Related papers: A model for chaotic dielectric microresonators
We show analytically that the quality ($Q$) factor of magnetic and electric Mie modes in a lossless dielectric spherical resonator with high refractive index ($n \gg 1$) scales as $n^{2j+1}$ and $n^{2j+3}$ respectively, where $j$ denotes…
The aim of this paper is to provide a mathematical theory for understanding the mechanism behind the double-negative refractive index phenomenon in chiral materials. The design of double-negative metamaterials generally requires the use of…
We study the spectral density of factor models of multivariate time series. By making use of the Random Matrix Theory we analytically quantify the effect of noise dressing on the spectral density due to the finiteness of the sample. We…
Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long range interactions, whose properties can be tailored by choice of injected laser powers, frequencies and polarizations. We use a…
This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions…
To trace the particle nature of dark matter (DM) from cosmic microwave background observations, we study the co-evolution of DM density perturbation and primordial metric perturbation during DM production. Solving the perturbative Einstein…
This paper considers how the finite dimensions of a photonic crystal placed inside a resonator or waveguide affect the law of electron beam instability. The dispersion equations describing e-beam instability in the finite photonic crystal…
Electromagnetic response of dielectric resonators with high refractive index is governed by optically induced electric and magnetic Mie resonances facilitating confinement of light with the amplitude enhancement. However, strong…
In this paper we theoretically study electromagnetic reflection, transmission, and scattering properties of periodic and random arrays of particles which exhibit both electric-mode and magnetic-mode resonances. We compare the properties of…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
We develop a microscopic large-$N$ theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory, which reduces to the well-known random…
With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with lossless impedance boundary. With increasing…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
Efficient micro-resonators simultaneously require a large quality factor $Q$ and a small volume $V$. However, the former is ultimately limited by bending losses, the unavoidable radiation of energy of a wave upon changing direction of…
The inelastic scattering rates of quasiparticles in a two-dimensional d-wave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We…
Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in…
We consider meta materials made from a two-dimensional dielectric rod-type photonic crystal. The magnetic response is studied within the recently developed homogenization theory and we in particular study the effects of topology and…
Here the multipole approach [13], in combination with the density matrix formalism is used for establishing of the model for MMs with gain. This approach allows us to investigate analytically or semi-analytically the interplay between gain…
We study wave propagation through a one-dimensional array of subwavelength resonators with periodically time-modulated material parameters. Focusing on a high-contrast regime, we use a scattering framework based on Fourier expansions and…
In this work, a long-cavity semiconductor laser subject to optical feedback is exploited to generate repetitive temporal patterns with enhanced intra-pattern sample diversity. Stable limit cycle dynamics characterized by multiple frequency…