A rigorous solution of the homogeneous Maxwell equations for hybrid modes of a microwave cylindrical cavity with a transverse annular slot in the perfectly conducting walls of arbitrary thickness and a plane infinite anisotropic dielectric passing through the slot is constructed based on eigenfunction expansion. In each of the field existence regions (the cavity itself, the interior of a slot a...

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights wh...

Consider the Dirichlet boundary value problem for the Helmholtz equation in a nonlocally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the...

When plane-wave destruction (PWD) is implemented by implicit finite differences, the local slope is estimated by an iterative algorithm. We propose an analytical estimator of the local slope that is based on convergence analysis of the iterative algorithm. Using the analytical estimator, we design a noniterative method to estimate slopes by a three-point PWD filter. Compared with the iterative ...

Starting from the three-dimensional Gross-Pitaevskii equation (3D GPE) we derive a 1D generalized nonpolynomial Schrödinger equation (1D g-NPSE) which describes the dynamics of Bose-Einstein condensates under the action of a generic potential in the longitudinal axial direction and of an anisotropic harmonic potential in the transverse radial direction. This equation reduces to the familiar 1D ...

We derive via the interaction "representation" the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field-the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement - the uniform electron gas - the GKT wave function reduces to the Kohn Theorem wa...

let denote the unit circle in the complex plane. given a function , one uses t usual (harmonic) poisson kernel for the unit disk to define the poisson integral of , namely . here we consider the biharmonic poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . we then consider the dilations for and . the ...

A concept of multistep cascading is applied to the problem of fourth-harmonic generation (FHG) in a single quadratic crystal, and a new model of parametric wave mixing is analyzed in detail. Important applications to the optical frequency division and efficient FHG as well as the realization of the double-phase-matching multistep cascading processes in engineered QPM structures with phase-rever...

A method of complex orthogonal decomposition is applied to the extraction of modes from simulation data of multi-modal traveling waves in one-dimensional continua. The decomposition of a transient wave is performed on a nondispersive pulse. Complex wave modes are then extracted from a two-harmonic simulation of a dispersive medium. The wave frequencies and wave numbers are obtained by looking a...

Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in R3. In this paper, existence and uniqueness of the variational problem for forward scattering are established. An energy estimate for the scattered field with a uniform bound with respect to the wavenumber is obtained in the case of low frequency on which the Born approximation is based. A c...