Abstract

On the basis of simple physical arguments involving energy flows and power invariants, we show that nonparaxiality stabilizes 1+2D soliton beams in Kerr media.

© 1998 Optical Society of America

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References

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  2. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  3. E. L. Dawes and J. H. Marburger, Phys. Rev. 152, 862 (1969).
    [CrossRef]
  4. J. A. Fleck and R. L. Carman, Appl. Phys. Lett. 20, 290 (1974).
    [CrossRef]
  5. S. K. Turitsyn, Teor. Mat. Fiz. 64, 226 (1985).
    [CrossRef]
  6. D. Suter and T. Blasberg, Phys. Rev. A 47, 250 (1993).
  7. M. D. Feit and J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988).
    [CrossRef]
  8. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Opt. Lett. 18, 411 (1993); J. Soto-Crespo and N. Akhmediev, Opt. Commun. 101, 223 (1993).
    [CrossRef] [PubMed]
  9. G. Fibich, Phys. Rev. Lett. 76, 4356 (1996).
    [CrossRef] [PubMed]
  10. G. Chi and Q. Guo, Opt. Lett. 20, 1598 (1995).
    [CrossRef] [PubMed]
  11. M. Grillakis, J. Shatah, and W. Strauss, J. Funct. Anal. 74, 160 (1987).
    [CrossRef]
  12. A. A. Kolokolov, J. Appl. Mech. Tech. Phys. (USSR) 11, 426 (1975).
    [CrossRef]

1996 (1)

G. Fibich, Phys. Rev. Lett. 76, 4356 (1996).
[CrossRef] [PubMed]

1995 (1)

1993 (2)

1988 (1)

1987 (1)

M. Grillakis, J. Shatah, and W. Strauss, J. Funct. Anal. 74, 160 (1987).
[CrossRef]

1985 (1)

S. K. Turitsyn, Teor. Mat. Fiz. 64, 226 (1985).
[CrossRef]

1975 (1)

A. A. Kolokolov, J. Appl. Mech. Tech. Phys. (USSR) 11, 426 (1975).
[CrossRef]

1974 (1)

J. A. Fleck and R. L. Carman, Appl. Phys. Lett. 20, 290 (1974).
[CrossRef]

1969 (1)

E. L. Dawes and J. H. Marburger, Phys. Rev. 152, 862 (1969).
[CrossRef]

1965 (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

1964 (1)

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

Akhmediev, N.

Ankiewicz, A.

Blasberg, T.

D. Suter and T. Blasberg, Phys. Rev. A 47, 250 (1993).

Carman, R. L.

J. A. Fleck and R. L. Carman, Appl. Phys. Lett. 20, 290 (1974).
[CrossRef]

Chi, G.

Chiao, R. Y.

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

Dawes, E. L.

E. L. Dawes and J. H. Marburger, Phys. Rev. 152, 862 (1969).
[CrossRef]

Feit, M. D.

Fibich, G.

G. Fibich, Phys. Rev. Lett. 76, 4356 (1996).
[CrossRef] [PubMed]

Fleck, J. A.

M. D. Feit and J. A. Fleck, J. Opt. Soc. Am. B 5, 633 (1988).
[CrossRef]

J. A. Fleck and R. L. Carman, Appl. Phys. Lett. 20, 290 (1974).
[CrossRef]

Garmire, E.

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

Grillakis, M.

M. Grillakis, J. Shatah, and W. Strauss, J. Funct. Anal. 74, 160 (1987).
[CrossRef]

Guo, Q.

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Kolokolov, A. A.

A. A. Kolokolov, J. Appl. Mech. Tech. Phys. (USSR) 11, 426 (1975).
[CrossRef]

Marburger, J. H.

E. L. Dawes and J. H. Marburger, Phys. Rev. 152, 862 (1969).
[CrossRef]

Shatah, J.

M. Grillakis, J. Shatah, and W. Strauss, J. Funct. Anal. 74, 160 (1987).
[CrossRef]

Soto-Crespo, J. M.

Strauss, W.

M. Grillakis, J. Shatah, and W. Strauss, J. Funct. Anal. 74, 160 (1987).
[CrossRef]

Suter, D.

D. Suter and T. Blasberg, Phys. Rev. A 47, 250 (1993).

Townes, C. H.

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

Turitsyn, S. K.

S. K. Turitsyn, Teor. Mat. Fiz. 64, 226 (1985).
[CrossRef]

Appl. Phys. Lett. (1)

J. A. Fleck and R. L. Carman, Appl. Phys. Lett. 20, 290 (1974).
[CrossRef]

J. Appl. Mech. Tech. Phys. (USSR) (1)

A. A. Kolokolov, J. Appl. Mech. Tech. Phys. (USSR) 11, 426 (1975).
[CrossRef]

J. Funct. Anal. (1)

M. Grillakis, J. Shatah, and W. Strauss, J. Funct. Anal. 74, 160 (1987).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. (1)

E. L. Dawes and J. H. Marburger, Phys. Rev. 152, 862 (1969).
[CrossRef]

Phys. Rev. A (1)

D. Suter and T. Blasberg, Phys. Rev. A 47, 250 (1993).

Phys. Rev. Lett. (3)

G. Fibich, Phys. Rev. Lett. 76, 4356 (1996).
[CrossRef] [PubMed]

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

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Teor. Mat. Fiz. (1)

S. K. Turitsyn, Teor. Mat. Fiz. 64, 226 (1985).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the soliton power invariant of Eq. (3) as a function of propagation constant for various degrees of nonparaxiality ε. The arrows indicate the evolution of beams with an initial excess or lack of power compared with the corresponding soliton. (a) ε=0 solitons are critically unstable; perturbed beams never approach the soliton state. (b) ε1 solitons are stable in response to slight perturbations but are not robust as they undergo large oscillations, even with small perturbations. (c) ε1; solitons are expected to be both stable and robust.

Fig. 2
Fig. 2

Evolution of the on-axis intensity for beams perturbed from a soliton of ε=0.005. (a) Perturbations of ±10% cause large amplitude oscillations and decay to radiation. (b) Perturbations of ±0.1%, showing stability of the NLH solitons. The dashed (solid) curve shows the evolution of beams with an initial power deficit (excess) with respect to the corresponding soliton. These oscillations occur quasi-adiabatically, with very little energy lost to radiation and no qualitative change in profile. The beam narrows (broadens) during focusing (defocusing) cycles and returns periodically to its original profile.

Fig. 3
Fig. 3

Same as for Fig. 2 but with ε=1 and perturbations of (a) δ=±10% and (b) δ=±1%. Solitons are unconditionally robust at this rather impractical intensity.

Equations (3)

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Ezz+Exx+Eyy+k02E+γ2E2E=0,
PNLH=cω  ImE*Ezd2r,
iAζ+εAζζ+Aξξ+Aηη+A2A=0,

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