Complexity of Chaos in Three Cascaded Vertical-Cavity Surface-Emitting Lasers

The complexity of chaos generated in two systems has been studied experimentally. The complexity of the chaos is quantified by calculating average normalized permutation entropy (H-S(P)). In the first system, a chaotic output from a master laser (ML) is injected into a CW slave laser (SL). The results show that the complexity of chaos generated in the SL decreases with absolute value of the frequency detuning Delta f(1), which means the complexity of the chaos is compromised with enhancing the bandwidth, as Delta f(1) is increased. The second system comprises three vertical-cavity surface-emitting lasers (VCSELs); the first VCSEL (used as ML) was rendered chaotic by optical feedback, the second VCSEL is used as intermediate laser (IL), which is rendered chaotic when it is subject to optical injection from the chaotic ML and the third VCSEL is used as a SL and is a subject of optical injection from the chaotic IL, thus entering chaotic dynamics. In this three-VCSEL system, small, intermediate and wide bandwidths of the injecting chaos signals, have been used to study the effect of the bandwidth of the injecting chaos on the complexity of chaos generated in the SL. The results show that the bandwidth of the chaotic injection beam does not impact the complexity of the chaos generated in the SL for positive frequency detuning; however, for large negative frequency detuning, the complexity of the chaos in the SL has been reduced significantly for the intermediate and lower bandwidth of the chaotic injection beam.