Abstract

We demonstrate the existence of a stable black self-guided beam of circular symmetry in a bulk self-defocusing Kerr medium. There are no gray or higher-order self-guided beams of circular symmetry. The stability of black beams of circular symmetry is in sharp contrast to analogous bright beams in a self-focusing medium, which are unstable. Black self-guided beams are ideal for all-optical devices in bulk material as they can induce a single-mode optical fiber to guide a (weak) signal beam.

© 1992 Optical Society of America

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References

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  1. R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  2. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
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    [CrossRef] [PubMed]
  4. A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Manuef, F. Reynaud, Opt. Commun. 66, 325 (1988).
    [CrossRef]
  5. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, P. W. E. Smith, Opt. Lett. 15, 471 (1990).
    [CrossRef] [PubMed]
  6. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).
  7. D. R. Anderson, D. E. Hoolon, G. A. Swartzlander, A. E. Kaplan, Opt. Lett. 15, 783 (1990).
    [CrossRef]
  8. G. R. Allan, S. R. Skinner, D. R. Anderson, A. L. Smerl, Opt. Lett. 16, 156 (1991).
    [PubMed]
  9. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  10. A. W. Snyder, D. J. Mitchell, L. Poladian, J. Opt. Soc. Am. B 8, 1618 (1991).
    [CrossRef]
  11. H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
    [CrossRef]
  12. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 263–264 and Chap. 25.
  13. P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).
  14. Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991).
    [CrossRef]
  15. A. W. Snyder, D. J. Mitchell, L. Poladian, Opt. Lett. 17, 267 (1992).
    [CrossRef] [PubMed]

1992

1991

1990

1985

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Manuef, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

1973

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

1972

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1966

H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

1965

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

1964

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Aitchison, J. S.

Allan, G. R.

Anderson, D. R.

Barthelemy, A.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Manuef, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Chen, Y.

Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Froehly, C.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Manuef, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Hasegawa, A.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Haus, H. A.

H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

Hoolon, D. E.

Jackel, J. L.

Kaplan, A. E.

Ladouceur, F.

Leaird, D. E.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 263–264 and Chap. 25.

Maker, P. D.

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

Maneuf, S.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Manuef, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Mitchell, D. J.

Oliver, M. K.

Poladian, L.

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Silberberg, Y.

Skinner, S. R.

Smerl, A. L.

Smith, P. W. E.

Snyder, A. W.

Swartzlander, G. A.

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

Townes, C. H.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Vogel, E. M.

Weiner, A. M.

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Appl. Phys. Lett.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

Electron. Lett.

Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985); S. Maneuf, R. Desailly, C. Froehly, Opt. Commun. 65, 193 (1988); S. Manuef, F. Reynaud, Opt. Commun. 66, 325 (1988).
[CrossRef]

Opt. Lett.

Phys. Rev. A

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

Phys. Rev. Lett.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Sov. Phys. JETP

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

Other

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 263–264 and Chap. 25.

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Figures (4)

Fig. 1
Fig. 1

Linear equivalence condition: (a) Intensity profile of a beam launched into a nonlinear (self-defocusing) Kerr medium, with the nonlinearity shown in (b). This input beam induces the graded refractive-index profile fiber shown in (c). The input beam is self-guided only when it exactly equals a mode (d) of the linear fiber that it induces, i.e., only when the intensity patterns in (a) and (d) are equal.

Fig. 2
Fig. 2

Intensity pattern of (a) the bright and (b) the black self-guided beams in self-focusing and self-defocusing media, respectively. We define a radius ρ (the width at half-height) to characterize the confinement.

Fig. 3
Fig. 3

Comparison of intensity patterns for bright and dark self-guided beams. Here I(0) minus the intensity of the black self-guided beam is shown, where ρ is for the bright beam.

Fig. 4
Fig. 4

Comparison of bright and dark self-guided beams of circular symmetry [Figs. 2(a) and 2(b), respectively] in a Kerr medium.

Equations (11)

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e t ( r ) = ψ ( r ) ϕ ^ ,             TE 01 ,
= ψ ( r ) r ^ ,             TM 01 ,
= ψ ( r ) exp ( i ϕ ) ( x ^ + i y ^ ) / 2 ,             HE 21 , = ψ ( r ) exp ( i ϕ ) ( x ^ - i y ^ ) / 2 ,             HE 21 ,
( d d r 2 + 1 r d d r - 1 r 2 + k 2 n 2 - β 2 ) ψ = 0.
( n 2 ) i j = ( n ¯ 2 + A ɛ 0 e 2 ) δ i j + B 2 ɛ 0 e i * e j
n 2 = n ¯ 2 + [ A + ( B / 2 ) ɛ 0 ] ψ 2 ( r )
V = 2 π ρ λ ( n 0 2 - n ¯ 2 ) 1 / 2 = const .
I 0 = V 2 ( k ρ ) 2 K
V 1.56 ,
P = 1.86 × 2 π k 2 n 0 K ,
V s = λ λ s 2 V ,

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