Lattices Of Split-ring Resonators Research Articles

Observation of topological corner states in a D4-symmetric square lattice of split-ring resonators

Topological states offer an increased versatility in disorder-robust localization of electromagnetic waves at the edges and corners of photonic structures. In most of the cases, such properties are achieved due to the appropriate lattice symmetry. Here, by contrast, we explore an alternative design strategy where the topological states in a simple square lattice are tailored due to the orientation of non-centrosymmetric split-ring resonators comprising the meta-structure. We numerically predict the emergence of the nontrivial topological properties and confirm our prediction by fabricating the structure and observing the localized edge and corner states experimentally.

(2+1)-Dimensional Envelope Solitons in Nonlinear Magnetic Metamaterials

The dynamics of nonlinear magnetoinductive waves in a two-dimensional monoatomic lattice of Split ring resonators (SRRs) with Kerr nonlinear interaction between nearest neighbors is studied analytically. The soliton excitation genuine of the discreteness and nonlinearity in such a system based on an extended quasidiscreteness approach are obtained.

Soliton excitations in a one-dimensional nonlinear diatomic chain of split-ring resonators

We present a systematic analytical study of the dynamics of nonlinear magnetoinductive waves in a one-dimensional diatomic lattice of split ring resonators (SRRs) with Kerr nonlinear interaction between nearest neighbors. The linear spectrum of this model have two branches and exhibits a gap, which is proportional to the difference between two types of SRRs. We analyze the nonlinear excitations genuine of the discreteness and nonlinearity in such a diatomic chain based on an extended quasidiscreteness approach. Gap solitons (with vibrating frequency lying in the gap), resonant kinks (with the vibrating frequency lying in the frequency bands), and intrinsic localized modes (with the vibrating frequency being above all the frequency bands) are obtained explicitly. It is also shown that the existence of different localized structures depend strongly on the type of nonlinearity of the embedded medium (a self-focusing or defocusing one).

Spatial dispersion in lattices of split ring resonators with permeability near zero

We demonstrate that metamaterials formed by split ring resonators may exhibit strong spatial dispersion when the effective permeability is near zero. It is shown that the nonlocal effects can be characterized using a generalized Clausius-Mossotti formula. The proposed theory is verified using full wave simulations.

Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald-Oseen extinction principle

The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of incident wave, eigenmodes excited in the crystal and scattered spatial harmonics. Generalized Ewald-Oseen extinction principle is formulated on the base of deduced boundary conditions. The knowledge of properties of infinite crystal's eigenmodes provides option to solve the diffraction problem for the corresponding semi-infinite crystal numerically. In the case when the crystal is formed by small inclusions which can be treated as point dipolar scatterers with fixed direction the problem admits complete rigorous analytical solution. The amplitudes of excited modes and scattered spatial harmonics are expressed in terms of the wave vectors of the infinite crystal by closed-form analytical formulae. The result is applied for study of reflection properties of metamaterial formed by cubic lattice of split-ring resonators.

Electric coupling to the magnetic resonance of split ring resonators

We study both theoretically and experimentally the transmission properties of a lattice of split ring resonators (SRRs) for different electromagnetic (EM) field polarizations and propagation directions. We find unexpectedly that the incident electric field E couples to the magnetic resonance of the SRR when the EM waves propagate perpendicular to the SRR plane and the incident E is parallel to the gap-bearing sides of the SRR. This is manifested by a dip in the transmission spectrum. A simple analytic model is introduced to explain this interesting behavior.