Abstract

Diffraction gratings were studied in cells of the homogeneously aligned liquid-crystal E7 doped with multiwall carbon nanotubes. These phase gratings were induced by interference modulation of two coherent optical beams, in conjunction with an applied dc field that was perpendicular to the unperturbed director axis. Self-diffraction was observed at all angles of incidence of the writing beams, including normal incidence. A superior nonlinear-index coefficient of 5×10-2 cm2/W was obtained after passage of a 44mW/cm2 beam through a film with a grating constant of 18 μm under an external voltage of 15  V. The observed phenomenon depends strongly on the applied dc field, and the memory effect in a nematic film depends strongly on the grating constant.

© 2001 Optical Society of America

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2000 (3)

S. Xie, W. Li, Z. Pan, B. Chang, and L. Sun, J. Phys. Chem. Solids 61, 1153 (2000).
[CrossRef]

G. Zhang, G. Montemezzani, and P. Günter, J. Appl. Phys. 88, 1709 (2000).
[CrossRef]

J. Zhang, V. Ostroverkhov, K. D. Singer, V. Reshetnyak, and Yu. Reznikov, Opt. Lett. 25, 414 (2000).
[CrossRef]

1999 (2)

C. Bower, R. Rosen, L. Jin, J. Han, and O. Zhou, Appl. Phys. Lett. 74, 3317 (1999).
[CrossRef]

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

1998 (2)

J. Jiang, J. Dong, X. Wan, and D. Xing, J. Phys. B 31, 3079 (1998).
[CrossRef]

Y. Saito, S. Uemura, and K. Hamaguchi, Jpn. J. Appl. Phys. 37, L346 (1998).
[CrossRef]

1997 (6)

P. G. Collons, A. Zettl, H. Bando, A. Thess, and R. E. Smalley, Science 278, 100 (1997).
[CrossRef]

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature 386, 377 (1997).
[CrossRef]

I. C. Khoo, B. D. Guenther, M. V. Mood, P. Chen, and M. Y. Shih, Opt. Lett. 22, 1229 (1997).
[CrossRef] [PubMed]

P. G. Collins and A. Zettl, Phys. Rev. B 55, 9391 (1997).
[CrossRef]

1996 (1)

L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 76, 971 (1996).
[CrossRef] [PubMed]

1995 (3)

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

W. A. de Heer, A. Chatelain, and D. Ugarte, Science 270, 1179 (1995).
[CrossRef]

I. C. Khoo, Opt. Lett. 20, 2137 (1995).
[CrossRef] [PubMed]

1994 (3)

E. V. Rudenko and A. V. Sukhov, JETP Lett. 59, 142 (1994).

E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994).

I. C. Khoo, H. Li, and Y. Liang, Opt. Lett. 19, 1723 (1994).
[CrossRef] [PubMed]

1992 (1)

Y. Wang and L.-T. Cheng, J. Phys. Chem. 96, 1530 (1992).
[CrossRef]

1991 (1)

S. Iijima, Nature 354, 56 (1991).
[CrossRef]

1969 (1)

W. Helfrich, J. Chem. Phys. 51, 4092 (1969).
[CrossRef]

Andrews, R.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Bando, H.

P. G. Collons, A. Zettl, H. Bando, A. Thess, and R. E. Smalley, Science 278, 100 (1997).
[CrossRef]

Bekkedahl, T. A.

A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature 386, 377 (1997).
[CrossRef]

Benedict, L. X.

L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 76, 971 (1996).
[CrossRef] [PubMed]

Bethune, D. S.

A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature 386, 377 (1997).
[CrossRef]

Bockrath, M.

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

Bower, C.

C. Bower, R. Rosen, L. Jin, J. Han, and O. Zhou, Appl. Phys. Lett. 74, 3317 (1999).
[CrossRef]

Chang, B.

S. Xie, W. Li, Z. Pan, B. Chang, and L. Sun, J. Phys. Chem. Solids 61, 1153 (2000).
[CrossRef]

Chatelain, A.

W. A. de Heer, A. Chatelain, and D. Ugarte, Science 270, 1179 (1995).
[CrossRef]

Chen, J.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Chen, P.

Chen, Y.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Cheng, L.-T.

Y. Wang and L.-T. Cheng, J. Phys. Chem. 96, 1530 (1992).
[CrossRef]

Chico, L.

L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 76, 971 (1996).
[CrossRef] [PubMed]

Chopra, N. G.

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

Cobden, D. H.

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

Cohen, M. L.

L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 76, 971 (1996).
[CrossRef] [PubMed]

Colbert, D. T.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Collins, P. G.

P. G. Collins and A. Zettl, Phys. Rev. B 55, 9391 (1997).
[CrossRef]

Collons, P. G.

P. G. Collons, A. Zettl, H. Bando, A. Thess, and R. E. Smalley, Science 278, 100 (1997).
[CrossRef]

Crespi, V. H.

L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 76, 971 (1996).
[CrossRef] [PubMed]

Dai, H.

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

de Heer, W. A.

W. A. de Heer, A. Chatelain, and D. Ugarte, Science 270, 1179 (1995).
[CrossRef]

Dekker, C.

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

Derbyshire, F.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Devoret, M. H.

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

Dillon, A. C.

A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature 386, 377 (1997).
[CrossRef]

Dong, J.

J. Jiang, J. Dong, X. Wan, and D. Xing, J. Phys. B 31, 3079 (1998).
[CrossRef]

Dresselhaus, G.

R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).

Dresselhaus, M. S.

R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).

Geerlings, L. J.

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

Guenther, B. D.

Günter, P.

G. Zhang, G. Montemezzani, and P. Günter, J. Appl. Phys. 88, 1709 (2000).
[CrossRef]

Haddon, R. C.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Hafner, J. H.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Hamaguchi, K.

Y. Saito, S. Uemura, and K. Hamaguchi, Jpn. J. Appl. Phys. 37, L346 (1998).
[CrossRef]

Han, J.

C. Bower, R. Rosen, L. Jin, J. Han, and O. Zhou, Appl. Phys. Lett. 74, 3317 (1999).
[CrossRef]

Heben, M. J.

A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature 386, 377 (1997).
[CrossRef]

Helfrich, W.

W. Helfrich, J. Chem. Phys. 51, 4092 (1969).
[CrossRef]

Iijima, S.

S. Iijima, Nature 354, 56 (1991).
[CrossRef]

Jacques, D.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Jiang, J.

J. Jiang, J. Dong, X. Wan, and D. Xing, J. Phys. B 31, 3079 (1998).
[CrossRef]

Jin, L.

C. Bower, R. Rosen, L. Jin, J. Han, and O. Zhou, Appl. Phys. Lett. 74, 3317 (1999).
[CrossRef]

Jones, K. M.

A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature 386, 377 (1997).
[CrossRef]

Khoo, I. C.

Kiang, C. H.

A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune, and M. J. Heben, Nature 386, 377 (1997).
[CrossRef]

Kim, S. G.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Li, H.

Li, W.

S. Xie, W. Li, Z. Pan, B. Chang, and L. Sun, J. Phys. Chem. Solids 61, 1153 (2000).
[CrossRef]

Liang, Y.

Lou, L.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Louie, S. G.

L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 76, 971 (1996).
[CrossRef] [PubMed]

McEuen, P. L.

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

Montemezzani, G.

G. Zhang, G. Montemezzani, and P. Günter, J. Appl. Phys. 88, 1709 (2000).
[CrossRef]

Mood, M. V.

Nikolaev, P.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Norlander, P.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Ostroverkhov, V.

Pan, Z.

S. Xie, W. Li, Z. Pan, B. Chang, and L. Sun, J. Phys. Chem. Solids 61, 1153 (2000).
[CrossRef]

Rantell, T.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Rao, A. M.

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

Reshetnyak, V.

Reznikov, Yu.

Rinzler, A. G.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Rosen, R.

C. Bower, R. Rosen, L. Jin, J. Han, and O. Zhou, Appl. Phys. Lett. 74, 3317 (1999).
[CrossRef]

Rudenko, E. V.

E. V. Rudenko and A. V. Sukhov, JETP Lett. 59, 142 (1994).

E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994).

Saito, R.

R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).

Saito, Y.

Y. Saito, S. Uemura, and K. Hamaguchi, Jpn. J. Appl. Phys. 37, L346 (1998).
[CrossRef]

Shih, M. Y.

Singer, K. D.

Smalley, R. E.

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

P. G. Collons, A. Zettl, H. Bando, A. Thess, and R. E. Smalley, Science 278, 100 (1997).
[CrossRef]

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Sukhov, A. V.

E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994).

E. V. Rudenko and A. V. Sukhov, JETP Lett. 59, 142 (1994).

Sun, L.

S. Xie, W. Li, Z. Pan, B. Chang, and L. Sun, J. Phys. Chem. Solids 61, 1153 (2000).
[CrossRef]

Tans, S. J.

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

Thess, A.

S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerlings, and C. Dekker, Nature 386, 474 (1997).
[CrossRef]

P. G. Collons, A. Zettl, H. Bando, A. Thess, and R. E. Smalley, Science 278, 100 (1997).
[CrossRef]

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

Tomanek, D.

A. G. Rinzler, J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert, and R. E. Smalley, Science 269, 1550 (1995).
[CrossRef] [PubMed]

Uemura, S.

Y. Saito, S. Uemura, and K. Hamaguchi, Jpn. J. Appl. Phys. 37, L346 (1998).
[CrossRef]

Ugarte, D.

W. A. de Heer, A. Chatelain, and D. Ugarte, Science 270, 1179 (1995).
[CrossRef]

Wan, X.

J. Jiang, J. Dong, X. Wan, and D. Xing, J. Phys. B 31, 3079 (1998).
[CrossRef]

Wang, Y.

Y. Wang and L.-T. Cheng, J. Phys. Chem. 96, 1530 (1992).
[CrossRef]

Xie, S.

S. Xie, W. Li, Z. Pan, B. Chang, and L. Sun, J. Phys. Chem. Solids 61, 1153 (2000).
[CrossRef]

Xing, D.

J. Jiang, J. Dong, X. Wan, and D. Xing, J. Phys. B 31, 3079 (1998).
[CrossRef]

Zettl, A.

P. G. Collins and A. Zettl, Phys. Rev. B 55, 9391 (1997).
[CrossRef]

M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra, A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
[CrossRef] [PubMed]

P. G. Collons, A. Zettl, H. Bando, A. Thess, and R. E. Smalley, Science 278, 100 (1997).
[CrossRef]

Zhang, G.

G. Zhang, G. Montemezzani, and P. Günter, J. Appl. Phys. 88, 1709 (2000).
[CrossRef]

Zhang, J.

Zhou, O.

C. Bower, R. Rosen, L. Jin, J. Han, and O. Zhou, Appl. Phys. Lett. 74, 3317 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

C. Bower, R. Rosen, L. Jin, J. Han, and O. Zhou, Appl. Phys. Lett. 74, 3317 (1999).
[CrossRef]

R. Andrews, D. Jacques, A. M. Rao, T. Rantell, F. Derbyshire, Y. Chen, J. Chen, and R. C. Haddon, Appl. Phys. Lett. 75, 1329 (1999).
[CrossRef]

J. Appl. Phys. (1)

G. Zhang, G. Montemezzani, and P. Günter, J. Appl. Phys. 88, 1709 (2000).
[CrossRef]

J. Chem. Phys. (1)

W. Helfrich, J. Chem. Phys. 51, 4092 (1969).
[CrossRef]

J. Phys. B (1)

J. Jiang, J. Dong, X. Wan, and D. Xing, J. Phys. B 31, 3079 (1998).
[CrossRef]

J. Phys. Chem. (1)

Y. Wang and L.-T. Cheng, J. Phys. Chem. 96, 1530 (1992).
[CrossRef]

J. Phys. Chem. Solids (1)

S. Xie, W. Li, Z. Pan, B. Chang, and L. Sun, J. Phys. Chem. Solids 61, 1153 (2000).
[CrossRef]

JETP (1)

E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994).

JETP Lett. (1)

E. V. Rudenko and A. V. Sukhov, JETP Lett. 59, 142 (1994).

Jpn. J. Appl. Phys. (1)

Y. Saito, S. Uemura, and K. Hamaguchi, Jpn. J. Appl. Phys. 37, L346 (1998).
[CrossRef]

Nature (3)

S. Iijima, Nature 354, 56 (1991).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental geometry. This setup facilitates control of the ratio of the two excitation-beam fluxes, although both 44mW/cm2 beams are used in this work. M1M3, mirrors; L3, L2, lenses; λ/2, half-wave plates; PBS, polarizing beam splitter; LC, liquid crystal.

Fig. 2
Fig. 2

Self-diffraction pattern in the absence of one of the two incident beams. Vdc=15 V, ψ=0°, β=45°, Λ=36 μm. The direct beam is labeled 0.

Fig. 3
Fig. 3

Typical time evolution showing grating formation in a photorefractive film of the nematic E7 doped with carbon nanotubes. Vdc=15 V, ψ=0°, β=45°, Λ=18 μm.

Fig. 4
Fig. 4

Observed first-order diffraction as a function of the external dc voltage. Inset, expanded scale at low diffraction efficiencies. Conditions are as stated in the caption of Fig.  3.

Equations (3)

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η=I-1/I1×100%.
ηπdΔn/λ2,
Δn=n2I1.

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