Related papers: Resonant modes in triangular dielectric cavities
We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we…
Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…
It is shown that cavities formed between a multilayer quarter-wave Bragg reflector and a metal mirror which support Tamm plasmons can be modelled by using a hard-mirror approximation including appropriate penetration depths into the…
This report aims at establishing a theoretical framework for dealing with the reconstruction problem of a small acoustic inclusion. The objective is to introduce the new concept of time-dependent polarization tensors for the Helmholtz…
We consider the modes of the electric field of a cavity where there is an embedded polarized dielectric film. The model consists in the Maxwell equations coupled to a Duffing oscillator for the film which we assume infinitely thin. We…
Hot alkali metal vapors enclosed in sub-micron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at nanoscale. Here, we propose a novel approach for calculating the eigenmodes…
We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, i.e. the equation $\nabla\cdot(A \nabla u ) + k^2 n u =-f$ where both $A$ and $n$ are functions of position. We prove new a priori bounds on the solution…
Invariance in duality transformation, the self-dual property, has important applications in electromagnetic engineering. In the present paper, the problem of most general linear and local boundary conditions with self-dual property is…
The diffraction problem of a plane wave impinging on a grating formed by nested cavities is solved by means of the modal method, for $s$ and $p$ polarization modes. The cavities are formed by perfectly conducting sheets that describe…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the obstacle is trapping. There are two resolvent estimates for…
Recent improvements in the resonant-state expansion (RSE), focusing on the static mode contribution, have made it possible to treat transverse-magnetic (TM) modes of a spherically symmetric system with the same efficiency as their…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…
In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant…
Probing the radial collective oscillation of a trapped quantum system is an accurate experimental tool to investigate interactions and dimensionality effects. We consider a fully polarized quasi-one dimensional dipolar quantum gas of…
Micron-scale optical cavities are produced using a combination of template sphere self-assembly and electrochemical growth. Transmission measurements of the tunable microcavities show sharp resonant modes with a Q-factor>300, and 25-fold…
We study certain "geometric-invariant resonant cavitie"' introduced by Liberal et. al in a 2016 Nature Comm. paper, modeled using the transverse magnetic reduction of Maxwell's equations. The cross-section consists of a dielectric inclusion…
We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
We consider regular and singular perturbations of the Dirichlet and Neumann boundary value problems for the Helmholtz equation in $n$-dimensional cylinders. Existence of eigenvalues and their asymptotics are studied.