Related papers: Nonlinear eigenvalue problem for optimal resonance…
Optical cavities are a cornerstone of photonics. They are indispensable in lasers, optical filters, optical combs and clocks, in quantum physics, and have enabled the detection of gravitational waves. Cavities transmit light only at…
In this paper, we experimentally demonstrate how discrete resonances can be used to image acoustic sources and mechanical changes in thin plates with different boundary shapes. The proposed method uses coupled numerical and experimental…
We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…
This paper presents a novel algorithm, based on use of rational approximants of a randomly scalarized boundary integral resolvent in conjunction with an adaptive search strategy and an exponentially convergent secant-method termination…
Optical microcavities have received much attention over the last decade from different research fields ranging from fundamental issues of cavity QED to specific applications such as microlasers and bio-sensors. A major issue in the latter…
We report on the design, fabrication and optical characterization of bichromatic photonic crystal cavities in thin silicon membranes, with resonances around 1550 nm wavelength. The cavity designs are based on a recently proposed photonic…
We present numerical studies of two photonic crystal membrane microcavities, a short line-defect cavity with relatively low quality ($Q$) factor and a longer cavity with high $Q$. We use five state-of-the-art numerical simulation techniques…
We demonstrate a sideband-resolved cavity electromechanical system operating at room temperature. The mechanical resonator, a strongly pre-stressed silicon nitride string, is dielectrically coupled to a three-dimensional microwave cavity…
The ability to highly localize light with strong electric field enhancement is critical for enabling higher efficiency solar cells, light sources, and modulators. While deep subwavelength modes can be realized with plasmonic resonators,…
In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue…
As was shown by N. Engheta, electromagnetic fields in two adjacent slabs bounded by two metal walls can satisfy the boundary conditions even if the distance between the two walls is much smaller than the wavelength. This is possible if one…
We study the creation of photons in a one dimensional oscillating cavity with two perfectly conducting moving walls. By means of a conformal transformation we derive a set of generalized Moore's equations whose solution contains the whole…
Cavities, because they trap waves for long times due to their reflecting walls, are used in a vast number of scientific domains. Indeed, in these closed media and due to interferences, the free space continuum of solutions becomes a…
The eigenvalue problem for radial potentials is considered in a space whose spatial coordinates satisfy the SU(2) Lie algebra. As the consequence, the space has a lattice nature and the maximum value of momentum is bounded from above. The…
Near-unstable cavities have been proposed as an enabling technology for future gravitational wave detectors, as their compact structure and large beam spots can reduce the coating thermal noise of the interferometer. We present a tabletop…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
An analytical solution of the Helmholtz equation for electromagnetic field distribution in a resonant cavity with elliptic cross-section is found. We compare the frequencies of the eigenmodes with numerical and experimental values for a…
We study a variational model in nonlinear elasticity allowing for cavitation which penalizes both the volume and the perimeter of the cavities. Specifically, we investigate the approximation (in the sense of {\Gamma}-convergence) of the…
This article presents a detailed analysis, based on the first-principles finite-difference time-domain method, of the resonant frequency, quality factor (Q), mode volume (V), and radiation pattern of the fundamental (HE11) mode in a…
We discuss electromagnetic modes in cavities formed by metamaterials with negative refraction and demonstrate that the straightforward approach to substitute negative values of the electric permittivity and the magnetic permeability leads…