相关论文: Whispering gallery modes for a transmission proble…
In this paper, we provide uniform bounds for convergence rates of the low frequencies of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane of height $H$. The perforations are…
We present a novel approach for simulating acoustic (pressure) wave propagation across different media separated by a diffuse interface through the use of a weak compressibility formulation. Our method builds on our previous work on an…
Designing high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Previous approaches, e.g. the seminal nanometer-sized quantum corrals, depend on careful positioning of…
Optical energy flow inside a dielectric microsphere is usually codirected with the optical wavevector. At the same time, if the optical field in a microsphere is in resonance with one of the high-quality spatial eigenmodes…
Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in…
We show that the wide-spread concept of optical eigen modes in lossless waveguide structures, which assumes the separation on propagating and evanescent modes, fails in the case of metal-dielectric structures, including photonic crystals.…
In a recent breakthrough STOC~2015 paper, a continuous diffusion process was considered on hypergraphs (which has been refined in a recent JACM 2018 paper) to define a Laplacian operator, whose spectral properties satisfy the celebrated…
We report on microlasers based on high-quality micropillars with lasing on whispering-gallery modes. Usage of low-absorbing Al$\scriptsize 0.2$Ga$\scriptsize 0.8$As\Al$\scriptsize 0.9$Ga$\scriptsize 0.1$As distributed Bragg reflectors as…
We suggest the numerical approach to detect eigenfrequencies of trapped modes in waveguides or guided waves in diffraction gratings. At the same time, the approach works perfectly for computation of systems with finitely many scattering…
Motivated by the problem of the small-scale sign distribution of Laplace eigenfunctions, we introduce a strong notion of sign-balance for (eigen)functions, and prove that random eigenfunctions are sign-balanced above a precisely determined…
We report the first observation of low power drive level sensitivity, hyperparametric amplification, and single-mode hyperparametric oscillations in a dielectric rutile whispering-gallery mode resonator at 4.2 K. The latter gives rise to a…
The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…
We compute low-lying eigenmodes of the gauge covariant Laplace operator on the lattice at finite temperature. For classical configurations we show how the lowest mode localizes the monopole constituents inside calorons and that it hops upon…
One of the most fascinating topics in current quantum physics are hybridised systems, in which different quantum resonators are strongly coupled. Prominent examples are circular resonators with high quality factors that allow the coupling…
We investigate MIMO eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly-correlated MIMO channel model, which does not require separable spatial correlations at the transmitter…
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…
Whispering gallery mode biosensors allow selective unlabelled detection of single proteins and, combined with quantum limited sensitivity, the possibility for noninvasive realtime observation of motor molecule motion. However, to date…
Enhanced transmissions through a gold film with arrays of subwavelength holes are theoretically studied, employing the rigid full vectorial three dimensional finite difference time domain method. Influence of air-holes shape to the…
We consider Laplacian eigenfunctions in circular, spherical and elliptical domains in order to discuss three kinds of high-frequency localization: whispering gallery modes, bouncing ball modes, and focusing modes. Although the existence of…
An explicitly solvable model of sound sources detection and sound wave scattering by the lateral line of a fish or amphibian based on the theory of self-adjoint perturbations of the Laplace operator by arrays of additional boundary…