Abstract

We propose switchable two-dimensional (2D) diffractive gratings with periodic refractive-index modulation arising from layer undulations in cholesteric liquid crystals. The cholesteric cell can be switched between two states: (1) flat layers of a planar cholesteric texture and (2) a square lattice of periodic director modulation associated with layer undulations that produces 2D diffraction patterns. The intensities of the diffraction maxima can be tuned by changing the applied field. The diffractive properties can be optimized for different wavelengths by appropriately choosing cholesteric pitch, cell thickness, and surface treatment.

© 2005 Optical Society of America

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  1. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
    [CrossRef]
  2. A. Fernandez-Nieves, D. R. Link, D. Rudhardt, and D. A. Weitz, Phys. Rev. Lett. 92, 105503 (2004).
    [CrossRef]
  3. D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, Appl. Phys. Lett. 82, 2610 (2003).
    [CrossRef]
  4. E. Schulze and W. von Reden, Proc. SPIE 2408, 113 (1995).
    [CrossRef]
  5. D. Subacius, P. J. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 1350 (1997).
    [CrossRef]
  6. D. Subacius, S. V. Shiyanovskii, Ph. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
    [CrossRef]
  7. S. W. Kang, S. Sprunt, and L. C. Chien, Appl. Phys. Lett. 76, 3516 (2000).
    [CrossRef]
  8. A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, Appl. Phys. Lett. 74, 2572 (1999).
    [CrossRef]
  9. A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
    [CrossRef]
  10. I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, Chem. Phys. Lett. 336, 88 (2001).
  11. M. Kleman and O. D. Lavrentovich, Soft Matter:?An Introduction (Springer, New York, 2003), p. 405.
  12. T. Ishikawa and O. D. Lavrentovich, Phys. Rev. E 63, 030501(R) (2001).
    [CrossRef]
  13. W. Helfrich, Appl. Phys. Lett. 17, 531 (1970).
    [CrossRef]
  14. W. Helfrich, J. Chem. Phys. 55, 839 (1971).
  15. B. I. Senyuk, I. I. Smalyukh, and O. D. Lavrentovich, are preparing a paper titled “Undulations of lamellar liquid crystals in cells with finite surface anchoring.”
  16. I. I. Smalyukh and O. D. Lavrentovich, Phys. Rev. Lett. 90, 085503 (2003).
    [CrossRef]
  17. O. D. Lavrentovich and D.-K. Yang, Phys. Rev. E 57, R6269 (1998).
    [CrossRef]
  18. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), p. 318.

2004 (2)

A. Fernandez-Nieves, D. R. Link, D. Rudhardt, and D. A. Weitz, Phys. Rev. Lett. 92, 105503 (2004).
[CrossRef]

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

2003 (2)

D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, Appl. Phys. Lett. 82, 2610 (2003).
[CrossRef]

I. I. Smalyukh and O. D. Lavrentovich, Phys. Rev. Lett. 90, 085503 (2003).
[CrossRef]

2001 (2)

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, Chem. Phys. Lett. 336, 88 (2001).

T. Ishikawa and O. D. Lavrentovich, Phys. Rev. E 63, 030501(R) (2001).
[CrossRef]

2000 (1)

S. W. Kang, S. Sprunt, and L. C. Chien, Appl. Phys. Lett. 76, 3516 (2000).
[CrossRef]

1999 (1)

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, Appl. Phys. Lett. 74, 2572 (1999).
[CrossRef]

1998 (1)

O. D. Lavrentovich and D.-K. Yang, Phys. Rev. E 57, R6269 (1998).
[CrossRef]

1997 (2)

D. Subacius, P. J. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 1350 (1997).
[CrossRef]

D. Subacius, S. V. Shiyanovskii, Ph. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

1996 (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

1995 (1)

E. Schulze and W. von Reden, Proc. SPIE 2408, 113 (1995).
[CrossRef]

1971 (1)

W. Helfrich, J. Chem. Phys. 55, 839 (1971).

1970 (1)

W. Helfrich, Appl. Phys. Lett. 17, 531 (1970).
[CrossRef]

Bos, P. J.

D. Subacius, P. J. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 1350 (1997).
[CrossRef]

Bos, Ph.

D. Subacius, S. V. Shiyanovskii, Ph. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), p. 318.

Chien, L. C.

S. W. Kang, S. Sprunt, and L. C. Chien, Appl. Phys. Lett. 76, 3516 (2000).
[CrossRef]

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Fernandez-Nieves, A.

A. Fernandez-Nieves, D. R. Link, D. Rudhardt, and D. A. Weitz, Phys. Rev. Lett. 92, 105503 (2004).
[CrossRef]

D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, Appl. Phys. Lett. 82, 2610 (2003).
[CrossRef]

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Fuh, A. Y.-G.

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, Appl. Phys. Lett. 74, 2572 (1999).
[CrossRef]

Ghosh, A. K.

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

Helfrich, W.

W. Helfrich, J. Chem. Phys. 55, 839 (1971).

W. Helfrich, Appl. Phys. Lett. 17, 531 (1970).
[CrossRef]

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Huang, L.-J.

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, Appl. Phys. Lett. 74, 2572 (1999).
[CrossRef]

Ishikawa, K.

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

Ishikawa, T.

T. Ishikawa and O. D. Lavrentovich, Phys. Rev. E 63, 030501(R) (2001).
[CrossRef]

Kang, S. W.

S. W. Kang, S. Sprunt, and L. C. Chien, Appl. Phys. Lett. 76, 3516 (2000).
[CrossRef]

Kawamura, J.

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

Kleman, M.

M. Kleman and O. D. Lavrentovich, Soft Matter:?An Introduction (Springer, New York, 2003), p. 405.

Lavrentovich, O. D.

I. I. Smalyukh and O. D. Lavrentovich, Phys. Rev. Lett. 90, 085503 (2003).
[CrossRef]

T. Ishikawa and O. D. Lavrentovich, Phys. Rev. E 63, 030501(R) (2001).
[CrossRef]

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, Chem. Phys. Lett. 336, 88 (2001).

O. D. Lavrentovich and D.-K. Yang, Phys. Rev. E 57, R6269 (1998).
[CrossRef]

D. Subacius, S. V. Shiyanovskii, Ph. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

D. Subacius, P. J. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 1350 (1997).
[CrossRef]

M. Kleman and O. D. Lavrentovich, Soft Matter:?An Introduction (Springer, New York, 2003), p. 405.

B. I. Senyuk, I. I. Smalyukh, and O. D. Lavrentovich, are preparing a paper titled “Undulations of lamellar liquid crystals in cells with finite surface anchoring.”

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Link, D. R.

A. Fernandez-Nieves, D. R. Link, D. Rudhardt, and D. A. Weitz, Phys. Rev. Lett. 92, 105503 (2004).
[CrossRef]

D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, Appl. Phys. Lett. 82, 2610 (2003).
[CrossRef]

Liu, T.-C.

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, Appl. Phys. Lett. 74, 2572 (1999).
[CrossRef]

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Ono, Y.

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Rudhardt, D.

A. Fernandez-Nieves, D. R. Link, D. Rudhardt, and D. A. Weitz, Phys. Rev. Lett. 92, 105503 (2004).
[CrossRef]

D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, Appl. Phys. Lett. 82, 2610 (2003).
[CrossRef]

Schulze, E.

E. Schulze and W. von Reden, Proc. SPIE 2408, 113 (1995).
[CrossRef]

Senyuk, B. I.

B. I. Senyuk, I. I. Smalyukh, and O. D. Lavrentovich, are preparing a paper titled “Undulations of lamellar liquid crystals in cells with finite surface anchoring.”

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Shiyanovskii, S. V.

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, Chem. Phys. Lett. 336, 88 (2001).

D. Subacius, S. V. Shiyanovskii, Ph. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

Smalyukh, I. I.

I. I. Smalyukh and O. D. Lavrentovich, Phys. Rev. Lett. 90, 085503 (2003).
[CrossRef]

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, Chem. Phys. Lett. 336, 88 (2001).

B. I. Senyuk, I. I. Smalyukh, and O. D. Lavrentovich, are preparing a paper titled “Undulations of lamellar liquid crystals in cells with finite surface anchoring.”

Sprunt, S.

S. W. Kang, S. Sprunt, and L. C. Chien, Appl. Phys. Lett. 76, 3516 (2000).
[CrossRef]

Subacius, D.

D. Subacius, P. J. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 1350 (1997).
[CrossRef]

D. Subacius, S. V. Shiyanovskii, Ph. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

Takanishi, Y.

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

Takezoe, H.

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

Tsai, M.-S.

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, Appl. Phys. Lett. 74, 2572 (1999).
[CrossRef]

von Reden, W.

E. Schulze and W. von Reden, Proc. SPIE 2408, 113 (1995).
[CrossRef]

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Weitz, D. A.

A. Fernandez-Nieves, D. R. Link, D. Rudhardt, and D. A. Weitz, Phys. Rev. Lett. 92, 105503 (2004).
[CrossRef]

D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, Appl. Phys. Lett. 82, 2610 (2003).
[CrossRef]

Yang, D.-K.

O. D. Lavrentovich and D.-K. Yang, Phys. Rev. E 57, R6269 (1998).
[CrossRef]

Appl. Phys. Lett. (6)

D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, Appl. Phys. Lett. 82, 2610 (2003).
[CrossRef]

D. Subacius, P. J. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 1350 (1997).
[CrossRef]

D. Subacius, S. V. Shiyanovskii, Ph. Bos, and O. D. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

S. W. Kang, S. Sprunt, and L. C. Chien, Appl. Phys. Lett. 76, 3516 (2000).
[CrossRef]

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, Appl. Phys. Lett. 74, 2572 (1999).
[CrossRef]

W. Helfrich, Appl. Phys. Lett. 17, 531 (1970).
[CrossRef]

Chem. Phys. Lett. (1)

I. I. Smalyukh, S. V. Shiyanovskii, and O. D. Lavrentovich, Chem. Phys. Lett. 336, 88 (2001).

J. Appl. Phys. (1)

A. K. Ghosh, Y. Takanishi, K. Ishikawa, H. Takezoe, Y. Ono, and J. Kawamura, J. Appl. Phys. 95, 5241 (2004).
[CrossRef]

J. Chem. Phys. (1)

W. Helfrich, J. Chem. Phys. 55, 839 (1971).

Phys. Rev. E (2)

T. Ishikawa and O. D. Lavrentovich, Phys. Rev. E 63, 030501(R) (2001).
[CrossRef]

O. D. Lavrentovich and D.-K. Yang, Phys. Rev. E 57, R6269 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

I. I. Smalyukh and O. D. Lavrentovich, Phys. Rev. Lett. 90, 085503 (2003).
[CrossRef]

A. Fernandez-Nieves, D. R. Link, D. Rudhardt, and D. A. Weitz, Phys. Rev. Lett. 92, 105503 (2004).
[CrossRef]

Proc. IEEE (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, Proc. IEEE 84, 268 (1996).
[CrossRef]

Proc. SPIE (1)

E. Schulze and W. von Reden, Proc. SPIE 2408, 113 (1995).
[CrossRef]

Other (3)

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), p. 318.

B. I. Senyuk, I. I. Smalyukh, and O. D. Lavrentovich, are preparing a paper titled “Undulations of lamellar liquid crystals in cells with finite surface anchoring.”

M. Kleman and O. D. Lavrentovich, Soft Matter:?An Introduction (Springer, New York, 2003), p. 405.

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Figures (4)

Fig. 1
Fig. 1

Polarizing-microscopy textures of the 2D undulations in cholesteric cells under applied ac voltage U1 kHz: (a) E7+CB15, p=5 µm, d/p11, U=12 V; (b) 5CB+CB15, p=5 µm, d/p2.5, U=3.6 V; (c) BL015+ZLI811, p=0.31 µm, d/p40, U=14 V.

Fig. 2
Fig. 2

Diffraction patterns obtained for cholesteric cells with (a) 5CB+CB15, p=5 µm, d/p2.5, U=3.6 V; (b) BL015+ZLI811, p=0.31 µm, d/p40, U=14 V. Distance to the screen is D=0.25 m.

Fig. 3
Fig. 3

(a) FCPM cross section of 2D undulations in the cholesteric cell with a mixture of ZLI3412+CB15 p=5 µm,d/p11,U=12 V and (b) the reconstructed layer pattern. P marks the polarization direction of probing light in FCPM.

Fig. 4
Fig. 4

Intensities for different-order diffraction maxima versus voltage for the cholesteric cell with d=12.5 µm and p=5 µm.

Tables (1)

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Table 1 Materials and Their Electro-Optic Characteristics

Equations (2)

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mλ=Lg sin θ,
r=λDmx2+my21/2/Lg,    tan φ=my/mx,

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