Abstract

In a doubly resonant degenerate optical parametric oscillator below threshold the signal beam can be trapped in the form of stable bright temporal or spatial solitons. We characterize these soliton families and discuss how to excite them.

© 1998 Optical Society of America

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  1. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  2. P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, and R. Danielius, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. (to be published).
  3. P. Coullet, L. Gil, and D. Repaux, Phys. Rev. Lett. 62, 2957 (1989).
    [CrossRef] [PubMed]
  4. H. R. Brand and R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989).
    [CrossRef] [PubMed]
  5. D. T. Reid, J. M. Dudley, M. Ebrahimzadeh, and W. Sibbett, Opt. Lett. 19, 825 (1994).
    [CrossRef] [PubMed]
  6. G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
    [CrossRef] [PubMed]
  7. S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997).
    [CrossRef] [PubMed]
  8. K. Staliunas and V. J. Sanchez-Morcillo, Opt. Commun. 139, 306 (1997).
    [CrossRef]
  9. S. Longhi, Phys. Scr. 57, 611 (1997).
    [CrossRef]
  10. K. Staliunas and V. J. Sanchez-Morcillo, Phys. Rev. A 57, 1454 (1998).
    [CrossRef]
  11. C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
    [CrossRef]
  12. See, e.g., W. R. Bosenberg and R. C. Eckhardt, eds., feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995).
  13. A. Gatti and L. A. Lugiato, Phys. Rev. Lett. 78, 2092 (1997).
    [CrossRef]
  14. M. Brambilla, L. A. Lugiato, F. Prati, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
    [CrossRef]
  15. R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
    [CrossRef]

1998 (1)

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Rev. A 57, 1454 (1998).
[CrossRef]

1997 (7)

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

K. Staliunas and V. J. Sanchez-Morcillo, Opt. Commun. 139, 306 (1997).
[CrossRef]

S. Longhi, Phys. Scr. 57, 611 (1997).
[CrossRef]

A. Gatti and L. A. Lugiato, Phys. Rev. Lett. 78, 2092 (1997).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997).
[CrossRef] [PubMed]

1995 (2)

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

See, e.g., W. R. Bosenberg and R. C. Eckhardt, eds., feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995).

1994 (2)

1989 (2)

P. Coullet, L. Gil, and D. Repaux, Phys. Rev. Lett. 62, 2957 (1989).
[CrossRef] [PubMed]

H. R. Brand and R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989).
[CrossRef] [PubMed]

Baboiu, D. M.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Brambilla, M.

M. Brambilla, L. A. Lugiato, F. Prati, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

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

Brand, H. R.

H. R. Brand and R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989).
[CrossRef] [PubMed]

Caironi, D.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, and R. Danielius, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. (to be published).

Coullet, P.

P. Coullet, L. Gil, and D. Repaux, Phys. Rev. Lett. 62, 2957 (1989).
[CrossRef] [PubMed]

Danielius, R.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, and R. Danielius, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. (to be published).

Deissler, R. J.

H. R. Brand and R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989).
[CrossRef] [PubMed]

Di Trapani, P.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, and R. Danielius, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. (to be published).

Dubietis, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, and R. Danielius, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. (to be published).

Dudley, J. M.

Ebrahimzadeh, M.

Etrich, C.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

Firth, W. J.

M. Brambilla, L. A. Lugiato, F. Prati, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Fuerst, R. A.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Gatti, A.

A. Gatti and L. A. Lugiato, Phys. Rev. Lett. 78, 2092 (1997).
[CrossRef]

Gil, L.

P. Coullet, L. Gil, and D. Repaux, Phys. Rev. Lett. 62, 2957 (1989).
[CrossRef] [PubMed]

Haelterman, M.

Hagan, D. J.

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

Lawrence, B.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Lederer, F.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

Longhi, S.

S. Longhi, Phys. Scr. 57, 611 (1997).
[CrossRef]

Lugiato, L. A.

A. Gatti and L. A. Lugiato, Phys. Rev. Lett. 78, 2092 (1997).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

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

Menyuk, C. R.

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

Oppo, G. L.

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

Peschel, U.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

Prati, F.

M. Brambilla, L. A. Lugiato, F. Prati, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

Reid, D. T.

Repaux, D.

P. Coullet, L. Gil, and D. Repaux, Phys. Rev. Lett. 62, 2957 (1989).
[CrossRef] [PubMed]

Sanchez-Morcillo, V. J.

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Rev. A 57, 1454 (1998).
[CrossRef]

K. Staliunas and V. J. Sanchez-Morcillo, Opt. Commun. 139, 306 (1997).
[CrossRef]

Sheppard, A.

Sibbett, W.

Staliunas, K.

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Rev. A 57, 1454 (1998).
[CrossRef]

K. Staliunas and V. J. Sanchez-Morcillo, Opt. Commun. 139, 306 (1997).
[CrossRef]

Stegeman, G. I.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

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

Torner, L.

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

Torruellas, W. E.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

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

Trillo, S.

S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997).
[CrossRef] [PubMed]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Valiulis, G.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, and R. Danielius, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. (to be published).

Van Stryland, E. W.

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

Wabnitz, S.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Wang, Z.

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

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

See, e.g., W. R. Bosenberg and R. C. Eckhardt, eds., feature on optical parametric devices, J. Opt. Soc. Am. B 12, 2083–2320 (1995).

Opt. Commun. (1)

K. Staliunas and V. J. Sanchez-Morcillo, Opt. Commun. 139, 306 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

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

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Rev. A 57, 1454 (1998).
[CrossRef]

Phys. Rev. Lett. (7)

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

A. Gatti and L. A. Lugiato, Phys. Rev. Lett. 78, 2092 (1997).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

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

P. Coullet, L. Gil, and D. Repaux, Phys. Rev. Lett. 62, 2957 (1989).
[CrossRef] [PubMed]

H. R. Brand and R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989).
[CrossRef] [PubMed]

Phys. Scr. (1)

S. Longhi, Phys. Scr. 57, 611 (1997).
[CrossRef]

Other (1)

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, and R. Danielius, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. (to be published).

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Figures (5)

Fig. 1
Fig. 1

(a) Signal intensity versus PW pump intensity X=S2/Sth2: Solid and dashed curves refer to stable and unstable branches, respectively. The intensity of the homogeneous solution Pa± (PW) is compared with the peak intensity of the approximated 1D [GL; Eq. (7)], exact 1D, and exact 2D profiles. (b) Signal width (FWHM of intensity) of 1D and 2D branches.

Fig. 2
Fig. 2

(a) Intensity and (b) phase of upper-branch 1D soliton profiles from Eqs. (3) and (4) (thick curves) at the FF and the SH frequency compared with the approximate GL solutions [thin curves; Eq. (7)]. Here Δ1=1, Δ2=10, α=1, and S=13.

Fig. 3
Fig. 3

1D soliton bistability with PW illumination S=13.5 set close to threshold Sth14 with Δ1=1 and Δ2=10. The intracavity FF evolves dynamically from the initial lower-branch soliton into the upper-branch (much taller and narrower) localized solution.

Fig. 4
Fig. 4

Formation of a 1D bright signal soliton with Δ1=1 and Δ2=5: (a) FF, (b) SH frequency, (c) pump S. A wide Gaussian illumination Sr=3exp-r/3r02 superimposed upon the PW S=S0=7 for 5<t<35 brings the OPO temporarily and locally above threshold.

Fig. 5
Fig. 5

Formation of a 2D soliton Δ1=1,Δ2=5: Gaussian illumination Sr=40exp-r/3r02 superimposed upon a PW S=S0=25 is gradually switched off at t=30.

Equations (7)

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

ut=iη122u+vu*-1+iΔ1u,
vt=iη222v-u2-α+iΔ2v+S,
Δ1Δ2>α, S2>Ssub2Δ2+αΔ12,
u¨+D-1r-1u·=2ivu*-1+iΔ1u/η1,
v¨+D-1r-1v·=2i-u2-α+iΔ2v+S/η2,
iut+η122u+1Δ2u2u=Δ1-iu+SΔ2u*.
u=u±=2PGL±sechr/r0expiϕ,

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