Abstract

A simple scheme to steer optical beams is proposed. The basic idea is to impose a sinusoidal phase modulation on the optical beam and then propagate it in a nonlinear Kerr medium. Spatial phase modulation splits the input beam into multiple subbeams, while the nonlinear medium shapes a particular subbeam into a spatial soliton in such a way that most of the beam power appears in a narrow beam whose direction can be controlled by changing the modulation parameters. We present numerical results showing how spatial phase modulation can be used to alter the path of an optical beam propagating in a nonlinear Kerr medium.

© 1993 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  2. S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).
  3. Y. Li, D. Y. Chen, L. Yang, R. R. Alfano, Opt. Lett. 16, 438 (1991).
    [CrossRef] [PubMed]
  4. A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, R. W. Boyd, Opt. Lett. 17, 19 (1992).
    [CrossRef] [PubMed]
  5. G. A. Swartzlander, H. Yin, A. E. Kaplan, Opt. Lett. 13, 1011 (1988); J. Opt. Soc. Am. B 6, 1317 (1989); Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, Opt. Lett. 15, 1431 (1990).
    [CrossRef] [PubMed]
  6. B. Luther-Davies, X. Yang, Opt. Lett. 17, 1755 (1992).
    [CrossRef] [PubMed]
  7. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chaps. 8–10.
  8. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chap. 7.
  9. W. Golzos, M. Holz, Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 131 (1989).
  10. F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stouffer, Appl. Phys. Lett. 58, 2874 (1991).
    [CrossRef]
  11. S. Zhou, P. Yeh, H.-K. Liu, Opt. Lett. 18, 843 (1993).
    [CrossRef] [PubMed]
  12. V. L. da Silva, Y. Silberberg, J. P. Heritage, Opt. Lett. 18, 580 (1993).
    [CrossRef] [PubMed]

1993 (2)

1992 (2)

1991 (2)

F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stouffer, Appl. Phys. Lett. 58, 2874 (1991).
[CrossRef]

Y. Li, D. Y. Chen, L. Yang, R. R. Alfano, Opt. Lett. 16, 438 (1991).
[CrossRef] [PubMed]

1989 (1)

W. Golzos, M. Holz, Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 131 (1989).

1988 (1)

Agrawal, G. P.

A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, R. W. Boyd, Opt. Lett. 17, 19 (1992).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Alfano, R. R.

Boyd, R. W.

A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, R. W. Boyd, Opt. Lett. 17, 19 (1992).
[CrossRef] [PubMed]

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chap. 7.

Chen, D. Y.

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

da Silva, V. L.

Golzos, W.

W. Golzos, M. Holz, Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 131 (1989).

Heritage, J. P.

Holz, M.

W. Golzos, M. Holz, Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 131 (1989).

Houdré, R.

F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stouffer, Appl. Phys. Lett. 58, 2874 (1991).
[CrossRef]

Kaplan, A. E.

Kauranen, M.

Li, Y.

Liu, H.-K.

Luther-Davies, B.

Maki, J. J.

Reinhart, F. K.

F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stouffer, Appl. Phys. Lett. 58, 2874 (1991).
[CrossRef]

Silberberg, Y.

Stentz, A. J.

Stouffer, J. M.

F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stouffer, Appl. Phys. Lett. 58, 2874 (1991).
[CrossRef]

Swartzlander, G. A.

Vasey, F.

F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stouffer, Appl. Phys. Lett. 58, 2874 (1991).
[CrossRef]

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Yang, L.

Yang, X.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chaps. 8–10.

Yeh, P.

S. Zhou, P. Yeh, H.-K. Liu, Opt. Lett. 18, 843 (1993).
[CrossRef] [PubMed]

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chaps. 8–10.

Yin, H.

Zhou, S.

Appl. Phys. Lett. (1)

F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stouffer, Appl. Phys. Lett. 58, 2874 (1991).
[CrossRef]

Opt. Lett. (6)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. Golzos, M. Holz, Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 131 (1989).

Other (4)

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chaps. 8–10.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chap. 7.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

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Figures (2)

Fig. 1
Fig. 1

Spatially modulated phase profiles for δ = π/2 (dashed curve) and δ = π (dotted–dashed curve) with p = 0.2. The bottom plot shows for comparison the Gaussian intensity profile of the input Gaussian beam.

Fig. 2
Fig. 2

Evolution of a phase-modulated Gaussian beam in a Kerr medium for three different peak intensities: (a) N = 0, (b) N = 2, and (c) N = 3. The modulation parameters are p = 0.2, ϕ0 = 2.405, and δ = 0.

Equations (5)

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i u ζ + 1 2 ( 2 u ξ 2 + 2 u η 2 ) + N 2 | u | 2 u = 0 ,
u ( ξ , 0 ) = exp ( ξ 2 / 2 ) exp [ i ϕ ( ξ ) ] .
ϕ ( ξ ) = ϕ 0 sin ( 2 π p ξ + δ ) ,
u ( ξ , 0 ) = exp ( ξ 2 / 2 ) J m ( ϕ 0 ) exp [ i m ( 2 π p ξ + δ ) ] .
u ( ξ , η , 0 ) = exp [ ( ξ 2 + η 2 ) / 2 ] exp [ i ϕ 1 sin ( 2 π p 1 ξ + δ 1 ) + i ϕ 2 sin ( 2 π p 2 η + δ 2 ) ] ,

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