Abstract

Dark soliton stripes are robust but can decay into optical vortex solitons when subjected to a persistent, long-period, transverse modulation. We explore the nonlinear dynamics of this symmetry-breaking process and determine growth rates, vortex densities, and other characteristics by conducting a nonlinear stability analysis that uses numerical techniques for several cases of special interest.

© 1993 Optical Society of America

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  1. V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)]; A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [Crossref]
  2. P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
    [Crossref] [PubMed]
  3. G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
    [Crossref] [PubMed]
  4. G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
    [Crossref] [PubMed]
  5. R. Y. Chiao, I. H. Deutsch, J. C. Garrison, E. M. Wright, Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, Bristol, UK, 1992); A. W. Snyder, I. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
    [Crossref] [PubMed]
  6. E. W. Laedke, K. H. Spatschek, J. Math. Phys. 20, 1838 (1979); E. Infeld, G. Rowlands, Z. Phys. B 37, 277 (1980).
    [Crossref]
  7. E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].
  8. J. F. Nye, M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [Crossref]
  9. V. L. Ginzburg, L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)]; L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
  10. G. A. Swartzlander, Opt. Lett. 17, 493 (1992); B. Luther-Davies, Y. Xiaoping, Opt. Lett. 17, 496 (1992).
    [Crossref] [PubMed]
  11. D. R. Andersen, D. E. Hooton, G. A. Swartzlander, A. E. Kaplan, Opt. Lett. 15, 783 (1990).
    [Crossref] [PubMed]

1992 (2)

1991 (1)

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[Crossref] [PubMed]

1990 (1)

1988 (1)

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

1987 (1)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

1979 (1)

E. W. Laedke, K. H. Spatschek, J. Math. Phys. 20, 1838 (1979); E. Infeld, G. Rowlands, Z. Phys. B 37, 277 (1980).
[Crossref]

1974 (1)

J. F. Nye, M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[Crossref]

1973 (1)

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)]; A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

1958 (1)

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)]; L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

Andersen, D. R.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[Crossref] [PubMed]

D. R. Andersen, D. E. Hooton, G. A. Swartzlander, A. E. Kaplan, Opt. Lett. 15, 783 (1990).
[Crossref] [PubMed]

Barthelemy, A.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Berry, M. V.

J. F. Nye, M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, E. M. Wright, Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, Bristol, UK, 1992); A. W. Snyder, I. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
[Crossref] [PubMed]

Deutsch, I. H.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, E. M. Wright, Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, Bristol, UK, 1992); A. W. Snyder, I. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
[Crossref] [PubMed]

Emplit, P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Froehly, C.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Garrison, J. C.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, E. M. Wright, Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, Bristol, UK, 1992); A. W. Snyder, I. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
[Crossref] [PubMed]

Ginzburg, V. L.

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)]; L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

Hamaide, J. P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Hooton, D. E.

Kaplan, A. E.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[Crossref] [PubMed]

D. R. Andersen, D. E. Hooton, G. A. Swartzlander, A. E. Kaplan, Opt. Lett. 15, 783 (1990).
[Crossref] [PubMed]

Kuznetsov, E. A.

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Laedke, E. W.

E. W. Laedke, K. H. Spatschek, J. Math. Phys. 20, 1838 (1979); E. Infeld, G. Rowlands, Z. Phys. B 37, 277 (1980).
[Crossref]

Law, C. T.

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[Crossref] [PubMed]

Nye, J. F.

J. F. Nye, M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[Crossref]

Pitaevskii, L. P.

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)]; L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[Crossref] [PubMed]

Reynaud, F.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)]; A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

Spatschek, K. H.

E. W. Laedke, K. H. Spatschek, J. Math. Phys. 20, 1838 (1979); E. Infeld, G. Rowlands, Z. Phys. B 37, 277 (1980).
[Crossref]

Swartzlander, G. A.

Turitsyn, S. K.

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Wright, E. M.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, E. M. Wright, Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, Bristol, UK, 1992); A. W. Snyder, I. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
[Crossref] [PubMed]

Yin, H.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[Crossref] [PubMed]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)]; A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

J. Math. Phys. (1)

E. W. Laedke, K. H. Spatschek, J. Math. Phys. 20, 1838 (1979); E. Infeld, G. Rowlands, Z. Phys. B 37, 277 (1980).
[Crossref]

Opt. Commun. (1)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987); D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988); A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[Crossref] [PubMed]

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[Crossref] [PubMed]

Proc. R. Soc. London Ser. A (1)

J. F. Nye, M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[Crossref]

Zh. Eksp. Teor. Fiz. (3)

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)]; L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

E. A. Kuznetsov, S. K. Turitsyn, Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)]; A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

Other (1)

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, E. M. Wright, Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, Bristol, UK, 1992); A. W. Snyder, I. Poladian, D. J. Mitchell, Opt. Lett. 17, 789 (1992).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Intensity profiles of an initial dark soliton stripe (λs = 0.2 and Δn/n0 = 2.15 × 10−5) perturbed by means of a filter [see Eq. (2)] with modulation = 0.1 and t = 1 mm at Z = 0 (0 cm), 4.6 (6.8 cm), 6.0 (8.9 cm), and 8.5 (12.6 cm) in (a), (b), (c), and (d), respectively, with corresponding phase profiles (e), (f), (g), and (h), respectively (black and white represent a phase of 0 and 2π). OVS pairs are evident in (c), (d), (g), and (h).

Fig. 2
Fig. 2

Dark soliton in Fig. 1 propagating under the same settings except that the modulation is imposed by a standing wave [see Eq. (3)].

Fig. 3
Fig. 3

Average growth rate of instability γ versus normalized spatial period of the transverse modulation T (solid curve) obtained from numerical simulations with a 0.14-mm-wide opaque stripe as the initial condition (λs = ±0.47 and Δn/n0 = 10−5) and modulation amplitude = 0.1. The initial growth rate Γ0 from linear stability analysis (dashed curve) differs from γ by a factor of 1.8.

Equations (3)

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Γ 0 = 2 - 1 / 2 ν s 3 ( T cr / T ) ( 1 - T cr / T ) 1 / 2 .
u ( X , Y , Z = 0 ) - u s ( X ) [ 1 + cos ( k Y ) ] .
u ( X , Y , Z = 0 ) = u s ( X ) + cos ( k Y ) .

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