Electric-field-biased control of irregular oscillations via multistability in a nonlinear terahertz meta-atom

The split-ring resonator (SRR) has become widely popular in the design of artificial two-dimensional materials at the sub-wavelength scale, known as metasurfaces. When exposed to an intense electric field, this meta-atom deposited on a suitable substrate can exhibit electromagnetic coupling and become a bianisotropic meta-atom metasurface, where various nonlinear phenomena can occur. In this paper, the collective properties of the nonlinear SRR meta-atom model subjected to an alternating current (AC) and direct current (DC) field in the terahertz (THz) frequency portion of the spectrum are investigated in detail. Our investigation seeks to identify a new pathway to leverage the controlled bias field for reducing the required AC field that triggers the desired nonlinear effects. Using bi-parameter diagrams, we demonstrate how irregular oscillations emerge from controlling the DC field with a relatively low AC field. This result represents a key strategy and a promising route for translating these significant nonlinear interactions into practical, real-world applications utilizing nonlinear metasurfaces. To further examine some interesting properties correlated to the multi-sensitivity of the material in the low AC field regime, we first consider the normalized amplitude of the AC field as a control parameter for a fixed DC value. This approach reveals important phenomena, such as the transition to chaos via period-splitting bifurcation, as well as the emergence of multistable windows where the system exhibits a variety of coexisting periodic signals, including the coexistence of two and three distinct periodic patterns. Additionally, we uncover a rare case of bistability consisting of two different irregular signals. Next, the dynamic characteristics of the system are analyzed by varying the normalized DC field, for a fixed value of the normalized AC amplitude. In this situation, an interesting route to chaos is found through the creation and annihilation of periodic orbits. We also highlight a striking region in which the system exhibits the coexistence of three or two regular and irregular behaviors, resulting from a combination of hysteresis and parallel bifurcations. To distinguish these coexisting patterns, we compute the cross-sections of the initial domain, phase images, and time series associated with each signal. These findings substantially advance the development of multifunctional metasurface-based devices, with potential applications ranging from secure communication systems to enhanced signal detection.