Abstract

Spatiotemporal solitons (STSs) are waves that are localized in all three dimensions of space as well as in time. They are of interest intrinsically as well as for ultrafast optical information processing, but their experimental observation remains a major challenge in nonlinear science. Two decades of investigation of STSs in optics has yielded only a few experimental demonstrations in conservative media. We present the realistic design and modeling of a solid-state laser that depends on the formation of dissipative STSs, which balance nonlinear gain and loss as well as linear and nonlinear phases. Numerical calculations show that stable, three-dimensional solitons can form in lasers containing self-focusing nonlinear materials with large normal dispersion. Experimental realization will be challenging but appears to be technologically achievable.

© 2014 Optical Society of America

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  1. J. S. Russell, Report of the Fourteenth Meeting of the British Association for the Advancement of Science (1844), pp. 311–390.
  2. A. R. Osborne, T. L. Burch, Science 208, 451 (1980).
    [CrossRef]
  3. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  4. N. Zabusky, M. Kruskal, Phys. Rev. Lett. 15, 240 (1965).
    [CrossRef]
  5. L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
    [CrossRef]
  6. S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
    [CrossRef]
  7. B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005).
    [CrossRef]
  8. R. Chiao, E. Garmire, C. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  9. Y. Silberberg, Opt. Lett. 15, 1282 (1990).
    [CrossRef]
  10. R. McLeod, K. Wagner, S. Blair, Phys. Rev. A 52, 3254 (1995).
    [CrossRef]
  11. X. Liu, L. Qian, F. Wise, Phys. Rev. Lett. 82, 4631 (1999).
    [CrossRef]
  12. S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
    [CrossRef]
  13. N. Akhmediev, J. M. Soto-Crespo, P. Grelu, Chaos 17, 037112 (2007).
    [CrossRef]
  14. J. M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Express 14, 4013 (2006).
    [CrossRef]
  15. J. M. Soto-Crespo, N. Akhmediev, P. Grelu, Phys. Rev. E 74, 46612 (2006).
    [CrossRef]
  16. P. Grelu, J. M. Soto-Crespo, N. Akhmediev, Opt. Express 13, 9352 (2005).
    [CrossRef]
  17. T. Ackemann, W. J. Firth, G. Oppo, Adv. At. Mol. Opt. Phys. 57, 323 (2009).
    [CrossRef]
  18. A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
    [CrossRef]
  19. M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, Phys. Rev. Lett. 93, 203901 (2004).
    [CrossRef]
  20. B. Proctor, E. Westwig, F. Wise, Opt. Lett. 18, 1654 (1993).
    [CrossRef]
  21. S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
    [CrossRef]
  22. W. H. Renninger, A. Chong, F. W. Wise, Phys. Rev. A 77, 23814 (2008).
    [CrossRef]
  23. W. H. Renninger, F. W. Wise, “Fundamental limits to mode-locked lasers: toward terawatt peak powers,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2014.2329936 (to be published).
    [CrossRef]
  24. E. M. Vogel, M. J. Weber, D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).
  25. J. A. Berger, M. J. Greco, W. A. Schroeder, Opt. Express 16, 8629 (2008).
    [CrossRef]

2010 (1)

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

2009 (1)

T. Ackemann, W. J. Firth, G. Oppo, Adv. At. Mol. Opt. Phys. 57, 323 (2009).
[CrossRef]

2008 (2)

W. H. Renninger, A. Chong, F. W. Wise, Phys. Rev. A 77, 23814 (2008).
[CrossRef]

J. A. Berger, M. J. Greco, W. A. Schroeder, Opt. Express 16, 8629 (2008).
[CrossRef]

2007 (1)

N. Akhmediev, J. M. Soto-Crespo, P. Grelu, Chaos 17, 037112 (2007).
[CrossRef]

2006 (2)

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Express 14, 4013 (2006).
[CrossRef]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, Phys. Rev. E 74, 46612 (2006).
[CrossRef]

2005 (3)

P. Grelu, J. M. Soto-Crespo, N. Akhmediev, Opt. Express 13, 9352 (2005).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005).
[CrossRef]

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
[CrossRef]

2004 (1)

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef]

2003 (1)

S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
[CrossRef]

2002 (1)

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

1999 (2)

A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
[CrossRef]

X. Liu, L. Qian, F. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

1995 (1)

R. McLeod, K. Wagner, S. Blair, Phys. Rev. A 52, 3254 (1995).
[CrossRef]

1993 (1)

1991 (1)

E. M. Vogel, M. J. Weber, D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

1990 (1)

1980 (2)

A. R. Osborne, T. L. Burch, Science 208, 451 (1980).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1965 (1)

N. Zabusky, M. Kruskal, Phys. Rev. Lett. 15, 240 (1965).
[CrossRef]

1964 (1)

R. Chiao, E. Garmire, C. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Ackemann, T.

T. Ackemann, W. J. Firth, G. Oppo, Adv. At. Mol. Opt. Phys. 57, 323 (2009).
[CrossRef]

Akhmediev, N.

N. Akhmediev, J. M. Soto-Crespo, P. Grelu, Chaos 17, 037112 (2007).
[CrossRef]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, Phys. Rev. E 74, 46612 (2006).
[CrossRef]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Express 14, 4013 (2006).
[CrossRef]

P. Grelu, J. M. Soto-Crespo, N. Akhmediev, Opt. Express 13, 9352 (2005).
[CrossRef]

Apolonski, A.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
[CrossRef]

Bartelt, H.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Berger, J. A.

Blair, S.

R. McLeod, K. Wagner, S. Blair, Phys. Rev. A 52, 3254 (1995).
[CrossRef]

Bourdel, T.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Brambilla, M.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef]

Burch, T. L.

A. R. Osborne, T. L. Burch, Science 208, 451 (1980).
[CrossRef]

Carr, L. D.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Castin, Y.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Chiao, R.

R. Chiao, E. Garmire, C. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Chong, A.

W. H. Renninger, A. Chong, F. W. Wise, Phys. Rev. A 77, 23814 (2008).
[CrossRef]

Columbo, L.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef]

Cubizolles, J.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Demidov, V. E.

S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
[CrossRef]

Demokritov, S. O.

S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
[CrossRef]

Dombi, P.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
[CrossRef]

Eilenberger, F.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Fedorov, S. V.

A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
[CrossRef]

Fernandez, A.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
[CrossRef]

Ferrari, G.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Firth, W. J.

T. Ackemann, W. J. Firth, G. Oppo, Adv. At. Mol. Opt. Phys. 57, 323 (2009).
[CrossRef]

Garmire, E.

R. Chiao, E. Garmire, C. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Graf, R.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
[CrossRef]

Greco, M. J.

Grelu, P.

N. Akhmediev, J. M. Soto-Crespo, P. Grelu, Chaos 17, 037112 (2007).
[CrossRef]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Express 14, 4013 (2006).
[CrossRef]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, Phys. Rev. E 74, 46612 (2006).
[CrossRef]

P. Grelu, J. M. Soto-Crespo, N. Akhmediev, Opt. Express 13, 9352 (2005).
[CrossRef]

Hillebrands, B.

S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
[CrossRef]

Kalinikos, B. A.

S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
[CrossRef]

Kaliteevskii, N. A.

A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
[CrossRef]

Kartashov, Y. V.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Khaykovich, L.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Khodova, G. V.

A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
[CrossRef]

Kobelke, J.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Kostylev, M. P.

S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
[CrossRef]

Krausz, F.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
[CrossRef]

Krol, D. M.

E. M. Vogel, M. J. Weber, D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

Kruskal, M.

N. Zabusky, M. Kruskal, Phys. Rev. Lett. 15, 240 (1965).
[CrossRef]

Lederer, F.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Liu, X.

X. Liu, L. Qian, F. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Maggipinto, T.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef]

Malomed, B. A.

B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005).
[CrossRef]

McLeod, R.

R. McLeod, K. Wagner, S. Blair, Phys. Rev. A 52, 3254 (1995).
[CrossRef]

Mihalache, D.

B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005).
[CrossRef]

Minardi, S.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Naumov, S.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, A. Apolonski, New J. Phys. 7, 216 (2005).
[CrossRef]

Nolte, S.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Oppo, G.

T. Ackemann, W. J. Firth, G. Oppo, Adv. At. Mol. Opt. Phys. 57, 323 (2009).
[CrossRef]

Osborne, A. R.

A. R. Osborne, T. L. Burch, Science 208, 451 (1980).
[CrossRef]

Patera, G.

M. Brambilla, T. Maggipinto, G. Patera, L. Columbo, Phys. Rev. Lett. 93, 203901 (2004).
[CrossRef]

Pertsch, T.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Proctor, B.

Qian, L.

X. Liu, L. Qian, F. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Renninger, W. H.

W. H. Renninger, A. Chong, F. W. Wise, Phys. Rev. A 77, 23814 (2008).
[CrossRef]

W. H. Renninger, F. W. Wise, “Fundamental limits to mode-locked lasers: toward terawatt peak powers,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2014.2329936 (to be published).
[CrossRef]

Röpke, U.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Rosanov, N. N.

A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
[CrossRef]

Russell, J. S.

J. S. Russell, Report of the Fourteenth Meeting of the British Association for the Advancement of Science (1844), pp. 311–390.

Salomon, C.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Schreck, F.

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002).
[CrossRef]

Schroeder, W. A.

Schuster, K.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Serga, A. A.

S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, B. A. Kalinikos, Nature 426, 159 (2003).
[CrossRef]

Silberberg, Y.

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, P. Grelu, Chaos 17, 037112 (2007).
[CrossRef]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Express 14, 4013 (2006).
[CrossRef]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, Phys. Rev. E 74, 46612 (2006).
[CrossRef]

P. Grelu, J. M. Soto-Crespo, N. Akhmediev, Opt. Express 13, 9352 (2005).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Szameit, A.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Torner, L.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005).
[CrossRef]

Townes, C.

R. Chiao, E. Garmire, C. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Tünnermann, A.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Vladimirov, A. G.

A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
[CrossRef]

Vogel, E. M.

E. M. Vogel, M. J. Weber, D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

Wagner, K.

R. McLeod, K. Wagner, S. Blair, Phys. Rev. A 52, 3254 (1995).
[CrossRef]

Weber, M. J.

E. M. Vogel, M. J. Weber, D. M. Krol, Phys. Chem. Glasses 32, 231 (1991).

Westwig, E.

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005).
[CrossRef]

X. Liu, L. Qian, F. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

B. Proctor, E. Westwig, F. Wise, Opt. Lett. 18, 1654 (1993).
[CrossRef]

Wise, F. W.

W. H. Renninger, A. Chong, F. W. Wise, Phys. Rev. A 77, 23814 (2008).
[CrossRef]

W. H. Renninger, F. W. Wise, “Fundamental limits to mode-locked lasers: toward terawatt peak powers,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2014.2329936 (to be published).
[CrossRef]

Zabusky, N.

N. Zabusky, M. Kruskal, Phys. Rev. Lett. 15, 240 (1965).
[CrossRef]

Adv. At. Mol. Opt. Phys. (1)

T. Ackemann, W. J. Firth, G. Oppo, Adv. At. Mol. Opt. Phys. 57, 323 (2009).
[CrossRef]

Chaos (1)

N. Akhmediev, J. M. Soto-Crespo, P. Grelu, Chaos 17, 037112 (2007).
[CrossRef]

J. Opt. B (2)

B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005).
[CrossRef]

A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, N. N. Rosanov, J. Opt. B 1, 101 (1999).
[CrossRef]

Nature (1)

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Supplementary Material (1)

» Media 1: AVI (10339 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Illustration of an STS laser.

Fig. 2.
Fig. 2.

Typical 2D simulation result: (a) energy convergence, (b) spatiotemporal color map of the pulse, (c) spectrum at the center of the beam, (d) temporal profile along with sech2 fit (dashed line), (e) spatial-frequency spectrum at the center of the pulse, and (f) spatial profile along with sech2 fit (dashed line). Parameters: the nonlinear material is 40 cm of SF11 glass (n=1.76, β2=1520fs2/cm [Schott glass], and n2=41×108μm2/W [24]). The gain bandwidth is 40 nm, Esat=600nJ, wp=308μm (assuming 400 μm multimode pump fiber), there is 10 cm of air, the filter bandwidth is 12 nm, 2% power is coupled out, lo=0.03, and Psat=51kW/μm (saturable absorber and output coupling parameters from Ref. [25]).

Fig. 3.
Fig. 3.

Evolution of the pulse energy as a function of round trip around the oscillator and spatiotemporal profiles of the output at the indicated numbers of round trips.

Fig. 4.
Fig. 4.

Evolution of the energy as a function of round trip for the spatiotemporal limit cycle, with representative spatiotemporal profiles of the output field at the half-periods of the oscillation (Media 1).

Fig. 5.
Fig. 5.

Results of 3D simulations. (a) Evolution of the energy as a function of round trip, (b) spatiotemporal profile at x=0 or y=0, (c) beam at the center of the pulse, and (d) isointensity surface of the bullet at 5% of the peak intensity.

Equations (2)

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Aout(x,y,ω)Ain(x,y,ω)=exp(g01+EEsat2x4+y4wp4ω2Δω2),
Az=i2k0(2Ax2+2Ay2)iβ222At2+iγ|A|2A,

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