Dynamics-dependent synchronization in on-chip coupled semiconductor lasers

Synchronization properties of chaotic dynamics in two mutually coupled semiconductor lasers with optical feedback embedded in a photonic integrated circuit are investigated from the point of view of their dynamical content. A phenomenon in which the two lasers can show qualitatively different synchronization properties according to the frequency range of investigation and their nonlinear dynamics is identified and termed dynamics-dependent synchronization. In-phase synchronization is observed for original signals and antiphase synchronization is observed for low-pass filtered signals in the case where one of the lasers shows chaotic oscillations while the other laser exhibits low-frequency fluctuations dynamics. The experimental conditions causing the synchronization states to vary according to the considered frequency interval are studied and the key roles of asymmetric coupling strength and injection currents are clarified.

Figure 1

Schematics of the photonic integrated circuit with two mutually coupled semiconductor lasers. PD, photodiode; Lasers 1 and 2, distributed feedback lasers; SOA, semiconductor optical amplifier.

Figure 2

Scheme of the experimental setup using photonic integrated circuit (PIC).

Figure 3

Experimental observation of chaos synchronization. (a, c) temporal waveforms and (b, d) correlation plots of the two lasers. (a, b) Asymmetric injection currents: $I_1/I_{\text{th},1}$ = 1.0, $I_2/I_{\text{th},2}$ = 4.0. (c, d) Symmetric injection currents: $I_1/I_{\text{th},1}$ = 4.0, $I_2/I_{\text{th},2}$ = 4.0. The SOA injection current is fixed at $I_{\text{SOA}}$ = 15.00 mA. The cross correlation value is calculated using temporal waveforms recorded on 4 $\mu \mathrm{s}$. The lag times for which the absolute value of the cross correlation is maximal are (b) $-0.42$ ns and (d) 0.08 ns.

Figure 4

Two-dimensional diagram of cross-correlation $C$ between the two laser outputs in the PIC. The delay time $\tau$ for the calculation of $C$ is adjusted in each case to maximize the absolute value of $C$. The color scale corresponds to the values of the cross correlation. The normalized injection current for laser 1 ($I_1/I_{\text{th},1}$) is changed from 0.5 to 3.5 with 0.5 interval, and that for laser 2 ($I_2/I_{\text{th},2}$) is changed from 1.5 to 4.0 with 0.5 interval. The SOA injection current is fixed at $I_{\text{SOA}}$ = 15.00 mA. Chaos and LFF dynamics are observed in this parameter region.

Figure 5

Dynamics for different SOA injection currents $I_{SOA}$. (a, c, e) Temporal waveforms and (b, d, f) RF spectra. (a, b) $I_{SOA}$ = 6.00 mA, (c, d) $I_{SOA}$ = 25.00 mA, and (e, f) $I_{\text{SOA}}$ = 39.00 mA. The injection currents are $I_1/I_{\text{th},1}$ = 1.5 and $I_2/I_{\text{th},2}$ = 3.5.

Figure 6

Synchronization state at small SOA injection current $I_{\text{SOA}}$ = 6.00 mA. (a, c) Temporal waveforms and (b, d) correlation plots. (a, b) Original signals and (c, d) low-pass filtered signals at $f_c=1$ GHz. The parameter values correspond to those in Figs. 5 and 5.

Figure 7

Synchronization state at intermediate SOA injection current $I_{\text{SOA}}$ = 25.00 mA. (a, c) Temporal waveforms and (b, d) correlation plots. (a, b) Original signals and (c, d) low-pass filtered signals at $f_c$ = 1 GHz. The parameter values corresponds to Figs. 5 and 5.

Figure 8

Synchronization state at strong SOA injection current $I_{\text{SOA}}$ = 39.00 mA. (a, c) Temporal waveforms and (b, d) correlation plots. (a, b) Original signals and (c, d) low-pass filtered signals at $f_c$ = 1 GHz. The parameter values corresponds to Figs. 5 and 5.

Figure 9

Cross-correlation functions for the original signals (red solid line) and the low-pass filtered signals at 1 GHz (blue dashed line) of the two laser outputs for different SOA injection currents. (a) $I_{\text{SOA}}$ = 6.00 mA, (b) $I_{\text{SOA}}$ = 25.00 mA, and (c) $I_{\text{SOA}}$ = 39.00 mA. (a, b, c) correspond to Figs. 6, 7, and 8, respectively. The correlation functions decay to zero when the lag time is over 5 ns (not shown).

Figure 10

Evolution of the cross-correlation value and dynamical states of the two lasers when the SOA injection current $I_{\text{SOA}}$ is changed continuously for the original signals (red solid line with circles) and the low-pass filtered signals (blue dotted line with triangles). The gray region corresponds to loss of synchronization.

Figure 11

Evolution of the cross-correlation value and dynamical states of the two lasers when the SOA injection current is changed continuously for the original signals (red solid line with circles) and the low-pass filtered signals (blue dotted line with triangles). We set different injection currents for laser 2: (a) $I_2/I_{\text{th},2}$ = 5.0 and (b) $I_2/I_{\text{th},2}$ = 2.0. The injection current for laser 1 is fixed at $I_1/I_{\text{th},1}$ = 1.5. The gray region corresponds to loss of synchronization.