Description and stability analysis of nonlinear transmission line type metamaterials using nonlinear dynamics theory

Nonlinear metamaterials offer a potential technology to realize applications at microwave, terahertz, and optical frequencies. However, due to the strong and controlled nonlinearity, the wave interactions can be quite complex. In the current article, a framework based on nonlinear dynamics theory is developed to describe such complex interactions. This is demonstrated for the case of a harmonically pumped nonlinear left handed transmission line through the use of bifurcation theory, stability analysis, and linearization about the limit cycle to calculate the autonomously generated frequencies and their spatial distributions. Higher order parametric interactions, which can be mediated by the strong nonlinearity, are automatically included in the model. It is demonstrated that autonomous components can be visualized in both the phase and the set of solution spaces. The framework is general in terms of the transmission line configuration, the nature and strength of the nonlinearity, and the number of stages. It also provides accurate results when the autonomous frequencies are in the vicinity of the Bragg frequency. Published by AIP Publishing.