fig. 3
Fig. 3 Variations of DPoma of “L1in or L4in” and DPomi of “L2in or L3in” as a function of position.
Fig. 4
Fig. 4 Experiment setup for demonstrating the polarization selective light scattering properties of the reported LC device achieved by PN-90° TNLCs.
Fig. 5
Fig. 5 Variations of transmittance and degree of polarization as functions of applied voltage. The unpolarized lights were incident from (a) command (S1) and (b) reference (S2) surfaces. Analyzertrans. represents the direction of the transmission axis of the analyzer.
Fig. 6
Fig. 6 Schematic diagram of PN-90° TNLCs structures without any application of external voltage.
Fig. 7
Fig. 7 Variations of overall reflection of L1 and L2, also known as RL1 and RL2, as a function of m. m represents the quantity of the boundary between p-RM257 and LCs.
Fig. 8
Fig. 8 Observation of the cases of L1in/out and L4in/out [Fig. 2(a)] through PN-90° TNLCs (a) with the application of a suitable external voltage according to the experimental setup shown in (b); (c) observation of the cases of L2in/out and L3in/out [Fig. 2(b)] with the application of a suitable external voltage according to the experimental setup shown in (d). Red, black, and blue arrows represent the linear polarization directions of the light source (known as the transmission axis of the polarizer), rubbing directions of the substrate S1, and rubbing directions of the substrate S2, respectively (see Visualization 1).
Fig. 9
Fig. 9 The red and blue curves represent the measured spectra of the PN-90° TNLC device with and without the application of a suitable external voltage using the setup consistent with that shown in Fig. 8(d), respectively.
Fig. 10
Fig. 10 Schematic diagrams of the asymmetrical polarization-dependent transmission using a single LC cell of PN-90° TNLCs with an applied AC voltage for the cases of incident lights with linear polarization directions parallel to (a) y-axis and (b) x-axis traveling along ± z-axis.

Equations (13)

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D P o ma=cos( π 2d h ),  0h< 5d 10 .
D P o ma=cos( π 2 π 2d h ),   5d 10 hd.
D P o mi=sin( π 2d h ),  0h< 5d 10 .
D P o mi=sin( π 2 π 2d h ),   5d 10 hd.
SP=1exp( C Δ n eff 2 λ 0 2 d )= 0 d C Δ n eff 2 λ 0 2 exp( C Δ n eff 2 λ 0 2 h )dh.
S P L1 or L4 = 0 5d 10 [ sin( π 2d h ) ] C D P 0 mi Δ n eff 2 λ 0 2 exp( C D P 0 mi Δ n eff 2 λ 0 2 h )dh+     5d 10 d [ sin( π 2 π 2d h ) ] C D P 0 mi Δ n eff 2 λ 0 2 exp( C D P 0 mi Δ n eff 2 λ 0 2 h )dh .
S P L2 or L3 = 0 5d 10 [ cos( π 2d h ) ] C D P 0 ma Δ n eff 2 λ 0 2 exp( C D P 0 ma Δ n eff 2 λ 0 2 h )dh+                   5d 10 d [ cos( π 2 π 2d h ) ] C D P 0 ma Δ n eff 2 λ 0 2 exp( C D P 0 ma Δ n eff 2 λ 0 2 h )dh .
DoL P L1 or L2 = L 1 out L 2 out L 1 out +L 2 out .
DoL P L3 or L4 = L 4 out L 3 out L 4 out +L 3 out .
R no = ( n noLC    n nopRM257 n noLC  +  n nopRM257 ) 2 =0.0000184.
R ne = ( n neLC    n nepRM257 n neLC  +  n nepRM257 ) 2 =0.000295.
R L1 ( 1 { [ 1cos( π 2d 0 ) R no ]××[ 1cos( π 2 π 2d d ) R no ] } mboundaries )+             ( 1 { [ 1sin( π 2d 0 ) R ne ]××[ 1sin( π 2 π 2d d ) R ne ] } mboundaries ).
R L2 ( 1 { [ 1sin( π 2d 0 ) R no ]××[ 1sin( π 2 π 2d d ) R no ] } mboundaries )            ( 1 { [ 1cos( π 2d 0 ) R ne ]××[ 1cos( π 2 π 2d d ) R ne ] } mboundaries ). 

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