Related papers: Tilted resonators in a triangular elastic lattice:…
Research on photonics and metamaterials constantly challenges our intuitive understanding of the behaviour of light. In recent years we have seen negative refraction, focusing of light by a flat slab, a ``perfect'' prism, and an…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
If the Electroweak Symmetry Breaking Sector turns out to be strongly interacting, the actively investigated effective theory for longitudinal gauge bosons plus Higgs can be efficiently extended to cover the regime of saturation of unitarity…
Elastic periodic lattices act as mechanical filters of incident vibrations. By and large, they forbid wave propagation within bandgaps and resonate outside them. However, they often encounter "truncation resonances" (TRs) inside bandgaps…
A generic class of metamaterials is introduced and is shown to exhibit frequency dependent double negative effective properties. We develop a rigorous method for calculating the frequency intervals where either double negative or double…
Electrically-excited electroelastic extensional vibrations of an arbitrarily cut three-dimensional piezocrystal resonator are analyzed variationally. A set of trigonometric trial functions applicable to a waveguide behavior of the resonator…
Elastic metamaterials may exhibit band gaps at wavelengths far exceeding feature sizes. This is attributed to local resonances of embedded or branching substructures. In branched configurations, such as a pillared plate, waves propagating…
The paper addresses novel dispersion properties of elastic flexural waves in periodic structures which possess rotational inertia. The structure is represented as a lattice, whose elementary links are formally defined as the Rayleigh beams.…
We present an extensive formulation of the inverse grating problem for exural waves, in which the energy of each diffracted mode is selected and the grating configuration is then obtained by solving a linear system of equations. The grating…
We describe the method for extracting the elastic scattering phase shift from a lattice simulation at an introductory level, for non-lattice practitioners. We consider the scattering in a resonant channel, where the resulting phase shift…
We present a procedure for the systematic estimation of the dispersion properties of linear discrete systems with periodic time-varying coefficients. The approach relies on the analysis of a single unit cell, making use of Bloch theorem…
The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals. Considering…
Along with other frequency selective structures [1] (circles and squares), triangular split-ring resonators (TSRRs) only allow frequencies near the center resonant frequency to propagate. Further, TSRRs are attractive due to their small…
The propagation of electrons in an orbital multiplet dispersing on a lattice can support anomalous transport phenomena deriving from an orbitally-induced Berry curvature. In striking contrast to the related situation in graphene, we find…
Dispersion relations are fundamental characteristics of the dynamics of quantum and wave systems. In this work we introduce a simple technique to generate arbitrary dispersion relations in a modulated tilted lattice. The technique is…
The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface…
For oblique anti-plane shear waves in periodic layered elastic composites, it is shown that negative energy refraction is accompanied by positive phase-velocity refraction and positive energy refraction is accompanied by negative…
A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and down-conversion processes are…
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…
We show that resonant frequencies of a system of coupled resonators in a truncated periodic lattice converge to the essential spectrum of corresponding infinite lattice. We use the capacitance matrix as a model for fully coupled resonators…