Numerical investigations of synchronization and communication based on an electro-optic phase chaos system with concealment of time delay.

A modified electro-optic phase chaos system that can conceal time delay (TD) and allows for unidirectional message transmission, is numerically investigated. The configuration includes two cascaded delay loops, and the parallel-coupled microresonators (PCMRs) in one of two loops result in a frequency-dependent group delay. The largest Lyapunov exponent (LLE), Lempel-Ziv complexity (LZC) and permutation entropy (PE) are used to distinguish the chaotic behavior and the degree of complexity in a time series, and the autocorrelation function (ACF) and the delayed mutual information (DMI) are plotted to extract the TD. The corresponding diagrams show that in the electro-optic system phase chaos with high complexity can occur within a certain range of feedback strength. The diagrams also show that, at a fixed feedback strength, the effect of the TD concealment becomes quite good with an increase in the number of PCMRs. The numerical simulation also reveals that the delayed chaotic dynamics can be identically synchronized, and the synchronization solution is robust. Moreover, based on the coherence of Mach-Zehnder interferometers, we convert the phase variations of the transmitter outputs and the receiver into the corresponding intensity variations, so the synchronization error of the two-phase chaotic series can be monitored. At last, we can successfully decipher the message introduced on the transmitting end of a link. In this scheme, the feedback TD has been concealed, which prevents eavesdroppers from listening and makes the proposed chaotic communication system secure.