Modeling of active and passive nonlinear metamaterials

We develop general results for nonlinear metamaterials based on simple circuit models that reflect the elementary nonlinear behavior of the medium. In particular, we consider both active and passive nonlinearities which can lead to gain, harmonic generation and a variety of nonlinear waves depending on circuit parameters and signal amplitude. We show that the medium can exhibit a phase transition to a synchronized state and derive conditions for the transformation based on a widely used multiple time scale approach that leads to the well-known Complex Ginzburg–Landau equation. Further, we examine the variety of nonlinear waves that can exist in such systems, and we present numerical results for both active and passive metamaterial cases.

► We develop a general mathematical approach to modeling nonlinear metamaterials based on a multiple time scale approach, leading to the well-known Complex Landau–Ginzburg equation.
► Our analysis shows the existence of phase transitions, solitons and domain walls in active media, along with complex frequency mixing in passive media.
► We find the critical points where synchronization or entrainment to an external source occurs.
► We show the existence of chaos in the metamaterial response and find the critical transition points where the transition to chaos occurs.