相关论文: Computation of whispering gallery modes for spheri…
Whispering gallery modes [WGM] are resonant modes displaying special features: They concentrate along the boundary of the optical cavity at high polar frequencies and they are associated with complex scattering resonances very close to the…
This article aims to present a general study of the Helmholtz problem in slowly varying waveguides. This work is of particular interest at locally resonant frequencies, where a phenomenon close to the tunnel effect for Schr\"odinger…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber $k$. Our analysis covers the heterogeneous…
We extend the nonconforming Trefftz virtual element method introduced in arXiv:1805.05634 to the case of the fluid-fluid interface problem, that is, a Helmholtz problem with piecewise constant wave number. With respect to the original…
Using quasiclassical approach rather precise analytical approximations for the eigenfrequencies of whispering gallery modes in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits of precision of…
Quasiclassical approach and geometric optics allow to describe rather accurately whispering gallery modes in convex axisymmetric bodies. Using this approach we obtain practical formulas for the calculation of eigenfrequencies and radiative…
We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity.…
This paper explains how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate, efficiently, the frequencies and…
In this paper, we propose and analyze an accurate numerical approach to simulate the Helmholtz problem in a bounded region with a random refractive index, where the random refractive index is denoted using an infinite series parameterized…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…
Numerical evolutions of whispering gallery modes of both isotropic and anisotropic spheroidal resonators are presented and used to build analytical approximations of these modes. Such approximations are carried out mainly to have the…
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
We derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent…
Diffraction of a high-frequency large-number whispering gallery mode is studied, which runs along a concave curve turning to a straight line. At the point of straitening, the curvature of the boundary suffers a jump. The parabolic equation…
We study the boundary localization phenomenon, known as whispering gallery modes, for weak solutions to semilinear Dirichlet eigenvalue problems in the unit ball $B_1 \subseteq \mathbb{R}^d$ ($d \geq 2$) of the form \[ \begin{cases} -\Delta…
We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…
In this work we compute the resonant wavelength of whispering gallery modes for bulk-fused silica microspheres including chromatic dispersion. This is done following two methods: by solving the exact characteristic equation and, on the…