Related papers: Additional Boundary Conditions for Nonconnected Wi…
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and…
We derive general coupled-mode equations describing the nonlinear interaction of electromagnetic modes in media with loss and gain. Our approach is rigorously based on the Lorentz reciprocity theorem, and it can be applied to a broad range…
Bragg scattering in periodic media generates band gaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these band gaps. This is caused by boundary…
The electrical and optical properties of ordered passive arrays, constituted of inductive and capacitive components, are usually deduced from Kirchhoff's rules. Under the assumption of periodic boundary conditions, comparable results may be…
Recent investigations have highlighted the failure of a sum of $R^{-6}$ terms to represent the dispersion interaction in parallel metallic, anisotropic, linear or planar nanostructures [J. F. Dobson, A. White, and A. Rubio, Phys. Rev. Lett.…
We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe,…
A local permittivity model is proposed to accurately characterize spatial dispersion in non-local wire-medium (WM) structures with arbitrary terminations. A closed-form expression for the local thickness-dependent permittivity is derived…
Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties…
In conventional plasmonic media and plasmonic metamaterials, such as metallic wire mesh, longitudinal mode of electromagnetic wave manifests itself in frequency overlapping transverse modes, which impedes clear observation of…
Motivated by recent theoretical and experimental interest in metamaterials comprising non-local coupling terms, we present an analytic framework to realise materials with arbitrary complex dispersion relations. Building on the inverse…
The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is…
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the…
The procedure for obtaining a difference equation, the solution of which is the components of the electric (or magnetic) field at the chosen set of volume points of the resonator chain, was developed. We started with the wave equation with…
Using the recent results found in [1, 2] we prove that it is possible to induce flexur in linear piezoelectric beams by means of quadratic Almansi type boundary conditions for the electric potential. Beams constituted by transversely…
The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary…
We present a theoretical framework for nonlinear optics of graphene and other 2D materials in layered structures. We derive a key equation to find the effective electric field and the sheet current density in the 2D material for given…
We have studied the bound states of the extra electron in a molecular wire, corresponding to the physical situation of the electron tunneling through the wire. Based on formalism of the scattering operator that accounts for many-electron…
Electrokinetic boundary conditions are derived for AC electrokinetic (ACEK) phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary conditions correlate the electric potentials across the semiconductor-electrolyte…
We present a theory which explains how to achieve an enhancement of nonlinear effects in a thin layer of nonlinear medium by involving a planar periodic structure specially designed to bear a trapped-mode resonant regime. In particular, the…
The electron states in a size-quantaized coated semiconductor wire in a uniform magnetic field applied parallel to the wire axis is considered. The wave functions are found and the equation for determination of energy eigenvalues depending…