Abstract

The existence of stable dissipative spatial solitons at low intensities in patterned electrode semiconductor optical amplifiers (SOAs) is predicted theoretically. In contrast to conventional SOAs, this system may support stable solitons because the inherent saturating losses provide subcritical bifurcations for both the plane-wave and the soliton solution.

© 2003 Optical Society of America

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References

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  1. M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
    [CrossRef]
  2. M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef]
  3. E. Garmire, IEEE J. Sel. Top. Quantum Electron. 6, 1094 (2000).
    [CrossRef]
  4. G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
    [CrossRef] [PubMed]
  5. C. Kutsche, P. LiKamWa, J. Loehr, and R. Kaspi, Electron. Lett. 34, 906 (1998).
    [CrossRef]
  6. Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
    [CrossRef]
  7. Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, and F. Lederer, J. Opt. Soc. Am. B 19, 487 (2002).
    [CrossRef]
  8. N. N. Rosanov, in Progress in Optics XXXV, E. Wolf, ed. (Elsevier, New York, 1996).
  9. V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).
    [CrossRef]
  10. L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
    [CrossRef]
  11. D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
    [CrossRef]
  12. V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
    [CrossRef]
  13. S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.
  14. S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
    [CrossRef] [PubMed]
  15. S. Longhi and A. Geraci, Appl. Phys. Lett. 67, 3062 (1995).
    [CrossRef]
  16. S. V. Federov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).
    [CrossRef]
  17. G. P. Agrawal, J. Appl. Phys. 56, 3100 (1984).
    [CrossRef]
  18. D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
    [CrossRef]
  19. H. Paxtion and G. C. Dente, J. Appl. Phys. 70, 2921 (1991).
    [CrossRef]
  20. L. Goldberg, M. R. Surette, and D. Mehuys, Appl. Phys. Lett. 62, 2304 (1993).
    [CrossRef]
  21. N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
    [CrossRef]

2002 (1)

2001 (1)

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

2000 (3)

S. V. Federov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).
[CrossRef]

E. Garmire, IEEE J. Sel. Top. Quantum Electron. 6, 1094 (2000).
[CrossRef]

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

1998 (3)

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

C. Kutsche, P. LiKamWa, J. Loehr, and R. Kaspi, Electron. Lett. 34, 906 (1998).
[CrossRef]

1997 (2)

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).
[CrossRef]

1996 (2)

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

1995 (1)

S. Longhi and A. Geraci, Appl. Phys. Lett. 67, 3062 (1995).
[CrossRef]

1993 (2)

L. Goldberg, M. R. Surette, and D. Mehuys, Appl. Phys. Lett. 62, 2304 (1993).
[CrossRef]

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

1991 (1)

H. Paxtion and G. C. Dente, J. Appl. Phys. 70, 2921 (1991).
[CrossRef]

1990 (1)

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

1987 (1)

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
[CrossRef]

1984 (1)

G. P. Agrawal, J. Appl. Phys. 56, 3100 (1984).
[CrossRef]

Afanasjev, V. V.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, J. Appl. Phys. 56, 3100 (1984).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

Bakonyi, Z.

Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, and F. Lederer, J. Opt. Soc. Am. B 19, 487 (2002).
[CrossRef]

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

Balle, S.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Barland, S.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Brambilla, M.

L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Dente, G. C.

H. Paxtion and G. C. Dente, J. Appl. Phys. 70, 2921 (1991).
[CrossRef]

Fauve, S.

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

Federov, S. V.

S. V. Federov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).
[CrossRef]

Ganne, I.

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

Garmire, E.

E. Garmire, IEEE J. Sel. Top. Quantum Electron. 6, 1094 (2000).
[CrossRef]

Geraci, A.

S. Longhi and A. Geraci, Appl. Phys. Lett. 67, 3062 (1995).
[CrossRef]

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Giudici, M.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Goldberg, L.

L. Goldberg, M. R. Surette, and D. Mehuys, Appl. Phys. Lett. 62, 2304 (1993).
[CrossRef]

Gölles, M.

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

Ikegami, T.

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Iwamura, H.

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Jager, R.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Kasamura, Y.

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Kaspi, R.

C. Kutsche, P. LiKamWa, J. Loehr, and R. Kaspi, Electron. Lett. 34, 906 (1998).
[CrossRef]

Khitrova, G.

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Khodova, G. V.

S. V. Federov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).
[CrossRef]

Knodl, T.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Knoll, C.

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

Kuszelewicz, R. J.

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

Kutsche, C.

C. Kutsche, P. LiKamWa, J. Loehr, and R. Kaspi, Electron. Lett. 34, 906 (1998).
[CrossRef]

Lang, R. J.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
[CrossRef]

Lederer, F.

Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, and F. Lederer, J. Opt. Soc. Am. B 19, 487 (2002).
[CrossRef]

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

LiKamWa, P.

C. Kutsche, P. LiKamWa, J. Loehr, and R. Kaspi, Electron. Lett. 34, 906 (1998).
[CrossRef]

Loehr, J.

C. Kutsche, P. LiKamWa, J. Loehr, and R. Kaspi, Electron. Lett. 34, 906 (1998).
[CrossRef]

Longhi, S.

S. Longhi and A. Geraci, Appl. Phys. Lett. 67, 3062 (1995).
[CrossRef]

Ludwig, R.

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

Lugiato, L. A.

L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Maggipinto, T.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Mehuys, D.

L. Goldberg, M. R. Surette, and D. Mehuys, Appl. Phys. Lett. 62, 2304 (1993).
[CrossRef]

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
[CrossRef]

Michaelis, D.

Miller, M.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Mittelstein, M.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
[CrossRef]

Onishchukov, G.

Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, and F. Lederer, J. Opt. Soc. Am. B 19, 487 (2002).
[CrossRef]

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

Paxtion, H.

H. Paxtion and G. C. Dente, J. Appl. Phys. 70, 2921 (1991).
[CrossRef]

Peschel, U.

Prati, F.

L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

Rosanov, N. N.

S. V. Federov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).
[CrossRef]

N. N. Rosanov, in Progress in Optics XXXV, E. Wolf, ed. (Elsevier, New York, 1996).

Salzaman, J.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
[CrossRef]

Segev, M.

Shih, M.

Sipe, J. E.

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

Spinelli, L.

L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Staliunas, K.

V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).
[CrossRef]

Stegeman, G. I.

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Surette, M. R.

L. Goldberg, M. R. Surette, and D. Mehuys, Appl. Phys. Lett. 62, 2304 (1993).
[CrossRef]

Taranenko, V. B.

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).
[CrossRef]

Thual, O.

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

Tissoni, G.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Tissoni, L. G.

L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

Tredicce, J. R.

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

Valley, G. C.

Vladimirov, A. G.

S. V. Federov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).
[CrossRef]

Weiss, C. O.

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).
[CrossRef]

Yariv, A.

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
[CrossRef]

Appl. Phys. B (1)

V. B. Taranenko, I. Ganne, R. J. Kuszelewicz, and C. O. Weiss, Appl. Phys. B 72, 377 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

S. Longhi and A. Geraci, Appl. Phys. Lett. 67, 3062 (1995).
[CrossRef]

L. Goldberg, M. R. Surette, and D. Mehuys, Appl. Phys. Lett. 62, 2304 (1993).
[CrossRef]

Electron. Lett. (1)

C. Kutsche, P. LiKamWa, J. Loehr, and R. Kaspi, Electron. Lett. 34, 906 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Mehuys, R. J. Lang, M. Mittelstein, J. Salzaman, and A. Yariv, IEEE J. Quantum Electron. 23, 1909 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Garmire, IEEE J. Sel. Top. Quantum Electron. 6, 1094 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Bakonyi, G. Onishchukov, C. Knoll, M. Gölles, F. Lederer, and R. Ludwig, IEEE Photon. Technol. Lett. 12, 570 (2000).
[CrossRef]

J. Appl. Phys. (2)

H. Paxtion and G. C. Dente, J. Appl. Phys. 70, 2921 (1991).
[CrossRef]

G. P. Agrawal, J. Appl. Phys. 56, 3100 (1984).
[CrossRef]

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

Phys. Rev. A (3)

V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).
[CrossRef]

L. Spinelli, L. G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, Phys. Rev. A 58, 2542 (1998).
[CrossRef]

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

Phys. Rev. E (2)

S. V. Federov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).
[CrossRef]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

G. Khitrova, H. M. Gibbs, Y. Kasamura, H. Iwamura, T. Ikegami, and J. E. Sipe, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

Phys. Today (1)

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Other (2)

N. N. Rosanov, in Progress in Optics XXXV, E. Wolf, ed. (Elsevier, New York, 1996).

S. Barland, M. Giudici, J. R. Tredicce, S. Balle, M. Brambilla, T. Maggipinto, L. A. Lugiato, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, paper QWA1 presented at the International Quantum Electronics Conference, Moscow, June 22–28, 2002.

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Figures (2)

Fig. 1
Fig. 1

(a) Gain and loss of the system versus field intensity. The dotted curve shows the saturating loss in the nonpumped region, and the dashed curve is the saturated gain in the pumped region. The solid curve represents the sum of these two contributions and the internal linear losses of the system. (b) PW and soliton bifurcation diagrams versus δG. The thick solid curve shows the PW solutions that subcritically bifurcate from the trivial solution. Between zero gain and the turning point the solution with negative slope is unstable. The dashed curve indicates the peak intensity of the stable soliton. This branch terminates because of Hopf instabilities. The dotted curve is the unstable trivial PW solution at positive small-signal gain, and the thin solid line is the stable zero PW solutions. The fields shown here are averaged along the pumped and unpumped segments.

Fig. 2
Fig. 2

(a) Soliton amplitude (solid curve) and phase profile (dashed curve). (b) Evolution at δG=-0.106 of a 179.2-mW total power input beam with a constant phase, sech2 intensity distribution, and 37.5µm beam waist (FWHM) into a 24.5µm beam waist (FWHM), 181.4-mW spatial soliton, with normalized parameters (B=0.7, C=0.005, D=1.56, α=0.067).

Equations (2)

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

ψz=i22ψx2+i-hN-iN-1ψ-αψ,  D2Nx2+πz-N-BN2-CN3- N-1ψ2=0.
ψz= i12-iβ2ψx2+π0-11+ψ2-ih+1-ihψ-αψ.

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