Abstract

Coherent amplification of a signal beam by a strong pump beam is observed in thin films of fullerene-doped nematic liquid crystal. Exponential gain constants as high as 2890  cm-1 with no phase cross talk are achieved at low applied dc bias voltage and pump beam intensity. The underlying mechanism is the electro-optically induced spatially reorientation of the liquid-crystal axis and the resultant phase-shifted index grating required for two-beam coupling.

© 1997 Optical Society of America

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References

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  1. For photorefractive crystals, see G. Gunter and J. P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1989), Vols. 1 and 2; P. Yeh, Photorefractive Nonlinear Optics (Wiley Interscience, New York, 1994).
  2. For photorefractive polymers, see S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991); S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Tweig, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature (London) 371, 497 (1994).
    [CrossRef] [PubMed]
  3. For photorefractivity in liquid crystals, see E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994); JETP Lett. 59, 142 (1994); and Refs.  4–7.
  4. I. C. Khoo, H. Li, and Y. Liang, Opt. Lett. 19, 1723 (1994).
    [CrossRef] [PubMed]
  5. I. C. Khoo, Opt. Lett. 20, 2137 (1995).
    [CrossRef] [PubMed]
  6. I. C. Khoo, IEEE J. Quantum Electronics 32, 525 (1996).
    [CrossRef]
  7. G. P. Widerrecht, B. A. Yoon, and M. R. Wasielewski, Science 270, 1794 (1995).
    [CrossRef]
  8. A. E. T. Chiou and P. Yeh, Opt. Lett. 10, 621 (1985); Opt. Lett. 11, 461 (1986).
    [CrossRef] [PubMed]
  9. See, for example, E. V. Degtiarev and M. A. Vorontsov, J. Opt. Soc. Am. B 12, 1238 (1995), and references therein.
    [CrossRef]
  10. I. C. Khoo and T. H. Liu, Phys. Rev. A 39, 4036 (1989).
    [CrossRef] [PubMed]
  11. J. J. Stankus, S. M. Silence, W. E. Moerner, and G. C. Bjorklund, Opt. Lett. 19, 1480 (1994), and references therein.
    [CrossRef] [PubMed]
  12. I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993), Chap.  2; I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1994), Chap.  6.

1996 (1)

I. C. Khoo, IEEE J. Quantum Electronics 32, 525 (1996).
[CrossRef]

1995 (3)

1994 (3)

For photorefractivity in liquid crystals, see E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994); JETP Lett. 59, 142 (1994); and Refs.  4–7.

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

J. J. Stankus, S. M. Silence, W. E. Moerner, and G. C. Bjorklund, Opt. Lett. 19, 1480 (1994), and references therein.
[CrossRef] [PubMed]

1991 (1)

For photorefractive polymers, see S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991); S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Tweig, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef] [PubMed]

1989 (1)

I. C. Khoo and T. H. Liu, Phys. Rev. A 39, 4036 (1989).
[CrossRef] [PubMed]

1985 (1)

Bjorklund, G. C.

Chiou, A. E. T.

Degtiarev, E. V.

Ducharme, S.

For photorefractive polymers, see S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991); S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Tweig, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef] [PubMed]

Khoo, I. C.

I. C. Khoo, IEEE J. Quantum Electronics 32, 525 (1996).
[CrossRef]

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

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

I. C. Khoo and T. H. Liu, Phys. Rev. A 39, 4036 (1989).
[CrossRef] [PubMed]

I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993), Chap.  2; I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1994), Chap.  6.

Li, H.

Liang, Y.

Liu, T. H.

I. C. Khoo and T. H. Liu, Phys. Rev. A 39, 4036 (1989).
[CrossRef] [PubMed]

Moerner, W. E.

J. J. Stankus, S. M. Silence, W. E. Moerner, and G. C. Bjorklund, Opt. Lett. 19, 1480 (1994), and references therein.
[CrossRef] [PubMed]

For photorefractive polymers, see S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991); S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Tweig, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef] [PubMed]

Rudenko, E. V.

For photorefractivity in liquid crystals, see E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994); JETP Lett. 59, 142 (1994); and Refs.  4–7.

Scott, J. C.

For photorefractive polymers, see S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991); S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Tweig, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef] [PubMed]

Silence, S. M.

Stankus, J. J.

Sukhov, A. V.

For photorefractivity in liquid crystals, see E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994); JETP Lett. 59, 142 (1994); and Refs.  4–7.

Tweig, R. J.

For photorefractive polymers, see S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991); S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Tweig, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef] [PubMed]

Vorontsov, M. A.

Wasielewski, M. R.

G. P. Widerrecht, B. A. Yoon, and M. R. Wasielewski, Science 270, 1794 (1995).
[CrossRef]

Widerrecht, G. P.

G. P. Widerrecht, B. A. Yoon, and M. R. Wasielewski, Science 270, 1794 (1995).
[CrossRef]

Wu, S. T.

I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993), Chap.  2; I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1994), Chap.  6.

Yeh, P.

Yoon, B. A.

G. P. Widerrecht, B. A. Yoon, and M. R. Wasielewski, Science 270, 1794 (1995).
[CrossRef]

IEEE J. Quantum Electronics (1)

I. C. Khoo, IEEE J. Quantum Electronics 32, 525 (1996).
[CrossRef]

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

JETP (1)

For photorefractivity in liquid crystals, see E. V. Rudenko and A. V. Sukhov, JETP 78, 875 (1994); JETP Lett. 59, 142 (1994); and Refs.  4–7.

Opt. Lett. (4)

Phys. Rev. A (1)

I. C. Khoo and T. H. Liu, Phys. Rev. A 39, 4036 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

For photorefractive polymers, see S. Ducharme, J. C. Scott, R. J. Tweig, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991); S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Tweig, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992); K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef] [PubMed]

Science (1)

G. P. Widerrecht, B. A. Yoon, and M. R. Wasielewski, Science 270, 1794 (1995).
[CrossRef]

Other (2)

For photorefractive crystals, see G. Gunter and J. P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1989), Vols. 1 and 2; P. Yeh, Photorefractive Nonlinear Optics (Wiley Interscience, New York, 1994).

I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993), Chap.  2; I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1994), Chap.  6.

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Figures (4)

Fig. 1
Fig. 1

Schematic depiction of the optical wave-mixing interaction in a homeotropically aligned sample: E1, pump beam; E 2, probe; E3, E4 generated side diffractions.

Fig. 2
Fig. 2

Dependence of the probe beam gain on the pump/probe beam power ratio for two sample thicknesses. dc voltages used for the 10- and 25-µm samples are 3 and 1.7  V, respectively. Experimental conditions: α=1°; β=22.5°; pump power, 33  mW.

Fig. 3
Fig. 3

Dependence of the probe amplification on the input pump power obtained with the 25-µm-thick sample:  applied dc voltage, 3  V; pump/probe beam ratio, 245; α=1°; β=22.5°.

Fig. 4
Fig. 4

(a) Intensity profiles of the aberrated pump beam before (upper trace) and after (lower trace) the application of the dc bias voltage. The lower trace is on a reduced scale ×0.2. (b) Intensity profiles of the probe beam before (lower trace) and after (upper trace) amplification. Experimental conditions: α=1°; β=22.5°; pump power, 33  mW; pump/probe ratio, 245; 25-µm-thick sample.

Equations (3)

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

dE1/dz=-gE1E2*E2+E1E3*E3+higher-order wave mixing terms,
dE2/dz=gE2E1*E1+E1E3*E1 expiΔkz+higher-order wave mixing terms,
dE3/dz=gE3E1*E1+E1E2*E1 expiΔkz+higher-order wave mixing terms,

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