Abstract

We show, taking dispersion into account, that second-harmonic generation in a cavity can be modulationally unstable. In the monostable mode of operation this instability might predominate with respect to self-pulsing instabilities, leading to the generation of stable solitarylike pulse trains.

© 1996 Optical Society of America

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References

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  1. See, e.g., the feature on optical parametric oscillation and amplification, J. Opt. Soc. Am. B 10, 1656–1791 (1993).
  2. J. A. Giordmaine, R. C. Miller, Phys. Rev. Lett. 14, 973 (1965).
    [CrossRef]
  3. K. J. McNeil, P. D. Drummond, D. F. Walls, Opt. Commun. 27, 292 (1978).
    [CrossRef]
  4. P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980 ); P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
    [CrossRef] [PubMed]
  5. P. Mandel, X. G. Wu, J. Opt. Soc. Am. B 3, 940 (1986).
    [CrossRef]
  6. N. P. Pettiaux, R. D. Li, P. Mandel, Opt. Commun. 72, 256 (1989).
    [CrossRef]
  7. D. T. Reid, J. M. Dudley, M. Ebrahimzadeh, W. Sibbett, Opt. Lett. 19, 825 (1994).
    [CrossRef] [PubMed]
  8. S. Longhi, Opt. Lett. 20, 1628 (1995).
    [CrossRef] [PubMed]
  9. W. Torruelas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef]
  10. S. Trillo, P. Ferro, Opt. Lett. 20, 438 (1995); Phys. Rev. E 51, 4994 (1995 ); A. V. Buryak, Y. S. Kivshar, Opt. Lett. 20, 8341995.
    [CrossRef] [PubMed]
  11. M. Haelterman, S. Trillo, S. Wabnitz, Opt. Lett. 17, 745 (1992).
    [CrossRef] [PubMed]
  12. T. Debuisschert, A. Sizmann, E. Giacobino, C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).
    [CrossRef]
  13. V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1990).
  14. G. Oppo, M. Brambilla, L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
    [CrossRef] [PubMed]
  15. M. A. M. Marte, Phys. Rev. A 49, R3166 (1994 ); Phys. Rev. Lett. 74, 4815 (1995).
    [CrossRef] [PubMed]

1995 (3)

1994 (3)

D. T. Reid, J. M. Dudley, M. Ebrahimzadeh, W. Sibbett, Opt. Lett. 19, 825 (1994).
[CrossRef] [PubMed]

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

M. A. M. Marte, Phys. Rev. A 49, R3166 (1994 ); Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef] [PubMed]

1993 (2)

T. Debuisschert, A. Sizmann, E. Giacobino, C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).
[CrossRef]

See, e.g., the feature on optical parametric oscillation and amplification, J. Opt. Soc. Am. B 10, 1656–1791 (1993).

1992 (1)

1989 (1)

N. P. Pettiaux, R. D. Li, P. Mandel, Opt. Commun. 72, 256 (1989).
[CrossRef]

1986 (1)

1980 (1)

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980 ); P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef] [PubMed]

1978 (1)

K. J. McNeil, P. D. Drummond, D. F. Walls, Opt. Commun. 27, 292 (1978).
[CrossRef]

1965 (1)

J. A. Giordmaine, R. C. Miller, Phys. Rev. Lett. 14, 973 (1965).
[CrossRef]

Brambilla, M.

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

Debuisschert, T.

T. Debuisschert, A. Sizmann, E. Giacobino, C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).
[CrossRef]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1990).

Drummond, P. D.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980 ); P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef] [PubMed]

K. J. McNeil, P. D. Drummond, D. F. Walls, Opt. Commun. 27, 292 (1978).
[CrossRef]

Dudley, J. M.

Ebrahimzadeh, M.

Fabre, C.

T. Debuisschert, A. Sizmann, E. Giacobino, C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).
[CrossRef]

Ferro, P.

Giacobino, E.

T. Debuisschert, A. Sizmann, E. Giacobino, C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, R. C. Miller, Phys. Rev. Lett. 14, 973 (1965).
[CrossRef]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1990).

Haelterman, M.

Hagan, D. J.

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

Li, R. D.

N. P. Pettiaux, R. D. Li, P. Mandel, Opt. Commun. 72, 256 (1989).
[CrossRef]

Longhi, S.

Lugiato, L. A.

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

Mandel, P.

N. P. Pettiaux, R. D. Li, P. Mandel, Opt. Commun. 72, 256 (1989).
[CrossRef]

P. Mandel, X. G. Wu, J. Opt. Soc. Am. B 3, 940 (1986).
[CrossRef]

Marte, M. A. M.

M. A. M. Marte, Phys. Rev. A 49, R3166 (1994 ); Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef] [PubMed]

McNeil, K. J.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980 ); P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef] [PubMed]

K. J. McNeil, P. D. Drummond, D. F. Walls, Opt. Commun. 27, 292 (1978).
[CrossRef]

Menyuk, C. R.

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

Miller, R. C.

J. A. Giordmaine, R. C. Miller, Phys. Rev. Lett. 14, 973 (1965).
[CrossRef]

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1990).

Oppo, G.

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

Pettiaux, N. P.

N. P. Pettiaux, R. D. Li, P. Mandel, Opt. Commun. 72, 256 (1989).
[CrossRef]

Reid, D. T.

Sibbett, W.

Sizmann, A.

T. Debuisschert, A. Sizmann, E. Giacobino, C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).
[CrossRef]

Stegeman, G. I.

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

Torner, L.

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

Torruelas, W.

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

Trillo, S.

Van Stryland, E. W.

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

Wabnitz, S.

Walls, D. F.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980 ); P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef] [PubMed]

K. J. McNeil, P. D. Drummond, D. F. Walls, Opt. Commun. 27, 292 (1978).
[CrossRef]

Wang, Z.

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

Wu, X. G.

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

See, e.g., the feature on optical parametric oscillation and amplification, J. Opt. Soc. Am. B 10, 1656–1791 (1993).

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

T. Debuisschert, A. Sizmann, E. Giacobino, C. Fabre, J. Opt. Soc. Am. B 9, 1668 (1993).
[CrossRef]

P. Mandel, X. G. Wu, J. Opt. Soc. Am. B 3, 940 (1986).
[CrossRef]

Opt. Acta (1)

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 27, 321 (1980 ); P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1981).
[CrossRef] [PubMed]

Opt. Commun. (2)

N. P. Pettiaux, R. D. Li, P. Mandel, Opt. Commun. 72, 256 (1989).
[CrossRef]

K. J. McNeil, P. D. Drummond, D. F. Walls, Opt. Commun. 27, 292 (1978).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (2)

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

M. A. M. Marte, Phys. Rev. A 49, R3166 (1994 ); Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

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

J. A. Giordmaine, R. C. Miller, Phys. Rev. Lett. 14, 973 (1965).
[CrossRef]

Other (1)

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1990).

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Figures (3)

Fig. 1
Fig. 1

Modulational instability gain versus modulation frequency Ω and intensity P1 for the exactly resonant case (i.e., Δ1 = Δ2 = 0), α = 1, and dispersions (a) β1 = ±1, β2 = ±0.5 and (b) β1 = ±1, β2 = ±5.

Fig. 2
Fig. 2

Real and imaginary parts of the eigenvalues λi, i = 1, 4 versus Ω for Δ1 = Δ2 = 0, α = 1, β1 = β2 = ±1, and P1 = P1SP = 4.

Fig. 3
Fig. 3

Pulse-train generation from a slightly perturbed steady state. Here Δ1 = Δ2 = 0, α = 1, P1 = 5, and β1 = 1 and β2 = 5 (i.e., normal dispersions).

Equations (6)

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i ( u 1 ξ + δ 1 u 1 τ ) β 1 2 2 u 1 τ 2 + u 2 u 1 * = ( Δ 1 i ) u 1 + i S , i ( u 2 ξ + δ 2 u 2 τ ) β 2 2 2 u 2 τ 2 + u 1 2 2 = ( Δ 2 i α ) u 2 ,
u ¯ 1 = 2 S ( α + i Δ 2 ) 2 ( 1 + i Δ 1 ) ( α + i Δ 2 ) + P 1 , u ¯ 2 = u ¯ 1 2 2 ( Δ 2 i α ) .
a j ( ξ , τ ) = j s ( ξ ) exp ( i Ω τ ) + ja ( ξ ) exp ( i Ω τ ) ( j = 1 , 2 ) .
Q = [ i Ω 1 u ¯ 2 u ¯ 1 * 0 u ¯ 2 * i + Ω 1 0 u ¯ 1 u ¯ 1 0 i α Ω 2 0 0 u ¯ 1 * 0 i α + Ω 2 ] .
λ 4 + a 3 λ 3 + a 2 λ 2 + a 1 λ + a 0 = 0 ,
λ ± = 1 + 1 2 2 { f 0 ( Ω ) ± [ f 0 ( Ω ) 2 f 1 ( Ω ) ] 1 / 2 } 1 / 2 ,

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