Nonlinear dynamics in chiral torsional metamaterials

The advent and rapid development of metamaterials introduced many revolutionary concepts for manipulating electromagnetic waves. As an important class of metamaterials, chiral metamaterials allow us to control the polarization of electromagnetic waves at the subwavelength scale. While much work has been done on using chiral metamaterials to control electromagnetic waves, the accompanying effects, such as the electromagnetic force and torque acting on the structures, as well as nonlinear optomechanical effects, are still largely unexplored. The exploration of these areas could provide useful insight from both fundamental and practical points of view. In this thesis, we study new properties of chiral metamaterials, in particular the optomechanical properties and nonlinear effects that arise from the coupling between electromagnetic and elastic degrees of freedom. An accurate and efficient model based on the free-space Green's function under the eigenmode approximation is developed for the study. In Chapter 1, we provide a comprehensive introduction to the basic concepts and history of metamaterials, followed by more focused reviews on chiral metamaterials, different paradigms of tunable metamaterials, the nontrivial electromagnetic force and torque, as well as the nonlinear optomechanical effect in different platforms. Finally, the motivation and the scope of the thesis are summarized. To understand the optical activity in coupled structures, in Chapter 2, we employ the model developed to study the rvear-field coupling, far-field scattering and optical activity of chiral meta-molecules based on twisted coupled cut-wire pairs. The numerical results from our model agree well quantitatively with full-wave calculation. We also discuss the optimum twist angle of the structure. After exploring the optical activity, in Chapter 3, we study the optomechanical properties of chiral meta-molecules based on a pair of twisted split-ring resonators. This structure can provide a strong and tunable torque, and can support different optomechanical dynamics, making it a good candidate for subwavelength light-driven actuators. To achieve strong coupling between electromagnetic resonance and elastic deformation in metamaterials, in Chapter 4, we introduce chiral torsional meta-molecules based on twisted split-ring pairs. We predict a rich range of nonlinear stationary effects including self-tuning and bistability. Importantly, these nonlinear effects including bistability are successfully observed in experiment. After understanding the nonlinear stationary responses of torsional meta-molecules, in Chapter 5, we study their nontrivial nonlinear dynamic effects. We introduce a simple structure based on three connected split-rings and find that this structure can support novel nonlinear dynamics such as chaos, damping-immune self-oscillations and dynamic nonlinear optical activity. To understand how intermolecular interaction can change system dynamics, in Chapter 6, we study the nonlinear effects of ensembles of enantiomeric torsional meta-molecules. We find that spontaneous chiral symmetry breaking can exist due to intermolecular interaction. For the first time in metamaterials, both spontaneous chiral symmetry breaking and self-oscillations are successfully demonstrated exper-