Abstract

We propose a novel formation method of arbitrary phase profiles of circular light by controlling azimuthal angles of liquid-crystal directors; its principle is described theoretically. A new liquid-crystal blazed grating is demonstrated by use of the proposed method. It is revealed that the first-order diffraction efficiency reaches the maximum value (theoretically 100%, experimentally approximately 90%) at an optimum applied voltage when the phase difference between the extraordinary and ordinary rays agrees with one-half the wavelength. Furthermore, the polarization states of the diffracted light beams are analyzed by Stokes parameter measurements, and unique polarization-splitting properties are revealed.

© 2004 Optical Society of America

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  1. Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
    [CrossRef]
  2. M. Honma, T. Nose, S. Sato, “Optical properties of anamorphic liquid crystal microlenses and their application for laser diode collimation,” Jpn. J. Appl. Phys. 38, 89–94 (1999).
    [CrossRef]
  3. M. Honma, T. Nose, S. Sato, “Enhancement of numerical aperture of liquid crystal microlenses using a stacked electrode structure,” Jpn. J. Appl. Phys. 39, 4799–4802 (2000).
    [CrossRef]
  4. P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.
  5. W. M. Gibbons, S.-T. Sun, “Optically generated liquid crystal gratings,” Appl. Phys. Lett. 65, 2542–2544 (1994).
    [CrossRef]
  6. J. Chen, P. J. Bos, H. Vithana, D. L. Johnson, “An electro-optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588–2590 (1995).
    [CrossRef]
  7. C. M. Titus, P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239–2241 (1997).
    [CrossRef]
  8. M. Lu, K.-H. Yang, “Nematic liquid crystal phase-gratings for reflective spatial light modulators,” Jpn. J. Appl. Phys. 37, L587–L590 (1998).
    [CrossRef]
  9. Z. He, S. Sato, “Polarization properties of inversely twisted nematic liquid-crystal gratings,” Appl. Opt. 37, 6755–6763 (1998).
    [CrossRef]
  10. X. Wang, D. Wilson, R. Muller, P. Maker, D. Psaltis, “Liquid-crystal blazed-grating beam deflector,” Appl. Opt. 39, 6545–6555 (2000).
    [CrossRef]
  11. C. M. Titus, J. R. Kelly, E. C. Gartland, S. V. Shiyanovskii, J. A. Anderson, P. J. Boss, “Asymmetric transmissive behavior of liquid-crystal diffraction gratings,” Opt. Lett. 26, 1188–1190 (2001).
    [CrossRef]
  12. B. Wen, R. G. Petschek, C. Rosenblatt, “Nematic liquid crystal polarization gratings by modification of surface alignment,” Appl. Opt. 41, 1246–1250 (2002).
    [CrossRef] [PubMed]
  13. H. Ren, Y.-H. Fan, S.-T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82, 3168–3170 (2003).
    [CrossRef]
  14. D. P. Resler, D. S. Hobbs, R. C. Sharp, L. J. Friedman, T. A. Dorschner, “High-efficiency liquid-crystal optical phased-array beam steering,” Opt. Lett. 21, 689–691 (1996).
    [CrossRef] [PubMed]
  15. W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
    [CrossRef]
  16. J.-H. Kim, M. Yoneya, H. Yokoyama, “Tristable nematic liquid-crystal device using micropatterned surface alignment,” Nature 420, 159–162 (2002).
    [CrossRef] [PubMed]
  17. M. Honma, T. Nose, “Polarization-independent liquid crystal grating fabricated by microrubbing process,” Jpn. J. Appl. Phys. 42, 6992–6997 (2003).
    [CrossRef]
  18. M. Honma, T. Nose, “Liquid-crystal depolarizer consisting of randomly aligned hybrid orientation domains,” Appl. Opt. 43, 4667–4671 (2004).
    [CrossRef] [PubMed]

2004 (1)

2003 (2)

M. Honma, T. Nose, “Polarization-independent liquid crystal grating fabricated by microrubbing process,” Jpn. J. Appl. Phys. 42, 6992–6997 (2003).
[CrossRef]

H. Ren, Y.-H. Fan, S.-T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82, 3168–3170 (2003).
[CrossRef]

2002 (2)

J.-H. Kim, M. Yoneya, H. Yokoyama, “Tristable nematic liquid-crystal device using micropatterned surface alignment,” Nature 420, 159–162 (2002).
[CrossRef] [PubMed]

B. Wen, R. G. Petschek, C. Rosenblatt, “Nematic liquid crystal polarization gratings by modification of surface alignment,” Appl. Opt. 41, 1246–1250 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (2)

X. Wang, D. Wilson, R. Muller, P. Maker, D. Psaltis, “Liquid-crystal blazed-grating beam deflector,” Appl. Opt. 39, 6545–6555 (2000).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Enhancement of numerical aperture of liquid crystal microlenses using a stacked electrode structure,” Jpn. J. Appl. Phys. 39, 4799–4802 (2000).
[CrossRef]

1999 (2)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Optical properties of anamorphic liquid crystal microlenses and their application for laser diode collimation,” Jpn. J. Appl. Phys. 38, 89–94 (1999).
[CrossRef]

1998 (2)

M. Lu, K.-H. Yang, “Nematic liquid crystal phase-gratings for reflective spatial light modulators,” Jpn. J. Appl. Phys. 37, L587–L590 (1998).
[CrossRef]

Z. He, S. Sato, “Polarization properties of inversely twisted nematic liquid-crystal gratings,” Appl. Opt. 37, 6755–6763 (1998).
[CrossRef]

1997 (2)

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

C. M. Titus, P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239–2241 (1997).
[CrossRef]

1996 (1)

1995 (1)

J. Chen, P. J. Bos, H. Vithana, D. L. Johnson, “An electro-optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588–2590 (1995).
[CrossRef]

1994 (1)

W. M. Gibbons, S.-T. Sun, “Optically generated liquid crystal gratings,” Appl. Phys. Lett. 65, 2542–2544 (1994).
[CrossRef]

Anderson, J. A.

Bos, P. J.

C. M. Titus, P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239–2241 (1997).
[CrossRef]

J. Chen, P. J. Bos, H. Vithana, D. L. Johnson, “An electro-optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588–2590 (1995).
[CrossRef]

P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.

Boss, P. J.

Chen, J.

J. Chen, P. J. Bos, H. Vithana, D. L. Johnson, “An electro-optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588–2590 (1995).
[CrossRef]

P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.

Doane, J. W.

P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.

Dorschner, T. A.

Fan, Y.-H.

H. Ren, Y.-H. Fan, S.-T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82, 3168–3170 (2003).
[CrossRef]

Friedman, L. J.

Gartland, E. C.

Gibbons, W. M.

W. M. Gibbons, S.-T. Sun, “Optically generated liquid crystal gratings,” Appl. Phys. Lett. 65, 2542–2544 (1994).
[CrossRef]

Glenn, W.

P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.

Hara, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

He, Z.

Hobbs, D. S.

Holton, C.

P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.

Honma, M.

M. Honma, T. Nose, “Liquid-crystal depolarizer consisting of randomly aligned hybrid orientation domains,” Appl. Opt. 43, 4667–4671 (2004).
[CrossRef] [PubMed]

M. Honma, T. Nose, “Polarization-independent liquid crystal grating fabricated by microrubbing process,” Jpn. J. Appl. Phys. 42, 6992–6997 (2003).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Enhancement of numerical aperture of liquid crystal microlenses using a stacked electrode structure,” Jpn. J. Appl. Phys. 39, 4799–4802 (2000).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Optical properties of anamorphic liquid crystal microlenses and their application for laser diode collimation,” Jpn. J. Appl. Phys. 38, 89–94 (1999).
[CrossRef]

Ide, M.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Igasaki, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Inoue, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Johnson, D. L.

J. Chen, P. J. Bos, H. Vithana, D. L. Johnson, “An electro-optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588–2590 (1995).
[CrossRef]

Kamiya, T.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Kelly, J. R.

Kim, J.-H.

J.-H. Kim, M. Yoneya, H. Yokoyama, “Tristable nematic liquid-crystal device using micropatterned surface alignment,” Nature 420, 159–162 (2002).
[CrossRef] [PubMed]

Klaus, W.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Kobayashi, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Li, F.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Lu, M.

M. Lu, K.-H. Yang, “Nematic liquid crystal phase-gratings for reflective spatial light modulators,” Jpn. J. Appl. Phys. 37, L587–L590 (1998).
[CrossRef]

Maker, P.

Morokawa, S.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Mukohzawa, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Muller, R.

Nose, T.

M. Honma, T. Nose, “Liquid-crystal depolarizer consisting of randomly aligned hybrid orientation domains,” Appl. Opt. 43, 4667–4671 (2004).
[CrossRef] [PubMed]

M. Honma, T. Nose, “Polarization-independent liquid crystal grating fabricated by microrubbing process,” Jpn. J. Appl. Phys. 42, 6992–6997 (2003).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Enhancement of numerical aperture of liquid crystal microlenses using a stacked electrode structure,” Jpn. J. Appl. Phys. 39, 4799–4802 (2000).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Optical properties of anamorphic liquid crystal microlenses and their application for laser diode collimation,” Jpn. J. Appl. Phys. 38, 89–94 (1999).
[CrossRef]

Petschek, R. G.

Psaltis, D.

Ren, H.

H. Ren, Y.-H. Fan, S.-T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82, 3168–3170 (2003).
[CrossRef]

Resler, D. P.

Rosenblatt, C.

Sato, S.

M. Honma, T. Nose, S. Sato, “Enhancement of numerical aperture of liquid crystal microlenses using a stacked electrode structure,” Jpn. J. Appl. Phys. 39, 4799–4802 (2000).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Optical properties of anamorphic liquid crystal microlenses and their application for laser diode collimation,” Jpn. J. Appl. Phys. 38, 89–94 (1999).
[CrossRef]

Z. He, S. Sato, “Polarization properties of inversely twisted nematic liquid-crystal gratings,” Appl. Opt. 37, 6755–6763 (1998).
[CrossRef]

Sharp, R. C.

Shiyanovskii, S. V.

Smith, B.

P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.

Sun, S.-T.

W. M. Gibbons, S.-T. Sun, “Optically generated liquid crystal gratings,” Appl. Phys. Lett. 65, 2542–2544 (1994).
[CrossRef]

Titus, C. M.

C. M. Titus, J. R. Kelly, E. C. Gartland, S. V. Shiyanovskii, J. A. Anderson, P. J. Boss, “Asymmetric transmissive behavior of liquid-crystal diffraction gratings,” Opt. Lett. 26, 1188–1190 (2001).
[CrossRef]

C. M. Titus, P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239–2241 (1997).
[CrossRef]

Toyoda, H.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Tsuchiya, M.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Vithana, H.

J. Chen, P. J. Bos, H. Vithana, D. L. Johnson, “An electro-optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588–2590 (1995).
[CrossRef]

Wang, X.

Wen, B.

Wilson, D.

Wu, S.-T.

H. Ren, Y.-H. Fan, S.-T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82, 3168–3170 (2003).
[CrossRef]

Yang, K.-H.

M. Lu, K.-H. Yang, “Nematic liquid crystal phase-gratings for reflective spatial light modulators,” Jpn. J. Appl. Phys. 37, L587–L590 (1998).
[CrossRef]

Yokoyama, H.

J.-H. Kim, M. Yoneya, H. Yokoyama, “Tristable nematic liquid-crystal device using micropatterned surface alignment,” Nature 420, 159–162 (2002).
[CrossRef] [PubMed]

Yoneya, M.

J.-H. Kim, M. Yoneya, H. Yokoyama, “Tristable nematic liquid-crystal device using micropatterned surface alignment,” Nature 420, 159–162 (2002).
[CrossRef] [PubMed]

Yoshida, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (4)

H. Ren, Y.-H. Fan, S.-T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82, 3168–3170 (2003).
[CrossRef]

W. M. Gibbons, S.-T. Sun, “Optically generated liquid crystal gratings,” Appl. Phys. Lett. 65, 2542–2544 (1994).
[CrossRef]

J. Chen, P. J. Bos, H. Vithana, D. L. Johnson, “An electro-optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588–2590 (1995).
[CrossRef]

C. M. Titus, P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239–2241 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (4)

M. Lu, K.-H. Yang, “Nematic liquid crystal phase-gratings for reflective spatial light modulators,” Jpn. J. Appl. Phys. 37, L587–L590 (1998).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Optical properties of anamorphic liquid crystal microlenses and their application for laser diode collimation,” Jpn. J. Appl. Phys. 38, 89–94 (1999).
[CrossRef]

M. Honma, T. Nose, S. Sato, “Enhancement of numerical aperture of liquid crystal microlenses using a stacked electrode structure,” Jpn. J. Appl. Phys. 39, 4799–4802 (2000).
[CrossRef]

M. Honma, T. Nose, “Polarization-independent liquid crystal grating fabricated by microrubbing process,” Jpn. J. Appl. Phys. 42, 6992–6997 (2003).
[CrossRef]

Nature (1)

J.-H. Kim, M. Yoneya, H. Yokoyama, “Tristable nematic liquid-crystal device using micropatterned surface alignment,” Nature 420, 159–162 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Opt. Lett. (2)

Opt. Rev. (1)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzawa, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Other (1)

P. J. Bos, J. Chen, J. W. Doane, B. Smith, C. Holton, W. Glenn, “An optically active diffractive device for a high-efficiency light valve,” in Society for Information Display Symposium Digest (Society for Information Display, San Jose, Calif., 1995), pp. 601–604.

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Figures (5)

Fig. 1
Fig. 1

(a) Microrubbing pattern for LC blazed grating with eight levels and (b) distribution function of the azimuthal angle of the rubbed direction. The grating period is 80 μm, the width of each level is 10 μm, the grating width is 1.2 mm, and the scanning pitch of the microrubbing is 3 μm.

Fig. 2
Fig. 2

Micrograph of the LC blazed grating fabricated by use of the microrubbing process.

Fig. 3
Fig. 3

Diffracted beams with respect to (a) right and (b) left-circular light incidence.

Fig. 4
Fig. 4

Relationship between the diffraction efficiencies and the applied voltage for the right-circular light incidence.

Fig. 5
Fig. 5

Relationship between the diffraction efficiencies and the applied voltage for the linearly polarized light incidence, of which the polarization direction makes an angle of π/4 with respect to the grating vector.

Equations (3)

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

ExoEyo=cos ϕ-sin ϕsin ϕcos ϕ -i00i cos ϕsin ϕ-sin ϕcos ϕ×ExiEyi=-i cos 2ϕ-i sin 2ϕ-i sin 2ϕi cos 2ϕ ExiEyi.
ExoEyo=-i expi2ϕ21-i.
ExoEyo=-i exp-i2ϕ21i.

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