Abstract

A subwavelength-period grating made in an intrinsic anisotropic medium was experimentally fabricated by means of imprinting and subsequent photoinduced molecular alignment of photocrosslinkable polymer liquid crystals (PCLC). Optical properties including the total birefringence and optic axis were theoretically and experimentally investigated by varying the crossing angle between the grating vector and the polarization azimuth of linearly polarized ultraviolet light for the photoalignment of PCLC. The total birefringence and optic axis were well-controlled by both form birefringence due to the subwavelength-period grating structure and intrinsic birefringence induced by photoalignment of PCLC. The finite-difference time-domain (FDTD) method was an effective tool for characterizing the optical properties of a subwavelength-period grating made in an intrinsic anisotropic medium.

© 2012 Optical Society of America

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References

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  1. Z. Yu, W. Wu, L. Chen, and S. Y. Chou, “Fabrication of large area 100 nm pitch grating by spatial frequency doubling and nanoimprint lithography for subwavelength optical applications,” J. Vac. Sci. Technol. B 19, 2816–2819 (2001).
    [CrossRef]
  2. Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
    [CrossRef]
  3. T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
    [CrossRef]
  4. J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
    [CrossRef]
  5. Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26, 1690–1695 (2008).
    [CrossRef]
  6. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Characterization of optically imprinted polarization gratings,” Appl. Opt. 48, 4062–4067 (2009).
    [CrossRef]
  7. S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
    [CrossRef]
  8. For example, M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980), p. 705.
  9. S. M. Rytov, “Electromagnetic preperties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  10. C. W. Han and R. K. Kostuk, “Enhanced phase shift in a zeroth-order beam from subwavelength grating structures formed in uniaxial birefringent materials,” J. Opt. Soc. Am. A 13, 1728–1736 (1996).
    [CrossRef]
  11. A. Emoto, M. Nishi, M. Okada, S. Manabe, S. Matsui, N. Kawatsuki, and H. Ono, “Form birefringence in intrinsic birefringent media possessing a subwavelength structure,” Appl. Opt. 49, 4355–4361 (2010).
    [CrossRef]
  12. N. Kawatsuki, K. Goto, T. Kawakami, and T. Yamamoto, “Reversion of alignment direction in the thermally enhanced photoorientation of photo-cross-linkable polymer liquid crystal films,” Macromolecules 35, 706–713 (2002).
    [CrossRef]
  13. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  14. S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo, “On application of finite methods in time domain to anisotropic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 2195–2206 (1996).
    [CrossRef]
  15. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]

2010 (2)

S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
[CrossRef]

A. Emoto, M. Nishi, M. Okada, S. Manabe, S. Matsui, N. Kawatsuki, and H. Ono, “Form birefringence in intrinsic birefringent media possessing a subwavelength structure,” Appl. Opt. 49, 4355–4361 (2010).
[CrossRef]

2009 (1)

2008 (1)

Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26, 1690–1695 (2008).
[CrossRef]

2006 (1)

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

2005 (2)

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

2002 (1)

N. Kawatsuki, K. Goto, T. Kawakami, and T. Yamamoto, “Reversion of alignment direction in the thermally enhanced photoorientation of photo-cross-linkable polymer liquid crystal films,” Macromolecules 35, 706–713 (2002).
[CrossRef]

2001 (1)

Z. Yu, W. Wu, L. Chen, and S. Y. Chou, “Fabrication of large area 100 nm pitch grating by spatial frequency doubling and nanoimprint lithography for subwavelength optical applications,” J. Vac. Sci. Technol. B 19, 2816–2819 (2001).
[CrossRef]

1996 (2)

C. W. Han and R. K. Kostuk, “Enhanced phase shift in a zeroth-order beam from subwavelength grating structures formed in uniaxial birefringent materials,” J. Opt. Soc. Am. A 13, 1728–1736 (1996).
[CrossRef]

S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo, “On application of finite methods in time domain to anisotropic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 2195–2206 (1996).
[CrossRef]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1956 (1)

S. M. Rytov, “Electromagnetic preperties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Born, M.

For example, M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980), p. 705.

Chang, J.-H.

Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26, 1690–1695 (2008).
[CrossRef]

Chen, L.

Z. Yu, W. Wu, L. Chen, and S. Y. Chou, “Fabrication of large area 100 nm pitch grating by spatial frequency doubling and nanoimprint lithography for subwavelength optical applications,” J. Vac. Sci. Technol. B 19, 2816–2819 (2001).
[CrossRef]

Chen, Y.

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

Chen, Y.-P.

Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26, 1690–1695 (2008).
[CrossRef]

Chou, S. Y.

Z. Yu, W. Wu, L. Chen, and S. Y. Chou, “Fabrication of large area 100 nm pitch grating by spatial frequency doubling and nanoimprint lithography for subwavelength optical applications,” J. Vac. Sci. Technol. B 19, 2816–2819 (2001).
[CrossRef]

Cui, Z.

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

Eberhardt, W.

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

Emoto, A.

Garcia, S. G.

S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo, “On application of finite methods in time domain to anisotropic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 2195–2206 (1996).
[CrossRef]

Goto, K.

N. Kawatsuki, K. Goto, T. Kawakami, and T. Yamamoto, “Reversion of alignment direction in the thermally enhanced photoorientation of photo-cross-linkable polymer liquid crystal films,” Macromolecules 35, 706–713 (2002).
[CrossRef]

Grego, S.

S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
[CrossRef]

Han, C. W.

Hirai, Y.

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

Huffman, A.

S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
[CrossRef]

Hung-Bao, T. M.

S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo, “On application of finite methods in time domain to anisotropic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 2195–2206 (1996).
[CrossRef]

Kawakami, T.

N. Kawatsuki, K. Goto, T. Kawakami, and T. Yamamoto, “Reversion of alignment direction in the thermally enhanced photoorientation of photo-cross-linkable polymer liquid crystal films,” Macromolecules 35, 706–713 (2002).
[CrossRef]

Kawata, H.

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

Kawatsuki, N.

A. Emoto, M. Nishi, M. Okada, S. Manabe, S. Matsui, N. Kawatsuki, and H. Ono, “Form birefringence in intrinsic birefringent media possessing a subwavelength structure,” Appl. Opt. 49, 4355–4361 (2010).
[CrossRef]

N. Kawatsuki, K. Goto, T. Kawakami, and T. Yamamoto, “Reversion of alignment direction in the thermally enhanced photoorientation of photo-cross-linkable polymer liquid crystal films,” Macromolecules 35, 706–713 (2002).
[CrossRef]

Kikuta, H.

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

Kimball, B. R.

Konichi, T.

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

Kostuk, R. K.

Kouba, J.

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

Kubenz, M.

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

Lannon, J.

S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
[CrossRef]

Lee, Y.-P.

Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26, 1690–1695 (2008).
[CrossRef]

Loechel, B.

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

Luech, M.

S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
[CrossRef]

Mai, A.

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

Manabe, S.

Martin, R. G.

S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo, “On application of finite methods in time domain to anisotropic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 2195–2206 (1996).
[CrossRef]

Matsui, S.

Nakajima, M.

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

Nersisyan, S. R.

Nishi, M.

Okada, M.

Olmedo, B. G.

S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo, “On application of finite methods in time domain to anisotropic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 2195–2206 (1996).
[CrossRef]

Ono, H.

Ropers, G.

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic preperties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Schwanecke, A. S.

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

Steeves, D. M.

Stoner, B. R.

S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
[CrossRef]

Tabiryan, N. V.

Tao, J.

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

Wang, L. A.

Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26, 1690–1695 (2008).
[CrossRef]

Wolf, E.

For example, M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980), p. 705.

Wu, W.

Z. Yu, W. Wu, L. Chen, and S. Y. Chou, “Fabrication of large area 100 nm pitch grating by spatial frequency doubling and nanoimprint lithography for subwavelength optical applications,” J. Vac. Sci. Technol. B 19, 2816–2819 (2001).
[CrossRef]

Yamamoto, T.

N. Kawatsuki, K. Goto, T. Kawakami, and T. Yamamoto, “Reversion of alignment direction in the thermally enhanced photoorientation of photo-cross-linkable polymer liquid crystal films,” Macromolecules 35, 706–713 (2002).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Yoshikawa, T.

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

Yu, Z.

Z. Yu, W. Wu, L. Chen, and S. Y. Chou, “Fabrication of large area 100 nm pitch grating by spatial frequency doubling and nanoimprint lithography for subwavelength optical applications,” J. Vac. Sci. Technol. B 19, 2816–2819 (2001).
[CrossRef]

Zhao, X.

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

Zheludev, N. I.

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo, “On application of finite methods in time domain to anisotropic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 44, 2195–2206 (1996).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

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

J. Phys. Conf. Ser. (1)

J. Kouba, M. Kubenz, A. Mai, G. Ropers, W. Eberhardt, and B. Loechel, “Fabrication of nanoimprint stamps for photonic crystals,” J. Phys. Conf. Ser. 34, 897–903 (2006).
[CrossRef]

J. Vac. Sci. Technol. B (3)

Y.-P. Chen, Y.-P. Lee, J.-H. Chang, and L. A. Wang, “Fabrication of concave gratings by curved surface UV-nanoimprint lithography,” J. Vac. Sci. Technol. B 26, 1690–1695 (2008).
[CrossRef]

Z. Yu, W. Wu, L. Chen, and S. Y. Chou, “Fabrication of large area 100 nm pitch grating by spatial frequency doubling and nanoimprint lithography for subwavelength optical applications,” J. Vac. Sci. Technol. B 19, 2816–2819 (2001).
[CrossRef]

T. Yoshikawa, T. Konichi, M. Nakajima, H. Kikuta, H. Kawata, and Y. Hirai, “Fabrication of 1/4 wave plate by nanocasting lithography,” J. Vac. Sci. Technol. B 23, 2939–2944 (2005).
[CrossRef]

Macromolecules (1)

N. Kawatsuki, K. Goto, T. Kawakami, and T. Yamamoto, “Reversion of alignment direction in the thermally enhanced photoorientation of photo-cross-linkable polymer liquid crystal films,” Macromolecules 35, 706–713 (2002).
[CrossRef]

Microelectron. Eng. (2)

Y. Chen, J. Tao, X. Zhao, Z. Cui, A. S. Schwanecke, and N. I. Zheludev, “Nanoimprint lithography for planar chiral photonic meta-materials,” Microelectron. Eng. 78–79, 612–617 (2005).
[CrossRef]

S. Grego, A. Huffman, M. Luech, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87, 1846–1851 (2010).
[CrossRef]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic preperties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (1)

For example, M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon, 1980), p. 705.

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Figures (8)

Fig. 1.
Fig. 1.

Chemical structure of a photocrosslinkable poly(methylmethacrylate) liquid crystal with 4-(4-methoxycinnamoyloxy)biphenyl side groups (PCLC).

Fig. 2.
Fig. 2.

(a) Schematics of imprinting and photoalignment processes for preparing the gratings with intrinsic birefringence, and (b) SEM observation of the cross section of the resulting gratings.

Fig. 3.
Fig. 3.

Experimental setup for measuring; (a) the optic axis and (b) total birefringence.

Fig. 4.
Fig. 4.

(a) Dependence of azimuth of grating vector on output intensity measured using optical system of Fig. 3(a) on varying director ϕD of the PCLC films. Open circles represent the experimental data and solid curves are obtained by theoretical fitting. (b) Dependence of azimuth of analyzer on output intensity measured using optical system of Fig. 3(b). Blue and red open circles represent experimental data for the sample before and after annealing, respectively, and solid curves are obtained by theoretical fitting.

Fig. 5.
Fig. 5.

Geometry used to calculate the form birefringence. The TE- and TM-polarized light is incident normal to the plate gratings.

Fig. 6.
Fig. 6.

(a) Schematics of spatial distribution of the director of the mesogenic molecules within one plane in subwavelength-period gratings. (b) Geometry of the director distributions to calculate the birefringence.

Fig. 7.
Fig. 7.

(a) Dependence of azimuth angles ϕD of the director on ellipticity p of the transmitted light observed in the optical system of Fig. 3(b). (b) Dependence of azimuth angles ϕD of the director on azimuth angles ϕo of index ellipsoid estimated from the θGmax observed in the optical system of Fig. 3(a). Full circles represented to the experimental data. Dotted and solid curves are obtained from FDTD calculations in the case of Δw=0nm and Δw=60nm, respectively. Open squares shows the EMT calculation.

Fig. 8.
Fig. 8.

Form birefringence ΔnF after removing the effects of birefringence in the uniaxial birefringent film under the subwavelength-period gratings by varying the azimuth angle ϕD of the director.

Equations (20)

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

Eout(θG)=[0001]R(θGΔϕ)[exp(iΓ/2)00exp(iΓ/2)]R(θG+Δϕ)[10],
Γ=2πλΔn(d+D),
R(ϕo)=[cosϕosinϕosinϕocosϕo].
T(Γ)=[exp(iΓ/2)00exp(iΓ/2)].
Eout(θA)=R(θA)[1000]R(θA)·R(ϕo)·T(Γ)·R(ϕo)12[1i].
p=1sinΓ1+sinΓ.
Δn=λ2π(d+D)sin1(1p21+p2).
nTE2=n0TE2+π23(Λλ)2F2(1F)2(npTE21)2,
nTM2=n0TM2+π23(Λλ)2F2(1F)2n0TM6n0TE2(1npTM21)2,
n0TE2=FnpTE2+(1F),
1n0TM2=F1npTM2+(1F)
F=wΛ,
iωε0ε˜E=×H,
iωμ0H=×E,
H(φ)=(cosφsinφ0sinφcosφ0001),
S(ϑ)=(cosϑ0sinϑ010sinϑ0cosϑ).
ε˜=H(φ)·S(ϑ)(εo000εo000εe)S(ϑ)·H(φ).
Eout=R(ϕS)·T(ΓS)·R(ϕS)·R(ϕF)·T(ΓF)·R(ϕF)·12[1i],
EF=R(ϕS)·T1(ΓS)·R(ϕS)·Eout.
ΔnF=λ2πdsin1(1pF21+pF2).

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