All-Optical Clock Recovery Using Multi-Section Distributed-Feedback Lasers

Recovering the frequency of incoming data sequences in optical transmission lines is important for signal processing. It has been suggested to use all-optical devices, for instance lasers diodes, for this purpose. Recently, self-pulsations have experimentally been discovered in multi-section distributed-feedback lasers. If a self-pulsating laser is exposed to an external data signal, it is expected that the frequency of the self-pulsation locks to the frequency of the data signal, and clock recovery would be obtained. Mathematically, this problem amounts to investigating frequency locking of periodic solutions, that is self-pulsating laser states, on invariant tori under external forcing which represents the external data sequence. In this article, Melnikov functions are derived for periodic forcing, and results on frequency locking under aperiodic forcing are given. The results are applied to a model describing the multi-section distributed-feedback lasers which have been used in experiments. AMS subject classi cation. 35B10,34C15,78A60.