Simultaneous prediction of two independent chaotic time series using semiconductor ring lasers with optical feedback

We demonstrate simultaneous prediction of two independent Santa-Fe time series using a single-longitudinal mode semiconductor ring laser with optical feedback. Our results indicate that a prediction with errors comparable to the state-ofthe-art can be achieved for each time series despite the two tasks are computed simultaneously. I by the way that the brain processes the information, computational approaches have been developed for tasks such as pattern recognition, time series prediction and classification [1], [2]. These approaches typically make use of a large number of randomly connected nonlinear nodes. With 10 − 10 nodes, such hard tasks have been solved with acceptable errors. In a recently introduced approach, this large number of nodes has been successulfully replaced by a single nonlinear node with delay, yielding comparable performance [3]–[7]. In this contribution, we attempt to mimic another ability of the brain consisting in processing simultaneously several independent tasks. We identify semiconductor ring lasers (SRLs) as suitable devices for this purpose thanks to their capability of lasing simultaneously in two directional modes. Thus, we simultaneously predict the next sample of two independent chaotic time series. In terms of the mean-field slowly varying complex amplitudes of the electric field associated with the two counterpropagating modes Ecw and Eccw, and the carrier number N , the theoretical model of the SRL-based system used is : Ėcw = κ (1 + iα) [GcwN − 1]Ecw − (kd + ikc)Eccw + ηcwFcw(t) + √ Dcwξcw(t) + k1E1(t), (1) Ėccw = κ (1 + iα) [GccwN − 1]Eccw − (kd + ikc)Ecw + ηccwFccw(t) + √ Dccwξccw(t) + k2E2(t), (2)