Episodic Synchronization via Dynamic Injection

We report the occurrence of spontaneous synchronizing events between two semiconductor lasers, when the emission of a frequency- and intensity-chaotic driving laser is unidirectionally coupled into a second stable response laser. The driving laser is driven chaotic by delayed optical feedback, the response laser is a device-identical solitary laser. We demonstrate the onset of an episodic synchronization regime when the two lasers are spectrally detuned with respect to each other. By a joint experimental and modeling analysis we can attribute the onset and the duration of the episodes to properties of spectral overlap of both lasers. This effect can even give rise to seemingly anticorrelated intensity behavior. We expect episodic synchronization to be a generic scenario for the loss of synchronization of chaotic oscillators exhibiting frequency cycles.

Figure 1

Output intensities of the driving (upper trace in each plot) and response (lower trace) lasers for three different frequency detunings. The time traces are separated via a vertical displacement for clarity. Left panel: experimental results with detuning 9 GHz (a), 0 GHz (b) and $-10\mathrm{GHz}$ (c). Right panel: numerical results with detuning $\Delta f=\Omega /2\pi =15.91\mathrm{GHz}$ (d), $\Delta f=0\mathrm{GHz}$ (e), and $\Delta f=-3.987\mathrm{GHz}$ (f). The parameters used in the numerical simulations are $C=1.01$, ${\gamma }_e=6.890\times {10}^{-4}{\mathrm{ps}}^{-1}$, $\gamma =0.480{\mathrm{ps}}^{-1}$, $g_N=1.20\times {10}^{-8}{\mathrm{ps}}^{-1}$, $\alpha =4.0$, $N_0=1.25\times {10}^8$, $\beta ={10}^{-10}{\mathrm{ps}}^{-1}$, ${\kappa }_f=0.030{\mathrm{ps}}^{-1}$, ${\kappa }_c=0.030{\mathrm{ps}}^{-1}$, ${\tau }_f={\tau }_c=3\mathrm{ns}$, ${\omega }_t{\tau }_f=0$.

Figure 2

Numerical time traces of the driving (top) and response (bottom) laser output intensities in the jump-up regime. (a),(b) Correspond to the filtered signal (100 MHz) while (c),(d) and (e),(f) correspond to the unfiltered signals (note the difference in time scales).

Figure 3

Schematic illustration combining a qualitative sketch of the dynamical injection locking regime of the response laser [12] and a typical trajectory of the driving laser in the power-frequency plane for both positive and negative detuning. The arrows indicate the nominal detuning between the solitary emitter laser and the receiver laser. The inset shows the intensity time trace corresponding to the depicted trajectory. Color coding represents the sliding correlation coefficient (see text).

Figure 4

Phase difference $\eta$ accumulated during ${\tau }_f$ (a),(c) and time-dependent correlation coefficient (b),(d) for positive (a),(b) and negative (c),(d) detuning. In (a),(c) the black line represents the driving laser, and the gray (red) one the response laser.