Abstract

We describe two different methods that exploit the intrinsic mobility properties of cavity solitons to realize periodic motion, suitable in principle to provide soliton-based, all-optical clocking or synchronization. The first method relies on the drift of solitons in phase gradients: when the holding beam corresponds to a doughnut mode (instead of a Gaussian as usually) cavity solitons undergo a rotational motion along the annulus of the doughnut. The second makes additional use of the recently discovered spontaneous motion of cavity solitons induced by the thermal dynamics, it demonstrates that it can be controlled by introducing phase or amplitude modulations in the holding beam. Finally, we show that in presence of a weak 2D phase modulation, the cavity soliton, under the thermally induced motion, performs a random walk from one maximum of the phase profile to another, always escaping from the temperature minimum generated by the soliton itself (Fugitive Soliton).

© 2003 Optical Society of America

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References

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  1. D. W. McLaughlin, J. V. Moloney and A. C. Newell, �??Solitary Waves as Fixed Points of Infinite-Dimensional Maps in an Optical Bistable Ring Cavity,�?? Phys. Rev. Lett. 51, 75-78 (1983).
    [CrossRef]
  2. N. N. Rosanov and G. V. Khodova, �??Autosolitons in bistable interferometers,�?? Opt. Spectrosc. 65, 449-450 (1988).
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  4. For review, see L. A. Lugiato, �??Introduction to the Special Issue on Cavity Solitons,�?? IEEE J. Quant. Electron.39, 193 (2003)
    [CrossRef]
  5. For review, see W. J. Firth and G. K. Harkness, �??Existence, Stability and Properties of Cavity Solitons,�?? in �??Spatial Solitons,�?? Springer Series in Optical Sciences Vol. 82, eds. S. Trillo and W. Torruellas, pp. 343-358 (Springer Velag, 2002).
  6. 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]
  7. M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli andW. J. Firth,�??Spatial soliton pixels in semiconductor devices,�?? Phys. Rev. Lett. 79, 2042 (1997).
    [CrossRef]
  8. D. Michaelis, U. Peschel and F. Lederer, �??Multistable localized structures and superlattices in semiconductor optical resonators,�?? Phys. Rev. A 56, R3366-R3369 (1997).
    [CrossRef]
  9. 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]
  10. G. Tissoni, L. Spinelli, M. Brambilla, T. Maggipinto, I. Perrini and L. A. Lugiato, �??Cavity solitons in passive bulk semiconductor microcavities. I. Microscopic model and modulational instabilities,�?? J. Opt. Soc. Am. B 16, 2083 (1999).
    [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. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knoedl, M. Miller and R. Jaeger,�??Cavity Solitons as pixels in semiconductor microcavities,�?? Nature 419, 699-702 (2002).
    [CrossRef] [PubMed]
  13. 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]
  14. A. J. Scroggie, J. M. McSloy, and W. J. Firth, �??Self-propelled cavity solitons in semiconductor microcavities,�?? Phys. Rev. E 66, 036607 (2002).
    [CrossRef]
  15. G. Tissoni, L. Spinelli and L. A. Lugiato,�??Spatio-temporal dynamics in semiconductor microresonators with thermal effects,�?? Opt. Ex. 10, 1009 (2002).
    [CrossRef]
  16. I. M. Perrini, G. Tissoni, T. Maggipinto, and M. Brambilla, �??Thermal effects and cavity solitons in passive semiconductor microresonators,�?? submitted to J. Opt. B (2003).
  17. D. V. Skryabin, A. Yulin, D. Michaelis, W. J. Firth, G-L. Oppo, U. Peschel and F. Lederer, �??Perturbation Theory for Domain Walls in the Parametric Ginzburg-Landau Equation,�?? Phys. Rev. E 64, 56618-1-9 (2001).
    [CrossRef]
  18. L. Allen, M.W. Beijersbergen, R. J. C. Spreuw and J. P.Woerdman, �??Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,�?? Phys. Rev. A 45, 8185-8189 (1992).
    [CrossRef] [PubMed]
  19. L. Allen, S. M. Barnett and M. J. Padgett, �??Optical angular Momentum,�?? Institute of Physics Publishing, Bristol, (2003).
  20. B. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz and R. Azoulay, �??High contrast multiple quantum well optical bistable device with integrated Bragg reflectors,�?? Appl. Phys. Lett. 57, 324 (1990).
    [CrossRef]
  21. W. J. Firth and G. Harkness, �??Cavity Solitons,�?? Asian J. Phys. 7, 665-677 (1998).
  22. G. Tissoni, L. Spinelli, M. Brambilla, T. Maggipinto, I. Perrini and L. A. Lugiato, �??Cavity solitons in passive bulk semiconductor microcavities. II. Dynamical proprties and control,�?? J. Opt. Soc. Am. B 16, 2095 (1999).
    [CrossRef]
  23. T. Maggipinto, M. Brambilla, G. K. Harkness and W. J. Firth, �??Cavity Solitons in Semiconductor Microresonators: Existence, Stability and Dynamical Properties,�?? Phys Rev E 62, 8726-8739 (2000).
    [CrossRef]
  24. G-L. Oppo, A. J. Scroggie and W. J. Firth, �??Characterization, Dynamics and Stabilization of Diffractive Domain Walls and Dark Ring Cavity Solitons in Optical Parametric Oscillators,�?? Phys Rev E 63 066209-1/15 (2001).
    [CrossRef]
  25. M. Tlidi, P. Mandel and R. Lefever, �??Localized structures and localized patterns in optical bistability,�?? Phys. Rev. Lett. 73, 640-643 (1994).
  26. B. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz and R. Azoulay, �??External-beam switching in monolithic bistable GaAs quantum well etalons,�?? Appl. Phys. Lett. 57, 1849 (1990).

Appl. Phys. Lett. (2)

B. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz and R. Azoulay, �??High contrast multiple quantum well optical bistable device with integrated Bragg reflectors,�?? Appl. Phys. Lett. 57, 324 (1990).
[CrossRef]

B. Sfez, J. L. Oudar, J. C. Michel, R. Kuszelewicz and R. Azoulay, �??External-beam switching in monolithic bistable GaAs quantum well etalons,�?? Appl. Phys. Lett. 57, 1849 (1990).

Asian J. Phys. (1)

W. J. Firth and G. Harkness, �??Cavity Solitons,�?? Asian J. Phys. 7, 665-677 (1998).

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]

IEEE J. Quant. Electron. (1)

For review, see L. A. Lugiato, �??Introduction to the Special Issue on Cavity Solitons,�?? IEEE J. Quant. Electron.39, 193 (2003)
[CrossRef]

J. Opt. B (1)

I. M. Perrini, G. Tissoni, T. Maggipinto, and M. Brambilla, �??Thermal effects and cavity solitons in passive semiconductor microresonators,�?? submitted to J. Opt. B (2003).

J. Opt. Soc. Am. B (3)

Nature (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knoedl, M. Miller and R. Jaeger,�??Cavity Solitons as pixels in semiconductor microcavities,�?? Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Opt. Ex. (1)

G. Tissoni, L. Spinelli and L. A. Lugiato,�??Spatio-temporal dynamics in semiconductor microresonators with thermal effects,�?? Opt. Ex. 10, 1009 (2002).
[CrossRef]

Opt. Spectrosc. (1)

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

Phys Rev E (2)

T. Maggipinto, M. Brambilla, G. K. Harkness and W. J. Firth, �??Cavity Solitons in Semiconductor Microresonators: Existence, Stability and Dynamical Properties,�?? Phys Rev E 62, 8726-8739 (2000).
[CrossRef]

G-L. Oppo, A. J. Scroggie and W. J. Firth, �??Characterization, Dynamics and Stabilization of Diffractive Domain Walls and Dark Ring Cavity Solitons in Optical Parametric Oscillators,�?? Phys Rev E 63 066209-1/15 (2001).
[CrossRef]

Phys. Rev. A (4)

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]

L. Allen, M.W. Beijersbergen, R. J. C. Spreuw and J. P.Woerdman, �??Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,�?? Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

D. Michaelis, U. Peschel and F. Lederer, �??Multistable localized structures and superlattices in semiconductor optical resonators,�?? Phys. Rev. A 56, R3366-R3369 (1997).
[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]

Phys. Rev. E (2)

D. V. Skryabin, A. Yulin, D. Michaelis, W. J. Firth, G-L. Oppo, U. Peschel and F. Lederer, �??Perturbation Theory for Domain Walls in the Parametric Ginzburg-Landau Equation,�?? Phys. Rev. E 64, 56618-1-9 (2001).
[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. (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]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli andW. J. Firth,�??Spatial soliton pixels in semiconductor devices,�?? Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

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

D. W. McLaughlin, J. V. Moloney and A. C. Newell, �??Solitary Waves as Fixed Points of Infinite-Dimensional Maps in an Optical Bistable Ring Cavity,�?? Phys. Rev. Lett. 51, 75-78 (1983).
[CrossRef]

Springer Series in Optical Sciences (1)

For review, see W. J. Firth and G. K. Harkness, �??Existence, Stability and Properties of Cavity Solitons,�?? in �??Spatial Solitons,�?? Springer Series in Optical Sciences Vol. 82, eds. S. Trillo and W. Torruellas, pp. 343-358 (Springer Velag, 2002).

Other (1)

L. Allen, S. M. Barnett and M. J. Padgett, �??Optical angular Momentum,�?? Institute of Physics Publishing, Bristol, (2003).

Supplementary Material (5)

» Media 1: MPG (545 KB)     
» Media 2: MPG (981 KB)     
» Media 3: MPG (140 KB)     
» Media 4: MPG (249 KB)     
» Media 5: MPG (1289 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Gauss-Laguerre mode (TEM*10) that we used as holding beam (a). The movie (b) shows the rotatory motion of CS due to the phase profile e + of the holding beam. Passive configuration, without thermal effects. Parameters are: κ -1=10ps, γ1=10ns, I=0, η=0.25; β=1.6, d=0.2, θ=-3, C=40, Δ=-1. [Media 1]

Fig. 2.
Fig. 2.

Active configuration without thermal effects: steady-state curve. Parameters are: C=0.45, θ=-2, α=5, I=2, η=0, β=0 and d=0.052.

Fig. 3.
Fig. 3.

Gauss-Laguerre mode (TEM*01) that we used as holding beam (a). The movie (b) shows the rotatory motion of 2 CSs due to the phase profile e- of the holding beam. Active configuration, without thermal effects. Temporal parameters are: κ -1=10ps-1=1ns. Other parameters are as in Fig. 2. [Media 2]

Fig. 4.
Fig. 4.

Active configuration with thermal effects: steady-state curve. Parameters are: κ -1=10ps,γ1=1ns,γth1 =1µs, DT =1, d=0.1, Δ=3, θ 0=-18.5, Σ=80, Z≃1.2·10-4, P≃8.1·10-8, I=1.43.

Fig. 5.
Fig. 5.

1D phase profile of the holding beam (a). The movie (b) shows the dynamics of two CSs. Parameters are as in Fig. 4. [Media 3]

Fig. 6.
Fig. 6.

The profile of the input holding beam with ring-shaped pure amplitude gradient is shown in (a). The movie (b) illustrates the motion of CS. Parameters are as in Fig. 4. [Media 4]

Fig. 7.
Fig. 7.

2D phase profile of the holding beam (a). The movie shows the time evolution of field intensity (b) and temperature (c). Parameters are as in Fig. 4. [Media 5]

Equations (9)

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

E t = κ [ ( 1 + η + i θ ) E + E I 2 C i Θ ( N 1 ) E + i 2 E ] ,
N t = γ [ N + β N 2 I + ( N 1 ) E 2 d 2 N ] ,
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 ] + γ Z N + γ P I 2 ,
θ = θ 0 λ ( T 1 ) ,
λ = 4 π T 0 n Γ n T ,
E I ( x , y ) = E I ( 0 ) [ 1 + i ( ε 1 cos K x + ε 2 cos K y ) ] ,
E I ( x , y ) E I ( 0 ) exp ( i φ ( x , y ) ) , φ ( x , y ) = ε 1 cos K x + ε 2 cos K y ,

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