Related papers: Trapped modes and reflectionless modes as eigenfun…
The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter $\epsilon>0$ while the distance of the body…
The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…
We predict and study theoretically a new nonlinear electromagnetic phenomenon in a sample of layered superconductor of finite length placed in a waveguide with ideal walls. Two geometries are considered here: when the superconducting layers…
We show that a specific superposition principle is valid for \emph{nonlinear} Josephson plasma waves in layered superconductors. We study theoretically the reflection and transmission of terahertz waves through a finite-size superconducting…
We consider scattering waves through truncated periodic potentials with perturbations that support localized gap eigenstates. In a small complex neighborhood around an assumed positive bound state of the model operator, we prove the…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…
We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue…
We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at well-defined resonance values. Based on detailed numerical and analytical calculations,…
In this paper, we study the so-called clamped transmission eigenvalue problem. This is a new transmission eigenvalue problem that is derived from the scattering of an impenetrable clamped obstacle in a thin elastic plate. The scattering…
The interior transmission eigenvalue problem (ITP) plays a central role in inverse scattering theory and in the spectral analysis of inhomogeneous media. Despite its smooth dependence on the refractive index at the PDE level, the…
Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar…
We present several applications of mode matching methods in spectral and scattering problems. First, we consider the eigenvalue problem for the Dirichlet Laplacian in a finite cylindrical domain that is split into two subdomains by a…
A linear scattering problem for which incoming and outgoing waves are restricted to a finite number of radiation channels can be precisely described by a frequency-dependent scattering matrix. The entries of the scattering matrix, as…
The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic…
We evaluate the sensing properties of plasmonic waveguide sensors by calculating their resonant transmission spectra in different regions of the non-Hermitian eigenmode space. We elucidate the pitfalls of using modal dispersion calculations…
The operating principle of traveling-wave parametric amplifiers is typically understood in terms of the standard coupled mode theory, which describes the evolution of forward propagating waves without any reflections, i.e. for perfect…
In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched…