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 al different values of the modulation frequency. In this experiment, the system displays chaotic behavior in three regions C-1/4, C-1/3, and C-1/2 of parameter space, located around the subharmonics omega(r)/4, omega(r)/3, and omega(r)/2 of the relaxation frequency omega(r). We observe that the topological structures of the chaotic regimes inside a given region Cli, are described by the same template. However, templates corresponding to different regions display different global torsions theta g, which we find to be related to the order of the subharmonics by theta(g)(C-1/n) = n-1.