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Rotating and Fugitive Cavity Solitons in semiconductor microresonators

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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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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)

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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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