相关论文: A method of effective potentials for calculating t…
We develop a theoretical method for solving Maxwell's equations to obtain the frequency spectra of inhomogeneous and asymmetric cavity resonators using a couple of effective Debye-type potentials. The structure we study specifically is the…
The influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields the method of…
Acoustics recently became a versatile platform for discovering novel physical effects and concepts at a relatively simple technological level. On this way, single resonators and the structure of their resonant modes play a central role and…
In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…
Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the…
A rigorous solution for the spectrum of quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained for the first time. To accomplish this task, we have developed a novel method for variables separation…
In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for…
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional…
Recent observations of rapidly rotating stars have revealed the presence of regular patterns in their pulsation spectra. This has raised the question as to their physical origin, and in particular, whether they can be explained by an…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
We present an easy-to-implement numerical method for analyzing electromagnetic wave propagation in dielectric rings. Our approach employs a finite-difference-based solver in cylindrical coordinates, solving a mixed electric-magnetic field…
The boundary integral equation method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of…
The classical and quantum mechanics of isolated, nonlinear resonances in integrable systems with N>=2 degrees of freedom is discussed in terms of geometry in the space of action variables. Energy surfaces and frequencies are calculated and…
A novel single-mode resonant structure which enables the rotation of the sample about two orthogonal axes is investigated in view of electron paramagnetic resonance applications. The proposed solution is based on cylindrical nonradiative…
This paper is concerned with uniqueness results in inverse acoustic and electromagnetic scattering problems with phaseless total-field data at a fixed frequency. Motivated by our previous work ({\em SIAM J. Appl. Math. \bf78} (2018),…
In this paper, we investigate a resonant system comprising $N$ closely packed spherical resonators ($N>2$). We analyze how the spatial arrangement of these resonators influences the distribution of resonant frequencies, focusing on…
We present a solution method which combines the method of matched asymptotics with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonators arrays in two dimensions. The resonator geometry is…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…