Abstract

We present a physical mechanism that explains the recent observations of incoherent writing and erasure of Cavity Solitons in a semiconductor optical amplifier [S. Barbay et al, Opt. Lett. 31, 1504–1506 (2006)]. This mechanism allows to understand the main observations of the experiment. In particular it perfectly explains why writing and erasure are possible as a result of a local perturbation in the carrier density, and why a delay is observed along with the writing process. Numerical simulations in 1D are performed and show very good qualitative agreement with the experimental observations.

© 2007 Optical Society of America

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  1. S. Barbay, Y. Ménesguen, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, "Incoherent and coherent writing and erasure of cavity solitons in an optically pumped semiconductor amplifier," Opt. Lett. 31, 1504-1506 (2006).
    [CrossRef] [PubMed]
  2. S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödel, M. Miller, and R. Jäger, "Cavity solitons work as pixels in semiconductors," Nature 419, 699-702 (2002).
    [CrossRef] [PubMed]
  3. X. Hachair, S. Barland, L. Furfaro, M. Giudici, S. Balle, J. R. Tredicce, M. Brambilla, T. Maggipinto, I. M. Perrini, G. Tissoni, and L. Lugiato, "Cavity solitons in broad-area vertical-cavity surface-emitting lasers below threshold," Phys. Rev. A 69, 043817 (2004).
  4. Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, "Optical self-organization and cavity solitons in optically pumped semiconductor microresonators," Phys. Rev. A 74, 023818 (2006).
    [CrossRef]
  5. Y. Tanguy, T. Ackemann, and R. Jager, "Characteristics of bistable localized emission states in broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 74, 053824 (2006).
    [CrossRef]
  6. I. Ganne and G. Slekys and I. Sagnes and R. Kuszelewicz, "Precursor forms of cavity solitons in nonlinear semiconductor microresonators," Phys. Rev. E 66, 066613 (2002).
    [CrossRef]
  7. F. Pedaci, P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, "Positioning cavity solitons with a phase mask," Appl. Phys. Lett. 89, 221111 (2006).
    [CrossRef]
  8. 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]
  9. M. Brambilla, L.A. Lugiato, F. Prati, L. Spinelli, andW. Firth, "Spatial Soliton Pixels in Semiconductor Devices," Phys. Rev. Lett. 79, 2042-2045 (1997).
    [CrossRef]
  10. W. J. Firth and A. J. Scroggie, "Optical Bullet Holes: Robust Controllable Localized States of a Nonlinear Cavity," Phys. Rev. Lett. 76, 1623-1626 (1996).
    [CrossRef] [PubMed]
  11. G. Tissoni and L. Spinelli and L. A. Lugiato and M. Brambilla and I. M. Perrini and T. Maggipinto, "Spatiotemporal dynamics in semiconductor microresonators with thermal effects," Opt. Express 10, 1009-1017 (2002).
    [PubMed]
  12. L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, "Thermal effects and transverse structures in semiconductor microcavities with population inversion," Phys. Rev. A 66, 023817 (2002).
    [CrossRef]
  13. A. J. Scroggie, J. M. McSloy, and W. J. Firth, "Self-propelled cavity solitons in semiconductor microcavities," Phys. Rev. E 66, 036607 (2002).
    [CrossRef]
  14. Y. Ménesguen and R. Kuszelewicz, unpublished.
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    [CrossRef] [PubMed]
  16. B. Segard, J. Zemmouri, and B. Macke, "Noncritical slowing down in optical bistability," Opt. Commun. 63, 339-343 (1987).
    [CrossRef]
  17. F. Mitschke, C. Boden, W. Lange, and P. Mandel, "Exploring the dynamics of the unstable branch of bistable systems," Opt. Commun. 71, 385-392 (1989).
    [CrossRef]
  18. D.N. Maywar, G.P. Agrawal, and Y. Nakano, "All-optical hysteresis control by means of cross-phase modulation in semiconductor optical amplifiers," J. Opt. Soc. Am. B 18, 1003-1013 (2001).
    [CrossRef]

2006 (4)

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, "Optical self-organization and cavity solitons in optically pumped semiconductor microresonators," Phys. Rev. A 74, 023818 (2006).
[CrossRef]

Y. Tanguy, T. Ackemann, and R. Jager, "Characteristics of bistable localized emission states in broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 74, 053824 (2006).
[CrossRef]

F. Pedaci, P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, "Positioning cavity solitons with a phase mask," Appl. Phys. Lett. 89, 221111 (2006).
[CrossRef]

S. Barbay, Y. Ménesguen, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, "Incoherent and coherent writing and erasure of cavity solitons in an optically pumped semiconductor amplifier," Opt. Lett. 31, 1504-1506 (2006).
[CrossRef] [PubMed]

2005 (1)

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]

2004 (1)

X. Hachair, S. Barland, L. Furfaro, M. Giudici, S. Balle, J. R. Tredicce, M. Brambilla, T. Maggipinto, I. M. Perrini, G. Tissoni, and L. Lugiato, "Cavity solitons in broad-area vertical-cavity surface-emitting lasers below threshold," Phys. Rev. A 69, 043817 (2004).

2002 (5)

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödel, M. Miller, and R. Jäger, "Cavity solitons work as pixels in semiconductors," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

I. Ganne and G. Slekys and I. Sagnes and R. Kuszelewicz, "Precursor forms of cavity solitons in nonlinear semiconductor microresonators," Phys. Rev. E 66, 066613 (2002).
[CrossRef]

G. Tissoni and L. Spinelli and L. A. Lugiato and M. Brambilla and I. M. Perrini and T. Maggipinto, "Spatiotemporal dynamics in semiconductor microresonators with thermal effects," Opt. Express 10, 1009-1017 (2002).
[PubMed]

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, "Thermal effects and transverse structures in semiconductor microcavities with population inversion," Phys. Rev. A 66, 023817 (2002).
[CrossRef]

A. J. Scroggie, J. M. McSloy, and W. J. Firth, "Self-propelled cavity solitons in semiconductor microcavities," Phys. Rev. E 66, 036607 (2002).
[CrossRef]

2001 (1)

1997 (1)

M. Brambilla, L.A. Lugiato, F. Prati, L. Spinelli, andW. Firth, "Spatial Soliton Pixels in Semiconductor Devices," Phys. Rev. Lett. 79, 2042-2045 (1997).
[CrossRef]

1996 (1)

W. J. Firth and A. J. Scroggie, "Optical Bullet Holes: Robust Controllable Localized States of a Nonlinear Cavity," Phys. Rev. Lett. 76, 1623-1626 (1996).
[CrossRef] [PubMed]

1992 (1)

R. L. Honeycutt, "Stochastic Runge-Kutta algorithms. I. White noise," Phys. Rev. A 45, 600-603 (1992).
[CrossRef] [PubMed]

1989 (1)

F. Mitschke, C. Boden, W. Lange, and P. Mandel, "Exploring the dynamics of the unstable branch of bistable systems," Opt. Commun. 71, 385-392 (1989).
[CrossRef]

1987 (1)

B. Segard, J. Zemmouri, and B. Macke, "Noncritical slowing down in optical bistability," Opt. Commun. 63, 339-343 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

F. Pedaci, P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, "Positioning cavity solitons with a phase mask," Appl. Phys. Lett. 89, 221111 (2006).
[CrossRef]

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

Nature (1)

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödel, M. Miller, and R. Jäger, "Cavity solitons work as pixels in semiconductors," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Opt. Commun. (2)

B. Segard, J. Zemmouri, and B. Macke, "Noncritical slowing down in optical bistability," Opt. Commun. 63, 339-343 (1987).
[CrossRef]

F. Mitschke, C. Boden, W. Lange, and P. Mandel, "Exploring the dynamics of the unstable branch of bistable systems," Opt. Commun. 71, 385-392 (1989).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (6)

R. L. Honeycutt, "Stochastic Runge-Kutta algorithms. I. White noise," Phys. Rev. A 45, 600-603 (1992).
[CrossRef] [PubMed]

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, "Thermal effects and transverse structures in semiconductor microcavities with population inversion," Phys. Rev. A 66, 023817 (2002).
[CrossRef]

X. Hachair, S. Barland, L. Furfaro, M. Giudici, S. Balle, J. R. Tredicce, M. Brambilla, T. Maggipinto, I. M. Perrini, G. Tissoni, and L. Lugiato, "Cavity solitons in broad-area vertical-cavity surface-emitting lasers below threshold," Phys. Rev. A 69, 043817 (2004).

Y. Menesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, "Optical self-organization and cavity solitons in optically pumped semiconductor microresonators," Phys. Rev. A 74, 023818 (2006).
[CrossRef]

Y. Tanguy, T. Ackemann, and R. Jager, "Characteristics of bistable localized emission states in broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 74, 053824 (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)

I. Ganne and G. Slekys and I. Sagnes and R. Kuszelewicz, "Precursor forms of cavity solitons in nonlinear semiconductor microresonators," Phys. Rev. E 66, 066613 (2002).
[CrossRef]

A. J. Scroggie, J. M. McSloy, and W. J. Firth, "Self-propelled cavity solitons in semiconductor microcavities," Phys. Rev. E 66, 036607 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

M. Brambilla, L.A. Lugiato, F. Prati, L. Spinelli, andW. Firth, "Spatial Soliton Pixels in Semiconductor Devices," Phys. Rev. Lett. 79, 2042-2045 (1997).
[CrossRef]

W. J. Firth and A. J. Scroggie, "Optical Bullet Holes: Robust Controllable Localized States of a Nonlinear Cavity," Phys. Rev. Lett. 76, 1623-1626 (1996).
[CrossRef] [PubMed]

Other (1)

Y. Ménesguen and R. Kuszelewicz, unpublished.

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Figures (5)

Fig. 1.
Fig. 1.

Plane-wave, bistability curves (Eqs.1 without spatial terms and without the equation for θ) with the parameters α=5,C=0.2, θ=-2 and Λ=3.2 except blue curve (Λ=3.3) and red curve (θ=-2.2). The portions of the curves with negative slopes are unstable.

Fig. 2.
Fig. 2.

Time traces of the intensity at a CS peak |E|2 vs time (blue line) and local injection of carrier (Λ, red line). Upper figure : experimental results obtained in [1]. Lower figure : incoherent switch-on and off of a CS, with respectively EI =0.76, δΛ=3.6, δx=20 and EI =0.75, δΛ=1.37 and δx=20 (in inset is a zoom of the initial part of the switch-off process).

Fig. 3.
Fig. 3.

Adiabatic response |E|2when ramping the pump Λ: 1D numerical simulation (full line, the maximum of the field is plotted) and plane wave hysteresis (dashed line). The injected field amplitude is EI =0.76. The arrows indicate the sense followed by the system on the hysteresis cycle.

Fig. 4.
Fig. 4.

Scaling of the switch-on delay versus writing power for a fixed duration of the writing pulse τ=20. The critical writing power is δΛ c ≃3.50.

Fig. 5.
Fig. 5.

Switch-off dynamics with succeeded (blue) and failed (red) switch-offs. From bottom to top, the erasing powers are δΛ c =1.10,1.03,1.0225,1.022,1.02. The erasing pulse in launched at t=100 and has a duration δτ=20.

Equations (3)

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E t = ( 1 + i θ ) E + E I 2 i C ( α + i ) ( N 1 ) E + 2 E x 2 + ξ
N t = γ [ N Λ + ( N 1 ) E 2 D 2 N x 2 ]
θ t = γ T [ ( θ θ 0 ) + f ( Λ ) D T 2 θ x 2 ]

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