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 C_1/4, C_1/3, and C_1/2 of parameter space, located around the subharmonics ω_r/4, ω_r/3, and ω_r/2 of the relaxation frequency ω_r. We observe that the topological structures of the chaotic regimes inside a given region C_1/n are described by the same template. However, templates corresponding to different regions display different global torsions θ_g, which we find to be related to the order of the subharmonics by θ_g(C_1/n)=n-1.