Abstract

In this paper we study the dynamics of the intracavity field, carriers and lattice temperature in externally driven semiconductor microcavities. The combination/competition of the different time-scales of the dynamical variables together with diffraction and carrier/thermal diffusions are responsible for new dynamical behaviors. We report here the occurrence of a spatio-temporal instability of the Hopf type giving rise to Regenerative Oscillations and travelling patterns and cavity solitons.

© 2002 Optical Society of America

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References

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  1. L. A. Lugiato, M. Brambilla and A. Gatti, �??Optical Pattern Formation,�?? in Advances in Atomic, Molecular and Optical Physics, Vol. 40, edited by B. Bederson and H. Walther, Academic Press, 1998, pp. 229-306, and references quoted therein.
  2. N. N. Rosanov and G. V. Khodova, �??Autosolitons in bistable interferometers,�?? Opt. Spectrosc. 65, 449-450 (1988).
  3. M. Tlidi, P. Mandel and R. Lefever, �??Localized structures and localized patterns in optical bistability,�?? Phys. Rev. Lett. 73, 640-643 (1994).
    [CrossRef] [PubMed]
  4. 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]
  5. M. Brambilla, L. A. Lugiato and M. Stefani, �??Interaction and control of optical localized structures,�?? Europhys. Lett. 34, 109-114 (1996).
    [CrossRef]
  6. M. Saffman, D. Montgomery and D. Z. Anderson, �??Collapse of a transverse-mode continuum in a self-imaging photorefractively pumped ring resonator,�?? Opt. Lett. 19, 518-520 (1994).
    [CrossRef] [PubMed]
  7. V. B. Taranenko, K. Staliunas and C. O. Weiss, �??Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator,�?? Phys. Rev. A 56, 1582-1591 (1997).
    [CrossRef]
  8. B. Schaepers, M. Feldmann, T. Ackemannand, W. Lange, �??Interaction of Localized Structures in an Optical Pattern-Forming System,�?? Phys. Rev. Lett. 85, 748-751 (2000).
    [CrossRef]
  9. S. Barland, J.R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Koedl, M. Miller and R. Jaeger, �??Cavity solitons work as pixels in semiconductors,�?? Nature, to appear. See also references quoted therein.
  10. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati and L. A. Lugiato, �??Spatial solitons in semiconductor microcavities,�?? Phys. Rev. A 58, 2542-2559 (1998) and references quoted therein.
    [CrossRef]
  11. L. Spinelli, G. Tissoni, M. Tarenghi and M. Brambilla, �??First principle theory for cavity solitons in semiconductor microresonators,�?? Eur. Phys. J. D 15, 257-266 (2001) and references quoted therein.
    [CrossRef]
  12. E. Abraham, �??Modelling of regenerative pulsations in an InSb etalon,�?? Opt. Commun. 61, 282-286 (1987) and references quoted therein.
    [CrossRef]
  13. S. Barland, O. Piro, S. Balle, M. Giudici and J. Tredicce, �??Thermo-optical pulsation in semiconductor lasers with injected signal: Relaxation oscillations, excitability, phase-locking and coherence resonance,�?? preprint.
  14. R. Kuszelewicz et al., 2nd yearly report of the PIANOS Project (2000). I. Ganne, Ph. D. Thesis (2000).
  15. L. Spinelli, G. Tissoni, L. A. Lugiato and M. Brambilla, �??Thermal instabilites in semiconductor amplifiers,�?? submitted to J. Mod. Opt., special issue for the Proceedings of the Physics of Quantum Electronics Conference (Snowbird USA January 6-10, 2002) edited by R. W. Boyd and M. O. Scully.
  16. L. Spinelli, G. Tissoni, L. A. Lugiato and M. Brambilla, �??Thermal e.ects and transverse structures in semiconductor microcavities with population inversion,�?? Phys. Rev. A 66, 023817(2002).
    [CrossRef]
  17. A. J. Scroggie, J. M. McSloy and W. J. Firth, �??Self-Propelled Cavity Solitons in Semiconductor Microcavities,�?? submitted to Phys. Rev. E.
  18. T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney and C. Z. Ning, �??Modeling the interplay of thermal e.ects and transverse mode behavior in native-oxide-confined vertical-cavity surfaceemitting lasers,�?? Phys. Rev. A 58, 3279-3292 (1998).
    [CrossRef]

Eur. Phys. J. D (1)

L. Spinelli, G. Tissoni, M. Tarenghi and M. Brambilla, �??First principle theory for cavity solitons in semiconductor microresonators,�?? Eur. Phys. J. D 15, 257-266 (2001) and references quoted therein.
[CrossRef]

Europhys. Lett. (1)

M. Brambilla, L. A. Lugiato and M. Stefani, �??Interaction and control of optical localized structures,�?? Europhys. Lett. 34, 109-114 (1996).
[CrossRef]

J. Mod. Opt. (1)

L. Spinelli, G. Tissoni, L. A. Lugiato and M. Brambilla, �??Thermal instabilites in semiconductor amplifiers,�?? submitted to J. Mod. Opt., special issue for the Proceedings of the Physics of Quantum Electronics Conference (Snowbird USA January 6-10, 2002) edited by R. W. Boyd and M. O. Scully.

Opt. Commun. (1)

E. Abraham, �??Modelling of regenerative pulsations in an InSb etalon,�?? Opt. Commun. 61, 282-286 (1987) and references quoted therein.
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

N. N. Rosanov and G. V. Khodova, �??Autosolitons in bistable interferometers,�?? Opt. Spectrosc. 65, 449-450 (1988).

Phys. Rev. A (4)

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney and C. Z. Ning, �??Modeling the interplay of thermal e.ects and transverse mode behavior in native-oxide-confined vertical-cavity surfaceemitting lasers,�?? Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati and L. A. Lugiato, �??Spatial solitons in semiconductor microcavities,�?? Phys. Rev. A 58, 2542-2559 (1998) and references quoted therein.
[CrossRef]

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

V. B. Taranenko, K. Staliunas and C. O. Weiss, �??Spatial soliton laser: localized structures in a laser with a saturable absorber in a self-imaging resonator,�?? Phys. Rev. A 56, 1582-1591 (1997).
[CrossRef]

Phys. Rev. E (1)

A. J. Scroggie, J. M. McSloy and W. J. Firth, �??Self-Propelled Cavity Solitons in Semiconductor Microcavities,�?? submitted to Phys. Rev. E.

Phys. Rev. Lett. (3)

B. Schaepers, M. Feldmann, T. Ackemannand, W. Lange, �??Interaction of Localized Structures in an Optical Pattern-Forming System,�?? Phys. Rev. Lett. 85, 748-751 (2000).
[CrossRef]

M. Tlidi, P. Mandel and R. Lefever, �??Localized structures and localized patterns in optical bistability,�?? Phys. Rev. Lett. 73, 640-643 (1994).
[CrossRef] [PubMed]

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 (4)

L. A. Lugiato, M. Brambilla and A. Gatti, �??Optical Pattern Formation,�?? in Advances in Atomic, Molecular and Optical Physics, Vol. 40, edited by B. Bederson and H. Walther, Academic Press, 1998, pp. 229-306, and references quoted therein.

S. Barland, J.R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Koedl, M. Miller and R. Jaeger, �??Cavity solitons work as pixels in semiconductors,�?? Nature, to appear. See also references quoted therein.

S. Barland, O. Piro, S. Balle, M. Giudici and J. Tredicce, �??Thermo-optical pulsation in semiconductor lasers with injected signal: Relaxation oscillations, excitability, phase-locking and coherence resonance,�?? preprint.

R. Kuszelewicz et al., 2nd yearly report of the PIANOS Project (2000). I. Ganne, Ph. D. Thesis (2000).

Supplementary Material (5)

» Media 1: MPG (1814 KB)     
» Media 2: MPG (1758 KB)     
» Media 3: MPG (1764 KB)     
» Media 4: MPG (273 KB)     
» Media 5: MPG (398 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Scheme of the broad-area vertical-cavity semiconductor microresonator.

Fig. 2.
Fig. 2.

(File size 1.77 MB) Movie showing the onset of Regenerative Oscillations in the passive configuration with a gaussian input field profile: we report the field intensity transverse cross-section. Integration window is about 140 × 140 μm wide, while the evolution time is 30 μs. Temporal parameters are: κ -1 = 10 ps, γ -1 = 10ns, γth1 = 20μs. Other parameters are ∆ = -3, θ 0 = 0, α, = 5, Z ≃ 2.06 · 10-3, Σ = 80, EI = 27.

Fig. 3.
Fig. 3.

(File size 1.71 MB) Movie showing the formation of a travelling honeycomb pattern in the transverse cross-section of the field intensity (left) and temperature (right), in the case of the passive configuration: integration window is about 140 × 140 μm wide, while the evolution time is 24 μs. White corresponds to field intensity and temperature maxima. Temporal parameters are set as in Fig. 2. Other parameters are ∆ = -1, θ 0 = -6, α = 10, Z ≃ 2.06 · 10-3, Σ = 40, EI = 15.5.

Fig. 4.
Fig. 4.

(File size 1.72 MB) Movie showing the time evolution of the field intensity (solid curve) and temperature (dashed curve) profiles when a CS is excited in the 1-D case, in the active configuration. The evolution time is 6μs. Temporal parameters are: κ -1 = 10ps, γ1 = 1ns, γth1 = 1μs. Other parameters are ∆ = 3, θ 0 = -18.5, α = 5, Σ = 40, Z ≃ 1.2 · 10-4, P ≃ 8.1 · 10-8, I = 1.43, EI = 2.55.

Fig. 5.
Fig. 5.

(File size 273 KB) Movie showing the time evolution of the field intensity (left) and temperature (right) cross-sections after the switching on of a CS, in the active configuration: the integration window is about 125 × 125 μm wide, while the evolution time is 0.96 μs. White corresponds to field intensity and temperature maxima. Parameters are set as in Fig. 4.

Fig. 6.
Fig. 6.

(File size 397KB) As in Fig. 5, but with two CS.

Equations (4)

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

E t = κ [ ( 1 + i θ ( T ) ) E E I i χ nl ( N , T , ω 0 ) E i 2 E ] ,
N t = γ [ N Im ( χ nl ( N , T , ω 0 ) ) E 2 I d 2 N ] ,
T t = γ th [ ( T 1 ) D T 2 T ] + γZN + γP I 2 ,
θ = θ 0 α ( T 1 ) ,

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