Related papers: Minimum Dielectric-Resonator Mode Volumes
Efficient coupling between on-chip sources and cavities plays a key role in silicon photonics. However, despite the importance of this basic functionality, there are few systematic design tools to simultaneously control coupling between…
A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
The ubiquity of parametric resonance is continually evident in the repeated experimental observations of this phenomenon in multiple physical systems. The elementary case of 2 mode parametric resonance of order 1 involves the excitation of…
Motivated by relativistic materials, we develop a numerical scheme to support existing or state new conjectures in the spectral optimisation of eigenvalues of the Dirac operator, subject to infinite-mass boundary conditions. We study the…
We develop a multidimensional coupled channel method suitable for studying the interplay of bound state resonance and phonon assisted scattering of inert gas atoms from solid surfaces in one, two and three dimensions. This enables us to get…
Inverse electromagnetic design has emerged as a way of efficiently designing active and passive electromagnetic devices. This maturing strategy involves optimizing the shape or topology of a device in order to improve a figure of merit--a…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
The paper is devoted to optimization of resonances in a 1-D open optical cavity. The cavity's structure is represented by its dielectric permittivity function e(s). It is assumed that e(s) takes values in the range 1 <= e_1 <= e(s) <= e_2.…
Mesons as bound states of quark and anti-quark in the framework of a relativistic potential model are studied. Interaction of constituents in bound state is described by the Lorentz-scalar QCD inspired funnel-type potential with the…
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…
We propose a duality scheme for solving constrained nonsmooth and nonconvex optimization problems in a reflexive Banach space. We establish strong duality for a very general type of augmented Lagrangian, in which we assume a less…
Having knowledge on the room acoustic properties, e.g., the location of acoustic reflectors, allows to better reproduce the sound field as intended. Current state-of-the-art methods for room boundary detection using microphone measurements…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
For each degree p, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that any positive eigenvalues of the rough and Hodge Laplacians acting on differential p-forms converge to zero. In particular, on…
Optical metasurfaces have been heralded as the platform to integrate multiple functionalities in a compact form-factor, potentially replacing bulky components. A central stepping stone towards realizing this promise is the demonstration of…
Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation [M. I . Dykman, M. A. Krivoglaz, Physica Status Solidi (b) 68, 111…
We prove an optimal exponential lower bound on the width of the resonance associated to the first eigenvalue of the cavity for a general Helmholtz resonator with straight neck, in any dimension.
We prove some sharp upper bounds on the number of resonances associated with the Laplacian, or Laplacian plus potential, on a manifold with infinite cylidrical ends.
In this paper, we report a shape synthesis method for multi-mode dielectric resonator antennas (DRA) using characteristic mode theory (CMT) and a binary genetic algorithm (BGA). By including the antenna's characteristic modal responses…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…