Abstract

Stabilization of chaotic intensity fluctuations of intracavity frequency-doubled solid-state (Nd: YAG) lasers using multiple-delay feedback control (MDFC) is demonstrated by numerical simulations. It is shown that MDFC not only provides stable (cw) output for constant pump rates but also works with slowly varying pump currents, resulting in corresponding (nonchaotic) intensity modulations.

© 2006 Optical Society of America

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    [CrossRef]
  2. W. P. Risk, T. R. Gosnell and A. V. Nurmikko, Compact Blue-Green Lasers (Cambridge U. Press, 2003).
    [CrossRef]
  3. C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
    [CrossRef]
  4. M. Oka and S. Kubota, Opt. Lett. 13, 805 (1988).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  8. V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
    [CrossRef]
  9. H.G.Schuster, ed., Handbook of Chaos Control (Wiley-VCH, 1999).
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  12. E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
    [CrossRef] [PubMed]
  13. K. Pyragas, Phys. Lett. A 170, 421 (1992).
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  14. J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
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  15. D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
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  16. J. E. S. Socolar and D. J. Gauthier, Phys. Rev. E 57, 6589 (1998).
    [CrossRef]
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    [CrossRef]
  18. K. Myneni, T. A. Barr, N. J. Corron, and S. D. Pethel, Phys. Rev. Lett. 83, 2175 (1999).
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  19. W. Just, H. Benner, and E. Reibold, Chaos 13, 259 (2003).
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    [CrossRef]
  21. A. Ahlborn and U. Parlitz, AIP Conf. Proc. 742, 241 (2004).
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  22. A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  27. T. W. Carr and I. B. Schwartz, Phys. Rev. E 51, 5109 (1995).
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  30. A. Schenck zu Schweinsberg and U. Dressler, Phys. Rev. E 63, 056210 (2001).
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  31. K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
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2005 (1)

A. Ahlborn and U. Parlitz, Phys. Rev. E 72, 016206 (2005).
[CrossRef]

2004 (2)

A. Ahlborn and U. Parlitz, AIP Conf. Proc. 742, 241 (2004).
[CrossRef]

A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004).
[CrossRef]

2003 (2)

W. Just, H. Benner, and E. Reibold, Chaos 13, 259 (2003).
[CrossRef] [PubMed]

W. P. Risk, T. R. Gosnell and A. V. Nurmikko, Compact Blue-Green Lasers (Cambridge U. Press, 2003).
[CrossRef]

2001 (1)

A. Schenck zu Schweinsberg and U. Dressler, Phys. Rev. E 63, 056210 (2001).
[CrossRef]

2000 (2)

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 61, 3721 (2000).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 63, 016204 (2000).
[CrossRef]

1999 (2)

K. Myneni, T. A. Barr, N. J. Corron, and S. D. Pethel, Phys. Rev. Lett. 83, 2175 (1999).
[CrossRef]

H.G.Schuster, ed., Handbook of Chaos Control (Wiley-VCH, 1999).
[CrossRef]

1998 (3)

J. E. S. Socolar and D. J. Gauthier, Phys. Rev. E 57, 6589 (1998).
[CrossRef]

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 762 (1998).
[CrossRef]

D. J. Gauthier, Opt. Lett. 23, 703 (1998).
[CrossRef]

1997 (3)

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
[CrossRef]

1996 (1)

T.Kapitaniak, ed., Controlling Chaos (Academic, 1996).

1995 (1)

T. W. Carr and I. B. Schwartz, Phys. Rev. E 51, 5109 (1995).
[CrossRef]

1994 (2)

P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994).
[CrossRef]

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

1992 (3)

K. Pyragas, Phys. Lett. A 170, 421 (1992).
[CrossRef]

R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[CrossRef] [PubMed]

1991 (3)

C. Bracikowski and R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

E. Ott, C. Grebogi, and J. Yorke, Phys. Rev. Lett. 64, 1196 (1991).
[CrossRef]

E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
[CrossRef] [PubMed]

1990 (3)

G. E. James, E. M. Harrell II, and R. Roy, Phys. Rev. A 41, 2778 (1990).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell II, C. Bracikowski, K. Wiesenfeldt, and R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

Abarbanel, H. D.

C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
[CrossRef]

Ahlborn, A.

A. Ahlborn and U. Parlitz, Phys. Rev. E 72, 016206 (2005).
[CrossRef]

A. Ahlborn and U. Parlitz, AIP Conf. Proc. 742, 241 (2004).
[CrossRef]

A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004).
[CrossRef]

Baer, T.

Barr, T. A.

K. Myneni, T. A. Barr, N. J. Corron, and S. D. Pethel, Phys. Rev. Lett. 83, 2175 (1999).
[CrossRef]

Benner, H.

W. Just, H. Benner, and E. Reibold, Chaos 13, 259 (2003).
[CrossRef] [PubMed]

Bienfang, J. C.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 762 (1998).
[CrossRef]

Bleich, M. E.

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

Bracikowski, C.

C. Bracikowski and R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell II, C. Bracikowski, K. Wiesenfeldt, and R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

Carr, T. W.

T. W. Carr and I. B. Schwartz, Phys. Rev. E 51, 5109 (1995).
[CrossRef]

Chang, A.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 762 (1998).
[CrossRef]

Colet, P.

P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994).
[CrossRef]

Corron, N. J.

K. Myneni, T. A. Barr, N. J. Corron, and S. D. Pethel, Phys. Rev. Lett. 83, 2175 (1999).
[CrossRef]

Dressler, U.

A. Schenck zu Schweinsberg and U. Dressler, Phys. Rev. E 63, 056210 (2001).
[CrossRef]

Gardner, J. R.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 762 (1998).
[CrossRef]

Gauthier, D. J.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 762 (1998).
[CrossRef]

J. E. S. Socolar and D. J. Gauthier, Phys. Rev. E 57, 6589 (1998).
[CrossRef]

D. J. Gauthier, Opt. Lett. 23, 703 (1998).
[CrossRef]

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

Gills, Z.

C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
[CrossRef]

R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[CrossRef] [PubMed]

Gosnell, T. R.

W. P. Risk, T. R. Gosnell and A. V. Nurmikko, Compact Blue-Green Lasers (Cambridge U. Press, 2003).
[CrossRef]

Grebogi, C.

E. Ott, C. Grebogi, and J. Yorke, Phys. Rev. Lett. 64, 1196 (1991).
[CrossRef]

Hall, G. M.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 762 (1998).
[CrossRef]

Harrell, E. M.

Hunt, E. R.

R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
[CrossRef] [PubMed]

Iwata, C.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[CrossRef] [PubMed]

James, G.

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

James, G. E.

Just, W.

W. Just, H. Benner, and E. Reibold, Chaos 13, 259 (2003).
[CrossRef] [PubMed]

Khaleev, M. M.

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

Kittel, A.

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 61, 3721 (2000).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 63, 016204 (2000).
[CrossRef]

Kubota, S.

Lange, F.

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 63, 016204 (2000).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 61, 3721 (2000).
[CrossRef]

Letz, T.

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 61, 3721 (2000).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 63, 016204 (2000).
[CrossRef]

Liu, C.

C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
[CrossRef]

Maier, T. D.

R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Mandel, P.

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

Murphy, T. W.

R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Myneni, K.

K. Myneni, T. A. Barr, N. J. Corron, and S. D. Pethel, Phys. Rev. Lett. 83, 2175 (1999).
[CrossRef]

Novikov, G. E.

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

Nunes, K.

C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
[CrossRef]

Nurmikko, A. V.

W. P. Risk, T. R. Gosnell and A. V. Nurmikko, Compact Blue-Green Lasers (Cambridge U. Press, 2003).
[CrossRef]

Oka, M.

Orlov, O. A.

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

Ott, E.

E. Ott, C. Grebogi, and J. Yorke, Phys. Rev. Lett. 64, 1196 (1991).
[CrossRef]

Parisi, J.

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 63, 016204 (2000).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 61, 3721 (2000).
[CrossRef]

Parlitz, U.

A. Ahlborn and U. Parlitz, Phys. Rev. E 72, 016206 (2005).
[CrossRef]

A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004).
[CrossRef]

A. Ahlborn and U. Parlitz, AIP Conf. Proc. 742, 241 (2004).
[CrossRef]

Pethel, S. D.

K. Myneni, T. A. Barr, N. J. Corron, and S. D. Pethel, Phys. Rev. Lett. 83, 2175 (1999).
[CrossRef]

Pyragas, K.

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 61, 3721 (2000).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 63, 016204 (2000).
[CrossRef]

K. Pyragas, Phys. Lett. A 170, 421 (1992).
[CrossRef]

Reibold, E.

W. Just, H. Benner, and E. Reibold, Chaos 13, 259 (2003).
[CrossRef] [PubMed]

Risk, W. P.

W. P. Risk, T. R. Gosnell and A. V. Nurmikko, Compact Blue-Green Lasers (Cambridge U. Press, 2003).
[CrossRef]

Roy, R.

C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
[CrossRef]

P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994).
[CrossRef]

R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[CrossRef] [PubMed]

C. Bracikowski and R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell II, and R. Roy, Phys. Rev. A 41, 2778 (1990).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell II, C. Bracikowski, K. Wiesenfeldt, and R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

Schwartz, I. B.

T. W. Carr and I. B. Schwartz, Phys. Rev. E 51, 5109 (1995).
[CrossRef]

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[CrossRef] [PubMed]

Socolar, J. E.

J. E. S. Socolar and D. J. Gauthier, Phys. Rev. E 57, 6589 (1998).
[CrossRef]

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

Sukow, D. W.

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

Triandaf, I.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[CrossRef] [PubMed]

Ustyugov, V. I.

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

Viktorov, E. A.

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

Wiesenfeld, K.

P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994).
[CrossRef]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

Wiesenfeldt, K.

Yorke, J.

E. Ott, C. Grebogi, and J. Yorke, Phys. Rev. Lett. 64, 1196 (1991).
[CrossRef]

zu Schweinsberg, A. Schenck

A. Schenck zu Schweinsberg and U. Dressler, Phys. Rev. E 63, 056210 (2001).
[CrossRef]

AIP Conf. Proc. (1)

A. Ahlborn and U. Parlitz, AIP Conf. Proc. 742, 241 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

V. I. Ustyugov, O. A. Orlov, M. M. Khaleev, G. E. Novikov, E. A. Viktorov, and P. Mandel, Appl. Phys. Lett. 71, 154 (1997).
[CrossRef]

Chaos (4)

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 762 (1998).
[CrossRef]

W. Just, H. Benner, and E. Reibold, Chaos 13, 259 (2003).
[CrossRef] [PubMed]

C. Bracikowski and R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

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

Opt. Lett. (3)

Phys. Lett. A (1)

K. Pyragas, Phys. Lett. A 170, 421 (1992).
[CrossRef]

Phys. Rev. A (1)

G. E. James, E. M. Harrell II, and R. Roy, Phys. Rev. A 41, 2778 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (9)

C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483 (1997).
[CrossRef]

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

J. E. S. Socolar and D. J. Gauthier, Phys. Rev. E 57, 6589 (1998).
[CrossRef]

P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994).
[CrossRef]

T. W. Carr and I. B. Schwartz, Phys. Rev. E 51, 5109 (1995).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 61, 3721 (2000).
[CrossRef]

K. Pyragas, F. Lange, T. Letz, J. Parisi, and A. Kittel, Phys. Rev. E 63, 016204 (2000).
[CrossRef]

A. Schenck zu Schweinsberg and U. Dressler, Phys. Rev. E 63, 056210 (2001).
[CrossRef]

A. Ahlborn and U. Parlitz, Phys. Rev. E 72, 016206 (2005).
[CrossRef]

Phys. Rev. Lett. (7)

R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
[CrossRef] [PubMed]

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[CrossRef] [PubMed]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004).
[CrossRef]

K. Myneni, T. A. Barr, N. J. Corron, and S. D. Pethel, Phys. Rev. Lett. 83, 2175 (1999).
[CrossRef]

E. Ott, C. Grebogi, and J. Yorke, Phys. Rev. Lett. 64, 1196 (1991).
[CrossRef]

E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
[CrossRef] [PubMed]

Other (3)

H.G.Schuster, ed., Handbook of Chaos Control (Wiley-VCH, 1999).
[CrossRef]

T.Kapitaniak, ed., Controlling Chaos (Academic, 1996).

W. P. Risk, T. R. Gosnell and A. V. Nurmikko, Compact Blue-Green Lasers (Cambridge U. Press, 2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Fixed-point stabilization using MDFC, Eq. (3), with two delay times τ x = 0.332 ms and τ y = 0.1 ms . The pump rate equals w 0 = 1.25 , and the gain parameters are a x = 0.8 , b x = 0.2 , a y = 0.1 , b y = 0.21 . After control is switched on at t = 8 ms , the system converges with a short transient to the fixed point. I i denote the intensities of the three active laser modes. I 1 and I 1 are polarized parallel to each other and perpendicular to I 0 . I IR stands for the total infrared intensity, and u for the applied feedback signal, Eq. (3). Input signals for the feedback loop are the ac-coupled infrared intensities I ̃ x = I ̃ 1 + I ̃ 1 and I ̃ y = I ̃ 0 .

Fig. 2
Fig. 2

Stability diagram of MDFC, Eq. (3), where parameter combinations that lead to successful steady-state stabilization are shaded gray. Varied are the pump rate w 0 and two of the gain parameters. The two delay times are fixed at τ x = 0.332 ms and τ y = 0.1 ms , and the remaining fixed gains are (a) the second delay line, a y = 0.23 , b y = 0.51 and (b) the first delay line a x = 1.09 , b x = 0.63 . In both cases the projection of the stability region has an extended compact shape.

Fig. 3
Fig. 3

Stabilization for slowly modulated pump current w ( t ) = w 0 + Δ w ( t ) = 1.25 + 0.029 sin ( ω t ) with ω = 2 π 20 ms . All control parameters are the same as in Fig. 1. Modulation and control are both switched on at t = 8 ms . I x and I y denote the infrared intensities in the x and the y directions, respectively. G is the intensity of the generated green laser light calculated from G 8 I x I y + 4 g ( I x I y ) 2 3 g i = 1 1 I i 2 with g = 0.1 , and u is the applied feedback signal, Eq. (3).

Equations (4)

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d I j d ϑ = { G j ϵ α η [ g ( I j I j 0 ) + 2 i j μ i j ( I i I i 0 ) ] } I j ,
d G j d ϑ = Δ w u j ( x ) + w 0 i β i j ( I i 0 I i ) η G j η i m T i j m I i G m ,
w = w 0 + Δ w
u ( t ) = a x I ̃ x ( t τ x ) b x I ̃ x ( t ) + a y I ̃ y ( t τ y ) b y I ̃ y ( t ) ,

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