Related papers: Modes of an elliptical cylindrical resonant cavity…
We study the long wavelength electromagnetic resonances of interacting cylinder arrays. By using a normal modes expansion where the effects of geometry and material are separated, it is shown that two parallel cylinders with different radii…
Cavities possess self-sustaining oscillations driven by the interaction of hydrodynamic and acoustic characteristics. These oscillations have applications in fuel-air mixing, heat exchangers, and landing gears, but resonance can damage the…
Plasmon modes of a two-dimensional lattice of long conducting circular wires are investigated by using an embedding technique to solve Maxwell's equations rigorously. The frequency-dependent density of states is calculated for various…
The work is motivated by the Faraday cage effect. We consider the Helmholtz equation over a 3D-domain containing a thin heterogeneous interface of thickness $\delta \ll 1$. The layer has a $\delta-$periodic structure in the in-plane…
We present a versatile numerical algorithm for computing resonances of open dielectric cavities. The emphasis is on the generality of the system's configuration, i.e. the geometry of the (main) cavity (and possible inclusions) and the…
In lima\c{c}on-shaped gradient index dielectric cavities designed by conformal transformation optics, the variation of Q-factors and emission directionality of resonant modes was traced in their system parameter space. For these cavities,…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
We present the discovery of a novel and intriguing global geometric structure of the (interior) transmission eigenfunctions associated with the Helmholtz system. It is shown in generic scenarios that there always exists a sequence of…
The existence of phase resonances in obliquely illuminated, perfectly conducting compound gratings is investigated. The diffraction problem of a p-polarized plane wave impinging on the structure is solved using the modal approach. The…
We consider resonances associated with excited eigenvalues of the cavity of a general Helmholtz resonator with straight neck. Under the assumption that the neck stays away from the nodal set of the corresponding eigenstate, we generalise…
We prove in this paper an existence result for frequency modes coupling seismic waves and vibrating tall buildings. The derivation from physical principles of a set of equations modeling this phenomenon was done in previous studies. In this…
Exact chirped elliptic wave solutions are obtained within the framework of coupled cubic nonlinear Helmholtz equations in the presence of non-Kerr nonlinearity like self steepening and self frequency shift. It is shown that, for a…
We study relativistically expanding electromagnetic fields of cylindrical geometry. The fields emerge from the side surface of a cylinder and are invariant under translations parallel to the axis of the cylinder. The expansion velocity is…
We investigate the Helmholtz equation in a two dimensional open waveguide with a thin and high contrast core layer. We develop an asymptotic analysis of the Green function of the problem, and through it we identify and characterize the…
Cavities in large-scale photonic integrated circuits often suffer from a wider distribution of resonance frequencies due to fabrication errors. It is crucial to adjust the resonances of cavities using post-processing methods to minimize the…
The behaviour of a particle with a spin 1/2 and a dipole magnetic moment in a time-varying magnetic field in the form $(h_0 cn(\omega t,k), h_0 sn(\omega t,k), H_0 dn(\omega t,k))$, where $\omega$ is the driving field frequency, $t$ is the…
Discussed in the present study are details of the behavior of low-frequency "acoustic" ($ac$) modes in the spectrum of edge magnetoplasma oscillations in axially symmetric degenerate 2D electron systems where electron density distribution…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…
The high-frequency Helmholtz equation on the entire space is truncated into a bounded domain using the perfectly matched layer (PML) technique and subsequently, discretized by the higher-order finite element method (FEM) and the continuous…
We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…