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]
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    [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 selftrapping soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [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]
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    [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

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

2006

S. Barbay, Y. M’enesguen, 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

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

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

D. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003)
[CrossRef] [PubMed]

2002

2001

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

1999

J. Marangos, "Slow Light in Cool Atoms," Nature 397, 559-560 (1999).
[CrossRef]

1998

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

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

1994

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

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete selftrapping 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. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "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.

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 Digest JTuB14 (2009)

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete selftrapping 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 Digest JTuB14 (2009)

Firth, W. J.

Y. Tanguy, T. Ackemann,W. J. Firth, and R. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Hachair, X.

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.

J¨ager, R.

Y. Tanguy, T. Ackemann,W. J. Firth, and R. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "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]

Kn¨odl, T.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Kn¨odl, M. Miller and R. J¨ager, "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]

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 Digest JTuB14 (2009)

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 selftrapping 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]

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. Kn¨odl, M. Miller and R. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "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]

Miller, M.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Kn¨odl, M. Miller and R. J¨ager, "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 Digest JTuB14 (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 selftrapping 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 selftrapping 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]

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).
[CrossRef]

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

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)
[CrossRef] [PubMed]

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).
[CrossRef]

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]

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 Digest JTuB14 (2009)

Spinelli, L.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Kn¨odl, M. Miller and R. J¨ager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

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. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "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. Kn¨odl, M. Miller and R. J¨ager, "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 selftrapping 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 selftrapping 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 Digest JTuB14 (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]

App. Phys. Lett.

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

Appl. Phys. B

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.

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]

IEEE Journal of

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]

J. Opt. B: Quantum Semiclass.

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

Nature

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. Kn¨odl, M. Miller and R. J¨ager, "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

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.

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

Opt. Lett.

Optics Letters

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

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

Phys. Rev. A

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

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete selftrapping 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.

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. J¨ager, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

Other

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 Digest JTuB14 (2009)

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

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

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).

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)

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

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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