Multiscale ordinal symbolic analysis of the Lang-Kobayashi model for external-cavity semiconductor lasers: a test of theory

Abstract

We study experimentally and theoretically the permutation entropy (PE) of the optical intensity I(t) of an external-cavity semiconductor distributed feedback laser in the coherence collapse regime. Our PE analysis allows us to uncover the intrinsic dynamical complexity at multiple timescales of the delayed-feedback system, as well as to investigate how the experimental observations can be determined by modeling. An overall good agreement between experiment and theory corroborates the effectiveness of the Lang–Kobayashi model, though the model underestimates the entropy on the timescale of the relaxation oscillations and can lead to a time-delay signature that is less evident than in experiment, indicating a potential vulnerability of chaos encryption. This provides a critical test of the standard theoretical framework in which chaotic externalcavity semiconductor lasers are understood.