Split-ring resonator based nonlinear metamaterials: from few to many, theory and experiments
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abstract
Metamaterials, namely artificial structures featuring negative refractive index at specific frequency bands, have been implemented and used in a plethora of applications, including implementation of switches, couplers, antennas, demonstration of super-lenses, electromagnetic cloaking, and so on [1]. This proposal focuses on nonlinear metamaterials, whose properties depend on the electromagnetic field intensity, and are operating in the microwave regime. In the proposed settings, metamaterialsâ structural components (so-called â meta-atomsâ ) will be split-ring resonators (SRRs) and complementary SRRs (CSRRs), which will be realized experimentally by means of modern microstrip technology. Nonlinearity will be used to control and tune the properties of these structures, and will be introduced by inserting diodes in the slits of SRRs/CSRRs. We will construct and study structures that consist of a small (2-4) or a large (~100) number of meta-atoms. The former are intended to provide a sense of the fundamental building blocks (couplers, trimers, quadrimer and more generally ``oligomersâ â ), while the latter will extend our understanding to the realm of nonlinear dynamical lattices. Experimental measurements of the properties of such structures will be used to theoretically describe corresponding configurations, and develop transmission line models of the metamaterials that we will construct. This way, we will be able to study fundamental electromagnetic phenomena that can occur in nonlinear metamaterials, combining experimental, theoretical and numerical techniques. Using such complementary and synergetic approaches, our plan is to start from â smallâ structures and then extend our considerations to â largeâ ones. For the small structures, we will study fundamental effects, including spontaneous symmetry breaking, as well as the interplay between gain and loss mechanisms in such nonlinear metamaterials. For the large, lattice structures, we will focus on the interplay between dispersion-inducing discreteness and nonlinearity, with our scope being the study of nonlinearity-induced localization of energy, and formation of fundamental nonlinear waveforms, in the form of solitons. The proposed connections between theory and experiments are expected to lead to a better understanding of nonlinear metamaterials and of the usefulness of nonlinear waves as fundamental carriers of information in them. Thus, the value of our results will be twofold, both expanding the current state-of-the-art in theoretical viewpoint, and in the process also suggesting/devising novel applications through the experimental connections.
