Dithered Time Delays and Chaos Synchronization in Lasers with Multiple Feedbacks

By studying laser systems with multiple time delays, we demonstrate that the signatures of time delays in the autocorrelation coefficient and the mutual information of the laser output can be erased for systems with variable time delays. This property makes such laser systems highly suitable for secure chaos-based communication systems. We also present the first report on chaos synchronization in both unidirectionally and bidirectionally coupled variable multiple time delay laser diodes with electro-optical feedbacks. Introduction.-In recent years due to its fundamental and applied interests chaos synchronization has been the subject of extensive studies [1-2]. From the application point of view, chaos based communication systems can offer improved privacy and security in data transmission, especially after the recent field demonstration using a metropolitan fibre network [3]. In optical chaos based communications, the chaotic waveform is generated by using semiconductor lasers with all-optical or electro-optical feedback(s). Mathematically such time delayed systems are described by delay differential equations (DDE)[4]. Recent studies have revealed that DDE-chaos based communication systems [1-2] could be more secure than one based on chaos in ODE (ordinary differential equations) [5], as DDEs usually have a very high dimensionality and many positive Lyapunov exponents. However, the authors of [6], were successful in extracting messages masked by a chaotic signal of a time delay system. In [6] the authors used the average fitting error as a function of the embedding delay, which had a pronounced minimum at the time delay. This allowed them to correctly identify the time delay of the system and to extract the message successfully using a simple local reconstruction of the time delay system. The delay time can also be exposed by several other measures, e.g. autocorrelation coefficient [7] and mutual information [8]. Quite recently it was suggested that multiple time delay systems can offer a higher complexity of dynamics than is achievable in more conventional single delay time systems [9]. The role of additional time delays in achieving a homogeneous steady state in coupled chaotic maps was investigated in recent work [10] with the stabilizing role of the additional time delays being emphasized. The stabilizing role of additional time delays in external cavity laser diodes with multiple feedbacks is highlighted in [11]. The high complexity of such multiple time delay systems can provide a new architecture for enhancing message security in chaos based encryption systems. However using the same approach as in [6], it was shown …