Abstract

We predict that nearly resonant optical parametric oscillators support stable topological spatial solitons as a result of the interplay between diffraction and parametric amplification due to χ2 nonlinearities. Robust soliton stripes are observed in two transverse dimensions. Their stability is ensured by the phase-sensitive nature of the underlying parametric process.

© 1997 Optical Society of America

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References

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  1. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [Crossref] [PubMed]
  2. S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995); Phys. Rev. E 51, 4994 (1995); A. V. Buryak and Y. S. Kivshar, Opt. Lett. 20, 834 (1995).
    [Crossref] [PubMed]
  3. See, e.g., the feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995).
  4. G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
    [Crossref] [PubMed]
  5. K. Staliunas, J. Mod. Opt. 42, 1261 (1995).
    [Crossref]
  6. S. Longhi, J. Mod. Opt. 43, 1089 (1996); S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
    [Crossref] [PubMed]
  7. G. J. de Valcarcel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
    [Crossref]
  8. L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
    [Crossref]
  9. W. Zhang and J. Vinals, Phys. Rev. Lett. 74, 690 (1995).
    [Crossref] [PubMed]
  10. S. Longhi, Phys. Rev. E 53, 5520 (1996), and references therein.
    [Crossref]
  11. M. J. Werner and P. D. Drummond, Opt. Lett. 19, 613 (1994).
    [Crossref] [PubMed]
  12. S. Longhi, Opt. Lett. 21, 860 (1996).
    [Crossref] [PubMed]
  13. D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
    [Crossref]
  14. V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 263.
  15. S. Schiller and R. L. Byer, J. Opt. Soc. Am. B 12, 1696 (1993).
    [Crossref]

1996 (4)

S. Longhi, J. Mod. Opt. 43, 1089 (1996); S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
[Crossref] [PubMed]

G. J. de Valcarcel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[Crossref]

S. Longhi, Phys. Rev. E 53, 5520 (1996), and references therein.
[Crossref]

S. Longhi, Opt. Lett. 21, 860 (1996).
[Crossref] [PubMed]

1995 (6)

K. Staliunas, J. Mod. Opt. 42, 1261 (1995).
[Crossref]

W. Zhang and J. Vinals, Phys. Rev. Lett. 74, 690 (1995).
[Crossref] [PubMed]

S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995); Phys. Rev. E 51, 4994 (1995); A. V. Buryak and Y. S. Kivshar, Opt. Lett. 20, 834 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[Crossref]

See, e.g., the feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995).

1994 (2)

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[Crossref] [PubMed]

M. J. Werner and P. D. Drummond, Opt. Lett. 19, 613 (1994).
[Crossref] [PubMed]

1993 (1)

S. Schiller and R. L. Byer, J. Opt. Soc. Am. B 12, 1696 (1993).
[Crossref]

1988 (1)

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[Crossref]

Brambilla, M.

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[Crossref] [PubMed]

Byer, R. L.

S. Schiller and R. L. Byer, J. Opt. Soc. Am. B 12, 1696 (1993).
[Crossref]

Christou, J.

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 263.

de Valcarcel, G. J.

G. J. de Valcarcel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[Crossref]

Drummond, P. D.

Fabre, C.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[Crossref]

Ferro, P.

Giacobino, E.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[Crossref]

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Horowicz, R.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[Crossref]

Kivshar, Yu. S.

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[Crossref]

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 263.

Longhi, S.

S. Longhi, Phys. Rev. E 53, 5520 (1996), and references therein.
[Crossref]

S. Longhi, J. Mod. Opt. 43, 1089 (1996); S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
[Crossref] [PubMed]

S. Longhi, Opt. Lett. 21, 860 (1996).
[Crossref] [PubMed]

Lugiato, L. A.

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[Crossref] [PubMed]

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[Crossref]

Luther-Davies, B.

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 263.

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Oldano, C.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[Crossref]

Oppo, G. L.

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[Crossref] [PubMed]

Pelinovsky, D. E.

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[Crossref]

Roldan, E.

G. J. de Valcarcel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[Crossref]

Sanchez-Morcillo, V. J.

G. J. de Valcarcel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[Crossref]

Schiller, S.

S. Schiller and R. L. Byer, J. Opt. Soc. Am. B 12, 1696 (1993).
[Crossref]

Staliunas, K.

G. J. de Valcarcel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[Crossref]

K. Staliunas, J. Mod. Opt. 42, 1261 (1995).
[Crossref]

Stegeman, G. I.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Stepanyants, Yu. A.

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[Crossref]

Tikhonenko, V.

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 263.

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Trillo, S.

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Vinals, J.

W. Zhang and J. Vinals, Phys. Rev. Lett. 74, 690 (1995).
[Crossref] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Werner, M. J.

Zhang, W.

W. Zhang and J. Vinals, Phys. Rev. Lett. 74, 690 (1995).
[Crossref] [PubMed]

J. Mod. Opt. (2)

K. Staliunas, J. Mod. Opt. 42, 1261 (1995).
[Crossref]

S. Longhi, J. Mod. Opt. 43, 1089 (1996); S. Longhi and A. Geraci, Phys. Rev. A 54, 4581 (1996).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (2)

See, e.g., the feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995).

S. Schiller and R. L. Byer, J. Opt. Soc. Am. B 12, 1696 (1993).
[Crossref]

Nuovo Cimento D (1)

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (2)

G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[Crossref] [PubMed]

G. J. de Valcarcel, K. Staliunas, E. Roldan, and V. J. Sanchez-Morcillo, Phys. Rev. A 54, 1609 (1996).
[Crossref]

Phys. Rev. E (2)

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar, Phys. Rev. E 51, 5016 (1995).
[Crossref]

S. Longhi, Phys. Rev. E 53, 5520 (1996), and references therein.
[Crossref]

Phys. Rev. Lett. (2)

W. Zhang and J. Vinals, Phys. Rev. Lett. 74, 690 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

Other (1)

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 263.

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Figures (4)

Fig. 1
Fig. 1

Bifurcation diagram: OPO stable (solid curve) and unstable (dashed curve) steady states versus driving intensity. (a) Monostable, Δ1=Δ2=0; (b) bistable, Δ1=Δ2=2.

Fig. 2
Fig. 2

Signal (solid curve) and pump (dotted curve) profiles of the phase-defect-field amplitudes (left) and intensities (right) obtained from the numerical solution of Eqs.  (1) and (2) with Δ1=Δ2=0, α=1, and S=2.

Fig. 3
Fig. 3

Comparison of the approximate solution of Eq.  (5) (solid curves) with the exact steady-state solutions of Eqs.  (1) and (2) (dotted curves for Δ1=-1, Δ2=-10, α=1, and S=12 (corresponding to the homogeneous monostable solution branch).

Fig. 4
Fig. 4

Spontaneous formation of a stable dark-soliton stripe (signal field) from white-noise seeding. The gray scale is proportional to the field intensity. Neumann boundary conditions were used.

Equations (7)

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

ut=i22u+vu*-1+iΔ1u,
vt=iρ22v-u2-α+iΔ2v+S,
us=±SP/1+iΔ1α+iΔ2+P1/2,
vs=S1+iΔ1/1+iΔ1α+iΔ2+P,
ut=i2Δu+iΔ2u2u-1+iΔ1u-iSΔ2u*.
us=±S+Δ2Si-Δ1iΔ2±S2-Δ221/2,
u=A tanhx/x0expiϕ,

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