Cascaded routes to chaos based on nanosecond soliton fiber lasers

Giant anomalous dispersion is numerically introduced into a nonlinear-polarization-rotation mode-locked fiber laser, achieving nanosecond solitons. By controlling the operation conditions, it is observed that the output can exhibit a transition from period doubling bifurcations route to chaos with an increase in pump power. In addition, cascaded routes to chaos, where period timing emerges from chaos then evolves into chaos through period doubling bifurcation again, are discovered with the help of a narrow-bandwidth spectral filter. Four distinct chaos regions can be identified. The maximum Lyapunov exponent at the center of the chaos region is used to represent the degree of chaos, where an increasing trend is observed. Consequently, these chaos regions are designated by hierarchical order, constituting a form of cascaded chaos. Numerical simulations based on other fiber lasers with different gain fiber lengths reproduce the cascaded chaos, suggesting the generality of cascaded chaos generation.