Abstract

We present the experimental observation of a spatial vector soliton formed by counterpropagation of coherent optical fields. This is to our knowledge the first observation of a vector soliton in which the induced waveguide (potential) is periodic in the propagation direction. This vector soliton induces a waveguide and a thick grating within the waveguide, which can be used as a tunable optical waveguide filter.

© 2002 Optical Society of America

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  1. See the review in G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  2. A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
    [CrossRef] [PubMed]
  3. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).
  4. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
    [CrossRef] [PubMed]
  5. M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1766 (1995).
    [CrossRef]
  6. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, Opt. Lett. 13, 871 (1988).
    [CrossRef] [PubMed]
  7. M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992).
    [CrossRef]
  8. D. N. Christodoulides, S. R. Singh, M. I. Carvalo, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
    [CrossRef]
  9. Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
    [CrossRef] [PubMed]
  10. M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
    [CrossRef]
  11. For plane waves and a fixed grating this π/2 retardation was obtained analytically; see H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
    [CrossRef]
  12. O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
    [CrossRef]
  13. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  14. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
  15. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
    [CrossRef]

2002

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

1999

See the review in G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1996

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalo, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

1995

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1766 (1995).
[CrossRef]

1994

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1993

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[CrossRef]

1992

M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992).
[CrossRef]

1988

1974

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

1969

For plane waves and a fixed grating this π/2 retardation was obtained analytically; see H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Aitchison, J. S.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

Akhmediev, N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

Barthelemy, A. J.

M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992).
[CrossRef]

Carmon, T.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Carvalho, M. I.

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1766 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

Carvalo, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalo, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalo, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1766 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

Cohen, O.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Coskun, T.

Crosignani, B.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

DiPorto, P.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Fleischer, J. W.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Haelterman, M.

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[CrossRef]

Hewlett, S. J.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Kang, J. U.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

Kogelnik, H.

For plane waves and a fixed grating this π/2 retardation was obtained analytically; see H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Mitchell, D. J.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Odoulov, S.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Salamo, G.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Segev, M.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

See the review in G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalo, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1766 (1995).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Shalaby, M.

M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992).
[CrossRef]

Sheppard, A. P.

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[CrossRef]

Shih, M.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalo, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1766 (1995).
[CrossRef]

Snyder, A. W.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[CrossRef]

Stegeman, G. I.

See the review in G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, Opt. Lett. 13, 871 (1988).
[CrossRef] [PubMed]

Trillo, S.

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Valley, G. C.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1766 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Wabnitz, S.

Wright, E. M.

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Appl. Phys. Lett.

D. N. Christodoulides, S. R. Singh, M. I. Carvalo, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Bell Syst. Tech. J.

For plane waves and a fixed grating this π/2 retardation was obtained analytically; see H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Electron. Lett.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

IEEE J. Quantum Electron.

M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

Science

See the review in G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Sov. Phys. JETP

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

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Figures (3)

Fig. 1
Fig. 1

a, Schematic of a spatial vector soliton formed by counterpropagating fields. b, Normalized vector soliton wave function versus dimensionless length ξ for several values of peak amplitude u0. c, FWHM of the intensity of the vector soliton versus u0.

Fig. 2
Fig. 2

The experimental setup.

Fig. 3
Fig. 3

Experimental results: Images and intensity profiles taken by camera A (of Fig. 2). Intensities of beam 2 at a, the input (left) and b, the output (right) surfaces of the crystal when beam 1 is blocked and the nonlinearity is off. c, Total intensity of the vector solitons at the left face of the crystal. d, Intensity at the left surface when beam 1 is blocked and the nonlinearity is on, showing that, at this value of nonlinearity, beam 2 alone does not form a soliton. e, Reflections of beam 1 by both the surfaces and the grating. f, Reflection of beam 1 by the surfaces alone.

Equations (4)

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

Δnx,z=Δn0m=-m=CmF,Bexp2imkz.
2Fx2+2ikFz=-2k2Δn0n0C0F+C1B,  2Bx2-2ikBz=-2k2Δn0n0C0B+C-1F.
C0=-1+f+b21+f-b2-1/2,  C1=-fb*2f2b21+C01+f2+b2,
u+βu-12u+12u1+4u2=0.

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