Multistability via field-enhanced carrier dynamics in a single-gap nonlinear terahertz split-ring resonator with loss parameter control

Metasurfaces, artificial materials with unique electromagnetic (EM) properties arising from electron oscillations in highly conductive metals, often utilize split-ring resonators (SRRs) as key components for nonlinear effects. In this paper, we investigate the nonlinear phenomena caused by charge carrier motion at the gap of a single SRR operating in the terahertz (THz) frequency range. Unlike previous approaches, our model incorporates an additional controlled field to adjust the loss parameter, providing a more generalized framework for understanding nonlinear behavior in SRRs. The nonlinear dynamics are revealed by the two-parameter space diagrams, which allow us to identify periodic and chaotic oscillations for different parameter sets of the nonlinear SRR material. In order to explore the multifunctionality of the material, we construct two-dimensional diagrams by sweeping each parameter in two directions for the same initial values and we find a plethora of hysteresis regions, demonstrating the interesting phenomenon of multistability. Our results show that this behavior occurs in extremely large dynamic regions for all cases studied, favoring the coexistence of up to three different signals/attractors. The different types of multistable patterns are studied in the cross-section of the demarcation region and presented as the coexistence of chaotic with periodic states, and the coexistence of only periodic states. We analyze the parallel branches in hysteresis regions, and we identify a parallel branch in some range where the bifurcation presents a jump. According to our results, the parallel branch has a key impact on multistability, since it increases the number of coexisting states. However, it appears in a very tiny range of parameters and annihilates after a collision crisis. Finally, we analyze the influence of the loss parameter on nonlinear material dynamics using two-parameter spatial diagrams, demonstrating that control of the loss parameter can gradually eliminate the presence of chaotic behavior, thus serving as a pivotal control mechanism for future applications.