As a result of the self-oscillations, the polarization rotation of chiral meta-molecules varies with time and incident power – an effect dubbed dynamic nonlinear opti- cal activity. For the first time in metamaterials, self-oscillations were experimentally demonstrated in a system composed of two coupled torsional meta-molecules. (5)The concept of spontaneous chiral symmetry breaking was introduced in meta- materials, where intermolecular interaction was found to be indispensable. For the first time in metamaterials, this effect was predicted and experimentally demon- strated with coupled enantiomeric torsional meta-molecules.
When torsional meta-molecules are assembled into large arrays, the intermolecu- lar electromagnetic interaction could bring in qualitatively new effects. We studied a nonlinear system composed of two or more coupled enantiomeric torsional meta- molecules, i.e. torsional chiral meta-molecules with opposite handedness. It was found that intermolecular electromagnetic coupling can change the system stability and lead to spontaneous breaking of the original chiral symmetry. Such symmetry breaking can be found in both the dynamic and stationary responses of the system, and it leads to a giant nonlinear polarization change, energy localization and mode splitting. We also showed how to manipulate such symmetry breaking in a large scale array by introducing a perturbation in the polarization. For the first time in metamaterials, such an effect was predicted and demonstrated successfully in a mi- crowave pump-probe experiment. This novel effect provides a new possibility for creating an artificial phase transition in metamaterials without requiring naturally occurring phase change materials.
7.2
Outlook
The studies presented in this thesis are of interest from both fundamental and applied points of view, and they could be extended in a number of new directions.
For the methodology part, the near-field interaction model introduced here can be applied to non-chiral structures and can become more sophisticated by taking into account fast nonlinearity, gain media and even quantum effects. It would be particularly useful when dealing with large scale and finite-sized coupled systems, as is often the case in practical devices; the introduction of randomness, special lattices such as quasi-crystalline structures, or gradients in structural geometries can also be taken into account. This would help us to predict and understand novel effects such as Anderson localization, topological states, random lasing, etc. in the context of metamaterials.
For the nonlinear optomechanical effects, although the experimental studies pre- sented here are in the microwave regime, we expect that similar effects can also be found in high frequency regimes such as terahertz, infrared or even visible light. In these high frequency regimes, structures that are easier to fabricate with top- down approaches, such as cantilevers or nano-beams would be more favorable. It is exciting to see that recent advances in bottom-up fabrication techniques, such as DNA origami, already allowed programmable fabrication of complex structures from the molecular level; plasmonic structures similar to the designed torsional meta- molecules in our study have been realized recently [158]. Importantly, since most of the novel effects predicted and demonstrated in this thesis are independent of me-
chanical damping, the liquid environment required for DNA origami will not be a detrimental factor; this could provide a novel bottom-up platform to study various optomechanical effects at visible light frequencies.
The spontaneous chiral symmetry breaking of enantiomeric metamaterials pro- vides a chiral analogy of the antiferromagnetic-ferrimagnetic transition found in mag- netic materials. The critical phenomena around the bifurcation points may reveal yet further interesting physics, since unlike many condensed matter systems, the system studied here is non-conservative. The possibility of using such instability around the critical points for ultra-high sensitivity measurements is quite exciting. For example, one can utilize this property as an event counter by measuring the symmetry break- ing triggered due to the perturbation of mechanical or electromagnetic environment. An event that can introduce mechanical vibration, or change the input electromag- netic signal could be measured. In addition, the excitation of self-oscillations around the bifurcation point could provide a further enhancement of the sensitivity due to the involvement of periodic oscillating signals – the tiny environmental perturbation can be characterized from the change of oscillating signals in either the time domain or the frequency domain. Furthermore, the achiral-chiral transition shown here is not the only one possible in metamaterials, there are also positive-negative index and elliptic-hyperbolic dispersion transitions which warrant exploration.
From the practical point of view, the coupling of electromagnetic and elastic prop- erties also provides a novel route for fully spatial control of meta-surfaces. It is par- ticularly useful for near infrared and optical frequencies where the introduction of electronic control to each individual meta-molecule becomes increasingly challenging or even undesirable due to the involvement of metals and semi-conductors that are absorptive at optical frequencies. Instead, one can use a spatial light modulator to control the spatial profile of the pump field to achieve active spatial tuning of meta- surfaces. While spatial light modulators widely used today focus on manipulation of far-field wave components, a metasurface with dynamic modulation property could do similar operation to the near-field components, and it would have great impact in a wide range of fields such as super-resolution imaging.
Appendix A
Theoretical Framework of
Electromagnetic Interaction in
Coupled Meta-atoms
In metamaterials, the electromagnetic (EM) interaction of meta-atoms, such as split rings and cut-wires, etc., can greatly alter the EM properties of the whole meta- material system, for example, the frequencies and linewidths of resonances as well as the efficiencies and profiles of far-field scattering. When the separation between meta-atoms is much smaller than the operation wavelength, such interaction is in the near-field regime and is thus callednear-field interaction. This is usually the case when two or more meta-atoms are closely packed and function as a meta-molecule. This appendix gives an overview of the background and the theoretical framework employed in this thesis. Particularly, the semi-analytical methods introduced here can be used to quantitatively describe the complex electromagnetic interaction of meta-atoms. Such interaction is related to both the energy and momentum aspects of electromagnetic waves.
Below, the first section will focus on the energy aspect of interaction of meta- atoms, a semi-analytical method based on free space Green’s function will be in- troduced; the second section emphasizes the momentum aspect of interaction, i.e. the electromagnetic force and torque; the third section will introduce the multipole expansion of the model for far-field interaction.
A.1
Electromagnetic Coupling of Meta-atoms
The interaction, particularly the near-field interaction of meta-atoms provides addi- tional degrees of freedom to control the properties of the composed meta-molecules. Such interaction can lead to hybridized modes with different resonant frequencies and bandwidths, and their properties are governed by the energy aspect of the in- teraction – for example, the amount of electric and magnetic energy that is mutually coupled among meta-atoms and the power lost as scattering and heat.
The calculation and interpretation of these hybridization effects generally rely on full wave simulation in conjunction with intuitive effective circuit models or coupled- oscillators description that require many fitted parameters [150,357,366,437]. Ap- parently, these approaches are only useful for understanding the effects in relatively simple systems and would become impractical when the number of meta-atoms in- volved is large. Below, we will introduce the semi-analytical method used in this thesis from the basis of electromagnetic theory. This method can be considered as an
eigenmode approximation of the full wave methods such as Method of Moment and Integral Equation Method. Unlike previous approach based on the effective circuit model, our method can be used to calculate the electromagnetic response of a large scale coupled system with no fitted parameters. This method can provide reasonably good accuracy, while remaining physically insightful and computationally efficient.