Abstract

We study a multimode semiconductor laser subject to moderate selective optical feedback. The steady state of the laser is destabilized by a Hopf bifurcation and exhibits a period-doubling route to chaos. We also show the existence of a heteroclinic connection between a saddle node and an unstable focus that can be associated with experimentally observed multimode low-frequency fluctuations. This heteroclinic connection coexists with a chaotic attractor resulting from the period-doubling process.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
    [Crossref]
  2. G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
    [Crossref]
  3. G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
    [Crossref]
  4. G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
    [Crossref]
  5. M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, Chaos Solitons Fractals 10, 811 (1999).
    [Crossref]
  6. D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
    [Crossref]
  7. E. A. Viktorov and P. Mandel, Phys. Rev. Lett. 85, 3157 (2000).
    [Crossref] [PubMed]
  8. C. L. Tang, H. Statz, and G. de Mars, J. Appl. Phys. 34, 2289 (1963).
    [Crossref]
  9. P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge U. Press, Cambridge, 1997).
    [Crossref]
  10. H. Statz, C. L. Tang, and J. M. Levine, J. Appl. Phys. 35, 2581 (1964).
    [Crossref]
  11. C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977); T. Sano, Phys. Rev. A 50, 2719 (1994); G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995); I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996); B. Tromborg, J. Mrk, and V. Velichansky, Quantum Semiclass. Opt. 9, 831 (1997).
    [Crossref] [PubMed]
  12. G. H. M. van Tartwijk and D. Lenstra, Quantum Semiclass. Opt. 7, 87 (1995).
    [Crossref]
  13. L. P. Shilnikov, Sov. Math. Dokl. 8, 102 (1967).
  14. M. Poliashenko and S. R. McKay, Phys. Rev. A 46, 5271 (1992).
    [Crossref] [PubMed]

2000 (1)

E. A. Viktorov and P. Mandel, Phys. Rev. Lett. 85, 3157 (2000).
[Crossref] [PubMed]

1999 (2)

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, Chaos Solitons Fractals 10, 811 (1999).
[Crossref]

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

1998 (2)

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

1997 (1)

G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
[Crossref]

1995 (1)

G. H. M. van Tartwijk and D. Lenstra, Quantum Semiclass. Opt. 7, 87 (1995).
[Crossref]

1992 (1)

M. Poliashenko and S. R. McKay, Phys. Rev. A 46, 5271 (1992).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[Crossref]

1977 (1)

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977); T. Sano, Phys. Rev. A 50, 2719 (1994); G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995); I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996); B. Tromborg, J. Mrk, and V. Velichansky, Quantum Semiclass. Opt. 9, 831 (1997).
[Crossref] [PubMed]

1967 (1)

L. P. Shilnikov, Sov. Math. Dokl. 8, 102 (1967).

1964 (1)

H. Statz, C. L. Tang, and J. M. Levine, J. Appl. Phys. 35, 2581 (1964).
[Crossref]

1963 (1)

C. L. Tang, H. Statz, and G. de Mars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Balle, S.

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

de Bruyn, B.

G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
[Crossref]

de Mars, G.

C. L. Tang, H. Statz, and G. de Mars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Elsasser, W.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

Fischer, I.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

Gavrielides, A.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

Giacomelli, G.

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

Giudici, M.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, Chaos Solitons Fractals 10, 811 (1999).
[Crossref]

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
[Crossref]

Giuggioli, L.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, Chaos Solitons Fractals 10, 811 (1999).
[Crossref]

Green, C.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, Chaos Solitons Fractals 10, 811 (1999).
[Crossref]

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

Hegarty, S. P.

G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
[Crossref]

Heil, T.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

Hohl-AbiChedid, A.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

Huyet, G.

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[Crossref]

Lenstra, D.

G. H. M. van Tartwijk and D. Lenstra, Quantum Semiclass. Opt. 7, 87 (1995).
[Crossref]

Levine, J. M.

H. Statz, C. L. Tang, and J. M. Levine, J. Appl. Phys. 35, 2581 (1964).
[Crossref]

Mandel, P.

E. A. Viktorov and P. Mandel, Phys. Rev. Lett. 85, 3157 (2000).
[Crossref] [PubMed]

P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge U. Press, Cambridge, 1997).
[Crossref]

McInerney, J. G.

G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
[Crossref]

McKay, S. R.

M. Poliashenko and S. R. McKay, Phys. Rev. A 46, 5271 (1992).
[Crossref] [PubMed]

Menoni, C. S.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

Poliashenko, M.

M. Poliashenko and S. R. McKay, Phys. Rev. A 46, 5271 (1992).
[Crossref] [PubMed]

Risch, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977); T. Sano, Phys. Rev. A 50, 2719 (1994); G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995); I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996); B. Tromborg, J. Mrk, and V. Velichansky, Quantum Semiclass. Opt. 9, 831 (1997).
[Crossref] [PubMed]

Rocca, J. J.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

Shilnikov, L. P.

L. P. Shilnikov, Sov. Math. Dokl. 8, 102 (1967).

Statz, H.

H. Statz, C. L. Tang, and J. M. Levine, J. Appl. Phys. 35, 2581 (1964).
[Crossref]

C. L. Tang, H. Statz, and G. de Mars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Sukow, D. W.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

Tang, C. L.

H. Statz, C. L. Tang, and J. M. Levine, J. Appl. Phys. 35, 2581 (1964).
[Crossref]

C. L. Tang, H. Statz, and G. de Mars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

Tredicce, J.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

Tredicce, J. R.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, Chaos Solitons Fractals 10, 811 (1999).
[Crossref]

van Tartwijk, G. H. M.

G. H. M. van Tartwijk and D. Lenstra, Quantum Semiclass. Opt. 7, 87 (1995).
[Crossref]

Vaschenko, G.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

Viktorov, E. A.

E. A. Viktorov and P. Mandel, Phys. Rev. Lett. 85, 3157 (2000).
[Crossref] [PubMed]

Voumard, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977); T. Sano, Phys. Rev. A 50, 2719 (1994); G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995); I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996); B. Tromborg, J. Mrk, and V. Velichansky, Quantum Semiclass. Opt. 9, 831 (1997).
[Crossref] [PubMed]

Chaos Solitons Fractals (1)

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, Chaos Solitons Fractals 10, 811 (1999).
[Crossref]

Europhys. Lett. (1)

G. Huyet, S. P. Hegarty, M. Giudici, B. de Bruyn, and J. G. McInerney, Europhys. Lett. 40, 619 (1997).
[Crossref]

IEEE J. Quantum Electron. (1)

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[Crossref]

J. Appl. Phys. (3)

C. L. Tang, H. Statz, and G. de Mars, J. Appl. Phys. 34, 2289 (1963).
[Crossref]

H. Statz, C. L. Tang, and J. M. Levine, J. Appl. Phys. 35, 2581 (1964).
[Crossref]

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977); T. Sano, Phys. Rev. A 50, 2719 (1994); G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995); I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsasser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996); B. Tromborg, J. Mrk, and V. Velichansky, Quantum Semiclass. Opt. 9, 831 (1997).
[Crossref] [PubMed]

Opt. Commun. (1)

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. Tredicce, Opt. Commun. 149, 341 (1998).
[Crossref]

Phys. Rev. A (2)

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedid, and W. Elsasser, Phys. Rev. A 60, 667 (1999).
[Crossref]

M. Poliashenko and S. R. McKay, Phys. Rev. A 46, 5271 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

E. A. Viktorov and P. Mandel, Phys. Rev. Lett. 85, 3157 (2000).
[Crossref] [PubMed]

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[Crossref]

Quantum Semiclass. Opt. (1)

G. H. M. van Tartwijk and D. Lenstra, Quantum Semiclass. Opt. 7, 87 (1995).
[Crossref]

Sov. Math. Dokl. (1)

L. P. Shilnikov, Sov. Math. Dokl. 8, 102 (1967).

Other (1)

P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge U. Press, Cambridge, 1997).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Modal output and phase portraits from Eqs. (3)–(5), featuring period doubling and chaos for N=3, obtained with a 500-MHz low-pass filter. The thick lower curves represent I2,3. The fixed parameters are P=10-3, T=103, γp=1 THz, α=5, β=0.9, τ=6 ns, and Ω=2nπ/τ, where n is an integer. The attenuations are (a) η=3×10-4, (b) η=3.25×10-4, (c) η=3.4×10-4, (d) η=3.5×10-4, (e) η=3.7×10-4. The motion in the dotted box in (e) corresponds to the chaotic attractor in (d).

Fig. 2
Fig. 2

Modal intensities featuring the heteroclinic connection. The parameters are the same as in Fig. 1(e). The dashed and dotted lines indicate the single-mode I10,I2=I3=0 and two-mode I1=0,I2=I30 steady states, respectively.

Equations (6)

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

dEmdt=121+iαNm-γpmEm+kmEmt-τexp-iΩmτ,
dNmdt=J-Nmτs-NmnNβnmEn2,
dA1/dγpt=1+iαF1A1+ηA1t-τexp-iΩτ,
dAj/dγpt=1+iαFjAj,
TdFmdγpt=P-Fm-1+2FmnNβnmAn2,
Am=τs/2Em,  Fm=nm/2γp,  P=J-Jth/2Jth,

Metrics