Abstract

To be self-guided, a beam must exactly equal the mode of the linear-optical fiber that it induces. From this elementary consistency condition we can borrow solutions and their associated physics directly from the familiar literature of linear-optical waveguides. By considering a nonlinear medium characterized by ideal saturation, we present what is to our knowledge the first exact analytical solution of a two-dimensional self-guided beam. This beam is the familiar fundamental mode of a step-profile fiber. The stability of the beam is also determined.

© 1991 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. P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
    [CrossRef]
  3. H. A. Haus, Appl. Phys. Lett. 8, 128 (1966).
    [CrossRef]
  4. Y. Silberberg, Opt. Lett. 15, 471 (1990).
    [CrossRef] [PubMed]
  5. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  6. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 248–263, Chap. 13, pp. 301–305, 311–326.
  7. X.-H. Zheng, W. M. Henry, A. W. Snyder, IEEE J. Lightwave Technol. 6, 1300 (1988).
    [CrossRef]
  8. A. A. Kolokolov, Zh. Eksp. Teor. Fiz. 3, 152 (1973).
  9. J. F. Lam, B. Leppman, Opt. Commun. 15, 419 (1975).
    [CrossRef]
  10. D. J. Mitchell, A. W. Snyder, Opt. Lett. 14, 1143 (1989).
    [CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (1)

X.-H. Zheng, W. M. Henry, A. W. Snyder, IEEE J. Lightwave Technol. 6, 1300 (1988).
[CrossRef]

1975 (1)

J. F. Lam, B. Leppman, Opt. Commun. 15, 419 (1975).
[CrossRef]

1973 (1)

A. A. Kolokolov, Zh. Eksp. Teor. Fiz. 3, 152 (1973).

1966 (1)

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

1965 (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

1964 (1)

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

Chiao, R. Y.

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

Garmire, E.

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

Haus, H. A.

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

Henry, W. M.

X.-H. Zheng, W. M. Henry, A. W. Snyder, IEEE J. Lightwave Technol. 6, 1300 (1988).
[CrossRef]

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

Kolokolov, A. A.

A. A. Kolokolov, Zh. Eksp. Teor. Fiz. 3, 152 (1973).

Lam, J. F.

J. F. Lam, B. Leppman, Opt. Commun. 15, 419 (1975).
[CrossRef]

Leppman, B.

J. F. Lam, B. Leppman, Opt. Commun. 15, 419 (1975).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 248–263, Chap. 13, pp. 301–305, 311–326.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Mitchell, D. J.

Silberberg, Y.

Snyder, A. W.

D. J. Mitchell, A. W. Snyder, Opt. Lett. 14, 1143 (1989).
[CrossRef] [PubMed]

X.-H. Zheng, W. M. Henry, A. W. Snyder, IEEE J. Lightwave Technol. 6, 1300 (1988).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 248–263, Chap. 13, pp. 301–305, 311–326.

Townes, C. H.

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

Zheng, X.-H.

X.-H. Zheng, W. M. Henry, A. W. Snyder, IEEE J. Lightwave Technol. 6, 1300 (1988).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE J. Lightwave Technol. (1)

X.-H. Zheng, W. M. Henry, A. W. Snyder, IEEE J. Lightwave Technol. 6, 1300 (1988).
[CrossRef]

Opt. Commun. (1)

J. F. Lam, B. Leppman, Opt. Commun. 15, 419 (1975).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

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

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

A. A. Kolokolov, Zh. Eksp. Teor. Fiz. 3, 152 (1973).

Other (2)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 248–263, Chap. 13, pp. 301–305, 311–326.

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Figures (3)

Fig. 1
Fig. 1

(a) Intensity profile of a beam in (b) a nonlinear medium characterized by idealized saturation. The dotted curve illustrates the particular Kerr-law nonlinearity with n = n + (n0n)I/It. (c) The beam induces a step-profile optical fiber whose mode is characterized by the intensity profile of (d). The beam is self-guided only when the intensity profile IB of the beam equals that (IM) of the mode.

Fig. 2
Fig. 2

Characterization of a self-guided beam through its dimensionless fiber parameter V, its power P, and its propagation constant β = [(kn0)2U2]1/2/ρ. Here I0 is the maximum beam power, while It is the threshold intensity of Fig. 1(b), where Pmin is the minimum value of P. To construct the β curves we have taken n0 = 1.450, n = 1.446, and λ = 1.3.

Fig. 3
Fig. 3

The e−1 radius or spot size rM of the self-guided beam versus intensity I0 and power P. The minimum power for self-guidance, Pmin, is approximately 1.69 times that required in the Kerr-law medium1,3 indicated by the dotted curve in Fig. 1(b).

Equations (5)

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E j ( x , y , z ) = e j ( x , y ) exp ( i β z ) ,
I M ( r ) = I 0 J 0 2 ( U r / ρ )
I 0 J 0 2 ( U ) = I t .
V = ρ k ( n 0 2 - n 2 ) 1 / 2 ,
r min 0.401 λ ( n 0 2 - n 2 ) 1 / 2 ,

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