Wave Propagation In Lattices Research Articles

Discrete N-fold Darboux transformation and infinite number of conservation laws of a four-component Toda lattice

In this paper, we investigate a four-component Toda lattice (TL), which may be used to model the wave propagation in lattices just like the famous TL. By means of the Lax pair and gauge transformation, we construct the [Formula: see text]-fold Darboux transformation (DT), which enables us to obtain multi-soliton or multi-solitary wave solution without complex iterative process. Through the obtained DT, [Formula: see text]-fold explicit exact solutions of the system and their figures with proper parameters are presented from which we find the [Formula: see text]-fold solution shows two-solitary wave structure, the amplitude and shape of the wave change with time. Finally, we derive an infinite number of conservation laws formulaically to illustrate the integrability of the system.

Wave propagation in micromorphic anisotropic continua with an application to tetragonal crystals

We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case, we obtain qualitative information on the frequencies and the dispersion relations. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic and optic frequencies and for the coupled vibrations modes are obtained for propagation directions along the tetragonal c-axis.

Anisotropy affects the lattice waves and phonon distributions in GaAs

The stress-strain relationship, anisotropy, heavy- and light-hole structures, and the Phillips ionicity in GaAs are theoretically investigated by Bond matrices model as well as Zener and Every anisotropies. The results show that there is a simple correspondence between anisotropy and the extreme directions of these physical properties, i.e., [0 0 1], [1 1 0] and [1 1 1] directions. Meanwhile the lattice wave propagation, phonon focusing, and phonon distributions in GaAs are also theoretically studied in detail based on lattice-dynamical method. The slowness surface of three lattice waves are the mixing of longitudinal and transverse modes. The feature is that the lattice waves, saddle Gaussian curvatures, and caustic structures are modulated by the anisotropy. The topology in phonon distribution is discussed by the presence of caustics in the anisotropic flux of phonons emanating from a localized phonon distribution. Their topological structures show the phonon distribution and the phonon focusing. The anisotropy not only affects lattice wave propagation and phonon distribution, but influences the phonon focusing.

Elastic properties and lattice waves of TiAl

The elastic properties, lattice wave propagation and phonon focusing of TiAl are studied in detail based on Bond matrices model and lattice-dynamical method. The results contain remarkably complex three-dimensional variations in the phonon flux with angular distribution. The feature of elastic waves and phonon distribution is affected by the elastic anisotropy of the lattice. The correspondence between these features and contours of Gaussian curvature on the slowness surface is explored and the phonon topology is discussed about the presence of caustics in the anistropic flux of phonons emanating from a localized phonon distribution. The topology slowness surface gives insights into the mixing of longitudinal and transverse modes and gives the origin of the phonon focusing. The elastic anisotropy not only affects lattice wave propagation but also influences phonon focusing.

Nonlinear wave propagation and dynamic reconfiguration in two-dimensional lattices with bistable elements

This paper examines the propagation of elastic waves of large amplitudes in two-dimensional square lattices that include an alternating pattern of linear springs and nonlinear bistable springs. Because of the presence of bistable springs, these lattices have multiple stable configurations. In this paper, a theoretical model that takes into account the non-linearity of the bistable springs while neglecting geometric nonlinearities is used to study non-linear wave propagation in these lattices. Results from numerical simulations demonstrate that, for a lattice that is initially in a deformed stable equilibrium configuration, stimuli of large amplitudes are able to cause a reconfiguration of the lattice to a configuration of lower potential energy. Even for initial stable configurations that exhibit omnidirectional or directional bandgaps for infinitesimal wave propagation, waves of large amplitudes can propagate in the lattice due to its reconfiguration; however, due to the nonlinearity of bistable springs, the transmitted response tends to have multiple spectral peaks or be broadband for narrow-band stimuli of large amplitude. Simulations are used to study how the reconfiguration of the lattice depends on the amplitude and duration of the stimulus, on damping, and on the energy barrier between the two stable equilibria of the bistable springs. These numerical results suggest that these multistable lattices can serve as reconfigurable wave guides for which the amplitude of the stimulus offers opportunities for enhanced tunability.

Tutorial: Computing Topological Invariants in 2D Photonic Crystals

AbstractThe field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple methods for diagnosing the topology of optical systems remain elusive for an important part of the community. Herein, a summary of numerical methods to calculate topological invariants emerging from the propagation of light in photonic crystals is provided. The fundamental properties of wave propagation in lattices with a space‐dependent periodic electric permittivity is first described. Next, an introduction to topological invariants is provided, proposing an optimal strategy to calculate them through the numerical evaluation of Maxwell's equation in a discretized reciprocal space. Finally, the tutorial is complemented with a few practical examples of photonic crystal systems showing different topological properties, such as photonic valley‐Chern insulators, photonic crystals presenting an “obstructed atomic limit”, photonic systems supporting fragile topology, and finally photonic Chern insulators, where the magnetic permeability is also periodically modulated.

Dynamic reconfiguration of two-dimensional lattices with bistable springs

This study focuses on wave propagation and reconfiguration in two-dimensional square mass-spring lattices that include bistable springs. Due to the presence of directional and/or omnidirectional bandgaps in stable deformed configurations in which some of the bistable springs are in a deformed equilibrium, these lattices have the ability to serve as reconfigurable wave filters and wave guides. In this work, we study non-linear wave propagation in response to stimulus of large amplitude. Mechanical stimuli of large amplitudes have the capability of causing a dynamic reconfiguration of the lattice to a configuration of lower potential energy, which dramatically affect wave propagation. Using numerical simulations, the influence of the stimulus amplitude, duration, and location of the applied stimulus on the reconfiguration is analyzed. The ability to alter in a predictable manner wave propagation in these lattices offers new opportunities for tunable phononic crystals.

Metasurfaces with Electric Quadrupole and Magnetic Dipole Resonant Coupling

Collective resonances in plasmonic nanoparticle arrays with electric dipole moment oriented along the lattice wave propagation are theoretically investigated. The role of electric quadrupole (EQ) and magnetic dipole (MD) moments of gold nanoparticles in the resonant features of the arrays is analyzed. We perform both semi-analytical calculations of coupled multipole equations and rigorous numerical simulations varying contributions of the electric and magnetic multipoles by changing particle size and shape (spheres and disks). The arrays in homogeneous and non-homogeneous environments are considered. We find that even very weak non-resonant EQ and MD moments of a single particle are significantly enhanced in the periodic lattice at the wavelength of collective (lattice) resonance excitation. Importantly, we show that in the infinite arrays, the EQ and MD moments of nanoparticles are coupled and affect each other resonant contributions. We also demonstrate that at the lattice-resonance wavelength, the enhanced EQ and MD moments have contributions to reflection comparable to the dipole one resulting in a significant decrease of reflection and providing the satisfaction of the generalized Kerker condition for reflection suppression.

Mode coupling of dust lattice wave propagation in an external magnetic field in 2D plasma crystal with wake effect

The effect of particle–wake interaction on the coupling between the longitudinal and transverse dust lattice waves in two-dimensional hexagonal lattice in an external magnetic field is investigated. Meanwhile the electrostatic interactions between a particle charge and all other particle charges together with the corresponding effective wake charges are taken into account. Explicit formulations of dispersion relations of dust lattice waves are given when both the primary wave vector and the external magnetic field are parallel to axes. The dispersion relations are calculated numerically and hybrid phonon mode and hybrid optical mode are obtained. Furthermore, the mode mixing rates of the hybrid phonon mode and the hybrid optical mode are calculated and the mode changing points are obtained. Finally, the mode coupling is very intense in the region where the dispersion curves are close together and the mode coupling intensity increases when the magnitude of the external magnetic field increases.