Multiscale Ordinal Symbolic Analysis of the Lang-Kobayashi Model for External-Cavity Semiconductor Lasers: A Test of Theory

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 external-cavity semiconductor lasers are understood.