Stable isochronal synchronization of mutually coupled chaotic lasers

The dynamics of two mutually coupled chaotic diode lasers are investigated experimentally and numerically. By adding self-feedback to each laser, stable isochronal synchronization is established. This stability, which can be achieved for symmetric operation, is essential for constructing an optical public-channel cryptographic system. The experimental results on diode lasers are well described by rate equations of coupled single mode lasers.

Figure 1

A schematic figure of the two coupled lasers. BS, beam splitter; PBS, polarization beam splitter; NDF, neutral density filter; PD, photodetector.

Figure 2

Correlation coefficient between laser intensities at different time delays for ${\tau }_c={\tau }_d=7\mathrm{ns}$; $\kappa$, self-feedback rate; $\sigma$, coupling rate. The results of the experiment are plotted with a solid black line and the results of the simulations with a gray line, which has been shifted up by 0.4 for clarity. Different $\kappa$ values affect the dynamics of the synchronization (in the simulations we kept $\kappa +\sigma =100{\mathrm{ns}}^{-1}$). For $\kappa =0$ (face to face configuration) we observe a coexistence of leader and/or laggard situation. When $\kappa >0$ the isochronal synchronization is stable (maximum correlation in zero time delay).

Figure 3

The phase space of $\kappa$ and $\sigma$, with ${\kappa }_A={\kappa }_B$, ${\sigma }_A={\sigma }_B$, and ${\tau }_c={\tau }_d$ [20].

Figure 4

A typical experimental time sequence of laser intensities for isochronal synchronization. The system parameters are $\kappa$=$\sigma$ and ${\tau }_c$=${\tau }_d$. The lower figure is a more detailed view of the figure above it.

Figure 5

Numerical simulations results for the achronal synchronization with $\kappa =0$, $\sigma =100{\mathrm{ns}}^{-1}$, and ${\tau }_c=7\mathrm{ns}$. The relative probability of the ratio of the cross correlation of two time delays $\rho (+{\tau }_c)$ and $\rho (-{\tau }_c)$. Inset: A histogram of the time delay between the breakdowns of the two lasers $A$ and $B$, for the same parameters as above.