Period doubling and route to chaos in reduced graphene oxide, an experimental evidence

We use Nonlinear Schrödinger Equation (NLSE) to investigate chaotic dynamics inside a graphene-based optical system. Numerical results show that with increasing the control parameters, the character of Modulation instability (MI) is changed from convective to absolute. In consequence, a hyper-chaotic map is more expressive to explain the dynamical state of the system. It is also indicated that a reverse transition from the chaotic regime to the stable state can be resulted if the optical input intensity is further increased. The optical input intensity and feedback strength are distinguished as the two control parameters of the system. We then use Reduced Graphene Oxide (RGO) dispersion with large nonlinear refractive index to verify if a transition to instability and chaotic behavior is experimentally realized for the visible input light wave. The observation begins with saturation in the nonlinear response followed by an Optical Bistability (OB) phenomena. Afterward, a quasi-periodic fluctuations appear expressing the absolute MI. In agreement with our simulation result based on the period doubling bifurcation diagram, this quasi-periodic state is recognized as a route to the chaos. We infer that the graphene Quantum Dots (QDs) which are formed as a result of reduction process are responsible for energy transfer through the optical near-field interactions and thus, strengthen the required feedback.