Abstract

A theoretical proposal is presented for the generation of mode-locked light-bullets in planar waveguide arrays, extending the concept of time-domain mode-locking in waveguide arrays to spatial (transverse) mode-locking in slab waveguides. The model presented yields three-dimensional localized states that act as global attractors to the waveguide array system. Single pulse stationary and time-periodic solutions as well as the transition to multi-pulse solutions as a function of gain are observed to be stabilized in such a system.

© 2009 Optical Society of America

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    [Crossref] [PubMed]
  2. D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003)
    [Crossref] [PubMed]
  3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
    [Crossref]
  4. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  8. S. Droulias, K. Hizanidis, D. N. Christodoulides, and R. Morandotti, “Waveguide array-grating compressors,” App. Phys. Lett. 87, 131104 (2005).
    [Crossref]
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    [Crossref]
  12. J. N. Kutz and B. Sandstede, “Theory of passive harmonic mode-locking using waveguide arrays,” Opt. Express 16, 636–650 (2008).
    [Crossref] [PubMed]
  13. B. G. Bale, J. N. Kutz, and B. Sandstede, “Optimizing waveguide array mode-locking for high-power fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 15220–231 (2009).
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    [Crossref] [PubMed]
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    [Crossref]
  20. U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Reports 429, 67–120 (2006).
    [Crossref]
  21. J. Marangos, “Slow Light in Cool Atoms,” Nature 397, 559–560 (1999).
    [Crossref]
  22. J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nature Physics 2, 775–780 (2006).
    [Crossref]
  23. P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).
    [Crossref]
  24. A. Yariv, Quantum Electronics (John Wiley and Sons, 1988).
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    [Crossref]
  26. P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
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  29. A. Barsella, C. Lepers, M. Taki, and M. Tlidi, “Moving localized structures in quadratic media with saturable absorber,” Opt. Comm. 232, 381–389 (2004).
    [Crossref]
  30. M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
    [Crossref]

2009 (1)

B. G. Bale, J. N. Kutz, and B. Sandstede, “Optimizing waveguide array mode-locking for high-power fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 15220–231 (2009).
[Crossref]

2008 (3)

2006 (4)

S. Barbay, Y. Ménesguen, X. Hachair, L. Lery, I. Sagnes, and R. Kuszelewics, “Incoherent and coherent writing and erasure of cavity solitons in an optically pumped semiconductor amplifier,” Opt. Lett. 31, 1504–1506 (2006).
[Crossref] [PubMed]

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Reports 429, 67–120 (2006).
[Crossref]

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nature Physics 2, 775–780 (2006).
[Crossref]

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

2005 (4)

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).
[Crossref]

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

S. Droulias, K. Hizanidis, D. N. Christodoulides, and R. Morandotti, “Waveguide array-grating compressors,” App. Phys. Lett. 87, 131104 (2005).
[Crossref]

J. Proctor and J. N. Kutz, “Theory and Simulation of Passive Mode-locking with Waveguide Arrays,” Optics Letters 13, 2013–2015 (2005).
[Crossref]

2004 (2)

A. Barsella, C. Lepers, M. Taki, and M. Tlidi, “Moving localized structures in quadratic media with saturable absorber,” Opt. Comm. 232, 381–389 (2004).
[Crossref]

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

2003 (1)

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003)
[Crossref] [PubMed]

2002 (3)

2001 (1)

V. B. Taranenko and C. O. Weiss, “Incoherent optical switching of semiconductor resonator solitons,” Appl. Phys. B 72, 893–895 (2001).

1999 (1)

J. Marangos, “Slow Light in Cool Atoms,” Nature 397, 559–560 (1999).
[Crossref]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[Crossref]

1996 (1)

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

1994 (1)

L. Rahman and H. Winful, “Nonlinear dynamics of semiconductor laser arrays: a mean field model,” Quantum Electronics, IEEE Journal of 30, 1405–1416 (1994).
[Crossref]

1988 (1)

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Ackemann, T.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, “Realization of a Semiconductor-Based Cavity Soliton Laser,” Phys. Rev. Lett. 100, 013907 (2008).
[Crossref] [PubMed]

Aitchison, J. S.

Arnold, J. M.

Bale, B. G.

B. G. Bale, J. N. Kutz, and B. Sandstede, “Optimizing waveguide array mode-locking for high-power fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 15220–231 (2009).
[Crossref]

Balle, S.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Barbay, S.

Barland, S.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Barsella, A.

A. Barsella, C. Lepers, M. Taki, and M. Tlidi, “Moving localized structures in quadratic media with saturable absorber,” Opt. Comm. 232, 381–389 (2004).
[Crossref]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[Crossref]

Brambilla, M.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Chen, P. Y. P.

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).
[Crossref]

Christodoulides, D.

D. Hudson, K. Shish, T. Schibli, J. N. Kutz, D. Christodoulides, R. Morandotti, and S. Cundiff ) “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33, 1440–1442 (2008)
[Crossref] [PubMed]

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003)
[Crossref] [PubMed]

Christodoulides, D. N.

S. Droulias, K. Hizanidis, D. N. Christodoulides, and R. Morandotti, “Waveguide array-grating compressors,” App. Phys. Lett. 87, 131104 (2005).
[Crossref]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
[Crossref] [PubMed]

Chu, P. L.

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).
[Crossref]

Cundiff, S.

D. Hudson, K. Shish, T. Schibli, J. N. Kutz, D. Christodoulides, R. Morandotti, and S. Cundiff ) “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33, 1440–1442 (2008)
[Crossref] [PubMed]

M. O. Williams, M. Feng, J. N. Kutz, K. Silverman, R. Mirin, and S. Cundiff, “Intensity Dynamics in Semiconductor Laser Arrays,” OSA Nonlinear Optics 2009 Technical DigestJTuB14 (2009)

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

de Sterke, C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nature Physics 2, 775–780 (2006).
[Crossref]

Di Menza, L.

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

Droulias, S.

S. Droulias, K. Hizanidis, D. N. Christodoulides, and R. Morandotti, “Waveguide array-grating compressors,” App. Phys. Lett. 87, 131104 (2005).
[Crossref]

Eggleton, B. J.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nature Physics 2, 775–780 (2006).
[Crossref]

Eisenberg, H. S.

Feng, M.

M. O. Williams, M. Feng, J. N. Kutz, K. Silverman, R. Mirin, and S. Cundiff, “Intensity Dynamics in Semiconductor Laser Arrays,” OSA Nonlinear Optics 2009 Technical DigestJTuB14 (2009)

Firth, W. J.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, “Realization of a Semiconductor-Based Cavity Soliton Laser,” Phys. Rev. Lett. 100, 013907 (2008).
[Crossref] [PubMed]

Furfaro, L.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

Giudici, M.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Hachair, X.

S. Barbay, Y. Ménesguen, X. Hachair, L. Lery, I. Sagnes, and R. Kuszelewics, “Incoherent and coherent writing and erasure of cavity solitons in an optically pumped semiconductor amplifier,” Opt. Lett. 31, 1504–1506 (2006).
[Crossref] [PubMed]

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

Hizanidis, K.

S. Droulias, K. Hizanidis, D. N. Christodoulides, and R. Morandotti, “Waveguide array-grating compressors,” App. Phys. Lett. 87, 131104 (2005).
[Crossref]

Hudson, D.

Jäger, R.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, “Realization of a Semiconductor-Based Cavity Soliton Laser,” Phys. Rev. Lett. 100, 013907 (2008).
[Crossref] [PubMed]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Javaloyes, J.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

Joseph, R. I.

Keller, U.

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Reports 429, 67–120 (2006).
[Crossref]

Knödl, T.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Kockaert, P.

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

Kuszelewics, R.

Kutz, J. N.

B. G. Bale, J. N. Kutz, and B. Sandstede, “Optimizing waveguide array mode-locking for high-power fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 15220–231 (2009).
[Crossref]

J. N. Kutz and B. Sandstede, “Theory of passive harmonic mode-locking using waveguide arrays,” Opt. Express 16, 636–650 (2008).
[Crossref] [PubMed]

D. Hudson, K. Shish, T. Schibli, J. N. Kutz, D. Christodoulides, R. Morandotti, and S. Cundiff ) “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33, 1440–1442 (2008)
[Crossref] [PubMed]

J. Proctor and J. N. Kutz, “Theory and Simulation of Passive Mode-locking with Waveguide Arrays,” Optics Letters 13, 2013–2015 (2005).
[Crossref]

M. O. Williams, M. Feng, J. N. Kutz, K. Silverman, R. Mirin, and S. Cundiff, “Intensity Dynamics in Semiconductor Laser Arrays,” OSA Nonlinear Optics 2009 Technical DigestJTuB14 (2009)

J. N. Kutz, Mode-Locking of Fiber Lasers via Nonlinear Mode-Coupling, vol. 661 of Lecture Notes in Physics (Springer Berlin/Heidelberg, 2005).

Le Berre, M.

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

Lederer, F.

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003)
[Crossref] [PubMed]

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, “Optical discrete solitons in waveguide arrays. 2. Dynamics properties,” J. Opt. Soc. Am. B 19, 2637–2644 (2002).
[Crossref]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Lepers, C.

A. Barsella, C. Lepers, M. Taki, and M. Tlidi, “Moving localized structures in quadratic media with saturable absorber,” Opt. Comm. 232, 381–389 (2004).
[Crossref]

Lery, L.

Liter, I. C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nature Physics 2, 775–780 (2006).
[Crossref]

Lugiato, L.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Maggipinto, T.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Malomed, B. A.

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).
[Crossref]

Marangos, J.

J. Marangos, “Slow Light in Cool Atoms,” Nature 397, 559–560 (1999).
[Crossref]

Ménesguen, Y.

Miller, M.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Mirin, R.

M. O. Williams, M. Feng, J. N. Kutz, K. Silverman, R. Mirin, and S. Cundiff, “Intensity Dynamics in Semiconductor Laser Arrays,” OSA Nonlinear Optics 2009 Technical DigestJTuB14 (2009)

Mok, J. T.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nature Physics 2, 775–780 (2006).
[Crossref]

Morandotti, R.

Muschall, R.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Pennelli, G.

Pertsch, T.

Peschel, T.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Peschel, U.

Proctor, J.

J. Proctor and J. N. Kutz, “Theory and Simulation of Passive Mode-locking with Waveguide Arrays,” Optics Letters 13, 2013–2015 (2005).
[Crossref]

Rahman, L.

L. Rahman and H. Winful, “Nonlinear dynamics of semiconductor laser arrays: a mean field model,” Quantum Electronics, IEEE Journal of 30, 1405–1416 (1994).
[Crossref]

Reyssayre, E.

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

Sagnes, I.

Sandstede, B.

B. G. Bale, J. N. Kutz, and B. Sandstede, “Optimizing waveguide array mode-locking for high-power fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 15220–231 (2009).
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J. N. Kutz and B. Sandstede, “Theory of passive harmonic mode-locking using waveguide arrays,” Opt. Express 16, 636–650 (2008).
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Schibli, T.

Shish, K.

Silberberg, Y.

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003)
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H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, “Optical discrete solitons in waveguide arrays. 1. Soliton formation,” J. Opt. Soc. Am. B 19, 2938–1944 (2002).
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U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, “Optical discrete solitons in waveguide arrays. 2. Dynamics properties,” J. Opt. Soc. Am. B 19, 2637–2644 (2002).
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H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[Crossref]

Silverman, K.

M. O. Williams, M. Feng, J. N. Kutz, K. Silverman, R. Mirin, and S. Cundiff, “Intensity Dynamics in Semiconductor Laser Arrays,” OSA Nonlinear Optics 2009 Technical DigestJTuB14 (2009)

Spinelli, L.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Sulem, C.

C. Sulem and P-L. Sulem, The nonlinear Schroedinger equation: self-focusing and wave collapse (Springer, 1999).

Sulem, P-L.

C. Sulem and P-L. Sulem, The nonlinear Schroedinger equation: self-focusing and wave collapse (Springer, 1999).

Taki, M.

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

A. Barsella, C. Lepers, M. Taki, and M. Tlidi, “Moving localized structures in quadratic media with saturable absorber,” Opt. Comm. 232, 381–389 (2004).
[Crossref]

Tallet, A.

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

Tanguy, Y.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, “Realization of a Semiconductor-Based Cavity Soliton Laser,” Phys. Rev. Lett. 100, 013907 (2008).
[Crossref] [PubMed]

Taranenko, V. B.

V. B. Taranenko and C. O. Weiss, “Incoherent optical switching of semiconductor resonator solitons,” Appl. Phys. B 72, 893–895 (2001).

Tassin, P.

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

Tissoni, G.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Tlidi, M.

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

A. Barsella, C. Lepers, M. Taki, and M. Tlidi, “Moving localized structures in quadratic media with saturable absorber,” Opt. Comm. 232, 381–389 (2004).
[Crossref]

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

Tredicce, J.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Trillo, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Tropper, A. C.

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Reports 429, 67–120 (2006).
[Crossref]

van der Sande, G.

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

Veretennicoff, I.

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

Wabnitz, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Weiss, C. O.

V. B. Taranenko and C. O. Weiss, “Incoherent optical switching of semiconductor resonator solitons,” Appl. Phys. B 72, 893–895 (2001).

Williams, M. O.

M. O. Williams, M. Feng, J. N. Kutz, K. Silverman, R. Mirin, and S. Cundiff, “Intensity Dynamics in Semiconductor Laser Arrays,” OSA Nonlinear Optics 2009 Technical DigestJTuB14 (2009)

Winful, H.

L. Rahman and H. Winful, “Nonlinear dynamics of semiconductor laser arrays: a mean field model,” Quantum Electronics, IEEE Journal of 30, 1405–1416 (1994).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (John Wiley and Sons, 1988).

App. Phys. Lett. (1)

S. Droulias, K. Hizanidis, D. N. Christodoulides, and R. Morandotti, “Waveguide array-grating compressors,” App. Phys. Lett. 87, 131104 (2005).
[Crossref]

Appl. Phys. B (1)

V. B. Taranenko and C. O. Weiss, “Incoherent optical switching of semiconductor resonator solitons,” Appl. Phys. B 72, 893–895 (2001).

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

B. G. Bale, J. N. Kutz, and B. Sandstede, “Optimizing waveguide array mode-locking for high-power fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 15220–231 (2009).
[Crossref]

J. Opt. B: Quantum Semiclass. (1)

M. Tlidi, M. Taki, M. Le Berre, E. Reyssayre, A. Tallet, and L. Di Menza, “Moving localized structures and spatial patterns in quadratic media with a saturable absorber,” J. Opt. B: Quantum Semiclass. 6, S421–S429 (2004).
[Crossref]

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

Nature (3)

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003)
[Crossref] [PubMed]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

J. Marangos, “Slow Light in Cool Atoms,” Nature 397, 559–560 (1999).
[Crossref]

Nature Physics (1)

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nature Physics 2, 775–780 (2006).
[Crossref]

Opt. Comm. (1)

A. Barsella, C. Lepers, M. Taki, and M. Tlidi, “Moving localized structures in quadratic media with saturable absorber,” Opt. Comm. 232, 381–389 (2004).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Optics Letters (1)

J. Proctor and J. N. Kutz, “Theory and Simulation of Passive Mode-locking with Waveguide Arrays,” Optics Letters 13, 2013–2015 (2005).
[Crossref]

Phys. Reports (1)

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Reports 429, 67–120 (2006).
[Crossref]

Phys. Rev. A (2)

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[Crossref]

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, and J. Tredicce, “Cavity-solitons switching in semiconductor microcavities,” Phys. Rev. A 72, 013815 (2005).
[Crossref]

Phys. Rev. E (2)

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).
[Crossref]

Phys. Rev. Lett. (2)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[Crossref]

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, “Realization of a Semiconductor-Based Cavity Soliton Laser,” Phys. Rev. Lett. 100, 013907 (2008).
[Crossref] [PubMed]

Quantum Electronics, IEEE Journal of (1)

L. Rahman and H. Winful, “Nonlinear dynamics of semiconductor laser arrays: a mean field model,” Quantum Electronics, IEEE Journal of 30, 1405–1416 (1994).
[Crossref]

Other (6)

C. Sulem and P-L. Sulem, The nonlinear Schroedinger equation: self-focusing and wave collapse (Springer, 1999).

N. N. Akhmediev and A. Ankiewicz, Eds. Dissipative Solitons, Lecture Notes in Physics, (Springer-Verlag, 2005).

A. Yariv, Quantum Electronics (John Wiley and Sons, 1988).

See the Fundamentals, Functionalities, and Applications of Cavity Solitons (FunFACS) webpage for a complete overview of current and potential methods and realizations of generating localized optical structures: www.funfacs.org.

M. O. Williams, M. Feng, J. N. Kutz, K. Silverman, R. Mirin, and S. Cundiff, “Intensity Dynamics in Semiconductor Laser Arrays,” OSA Nonlinear Optics 2009 Technical DigestJTuB14 (2009)

J. N. Kutz, Mode-Locking of Fiber Lasers via Nonlinear Mode-Coupling, vol. 661 of Lecture Notes in Physics (Springer Berlin/Heidelberg, 2005).

Supplementary Material (2)

» Media 1: MOV (1394 KB)     
» Media 2: MOV (343 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

A schematic of the two-dimensional waveguide array. The waveguides, shown in red, are separated by low-index insulating regions. The proposed structure of the waveguides are a Bragg grating structure, shown to the left. Gain is applied to waveguide 0 by means of an injection current created by biasing the conducting contact (See Ref. [9] for recent experiments). Additionally, attenuation is applied only to waveguide 2. The proto-typical vertical distribution of the intensity is shown on the right. The Bragg grating structure confines the fields to the waveguides with weak evanescent coupling allowing energy transfer.

Fig. 2.
Fig. 2.

Radial optical field amplitudes for the negative diffraction regime in the 0th, 1st, and 2nd waveguides respectively. Consistent with the assumptions of the model, the fields in waveguides 1 and 2 have inherited their shape from waveguide 0. Note that the radial solution forms from a white-noise initial condition in waveguide 0.

Fig. 3.
Fig. 3.

Optical field amplitudes in the positive diffraction regime in the 0th, 1st, and 2nd waveguides respectively. Compared to the results in Fig. 2, this pulse is obtained for far lower values of gain. In this case, this initial condition is a hyperbolic secant pulse in each of the waveguides.

Fig. 4.
Fig. 4.

The energy and derivative fluctuations for the negative diffraction (left) and positive diffraction (right) regimes. After an initial transient of tens of time units, the norms settle to a steady state indicating a stationary pulse. The solid lines are the energy and the dotted lines are the derivative fluctuations. The blue lines correspond to waveguide 0 data, the red lines to waveguide 1 data, and the black lines correspond to waveguide 2 data.

Fig. 5.
Fig. 5.

Formation of a radially symmetric mode-locked solution in the negative diffraction regime starting from seeded white-noise. The intermediate image shows the presence of both noise and a hyperbolic-secant like pulse. The intensity discrimination and saturating gain eliminate the background noise. This full simulation is the proto-typical mode-locking behavior expected in the slab waveguide array structure. (Media 1)

Fig. 6.
Fig. 6.

A time-periodic breathing solution (left panel), along with the energy fluctuations of the radially symmetric simulations (center panel), and energy fluctuations of the full governing equation simulations (right panel). The mean value of the energy fluctuations in both radial and cartesian cases are similar in magnitude, and both settle into periodic orbits.

Fig. 7.
Fig. 7.

Dynamics of pulse splitting for the negative-diffraction regime with g 0=100. The value of gain is too large to support either single-pulse stationary or time periodic solutions. The single pulse is unable to divide into two as shown the top row of images. Instead, an external seed, due to noise or other physical effects, is required to generate the second pulse. The two-pulse scenario is the long-time steady state solution of the system after the initial transients decay as observed. (Media 2)

Equations (7)

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i A0t + D2 2 A0 + β A02 A0 + CA1 + i γ0 A0 ig (t)(1+τ2)A0+A04A0=0
i A1t + C (A0+A2)+iγ1A1=0
i A2t + C A1+iγ2A2=0
g (t)=2g01+A02e0.
(D,C,γ0,γ1,γ2,e0,τ,p,g0)=(1,10,0,0,10,1,0.1,1,35).
(D,C,γ0,γ1,γ2,e0,τ,p,g0)=(1,5,1,1,10,1,0.08,0.5,4.88).
(D,C,γ0,γ1,γ2,e0,τ,p,g0)=(1,10,0,0,10,1,0.1,1,50),

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