Horseshoe templates with global torsion in a driven laser

We perform a topological analysis of chaotic signals from a Nd-doped fiber laser with pump modulation at different values of the modulation frequency. In this experiment, the system displays chaotic behavior in three regions C1/4, C1/3, and C1/2 of parameter space, located around the subharmonics ωᵣ/4, ωᵣ/3, and ωᵣ/2 of the relaxation frequency ωᵣ. We observe that the topological structures of the chaotic regimes inside a given region C1/n are described by the same template. However, templates corresponding to different regions display different global torsions θg, which we find to be related to the order of the subharmonics by θg(C1/n)=n-1.