Related papers: Nonlinear eigenvalue problem for optimal resonance…
In this paper, we propose to analyze stable and unstable modes of generic image denoisers through nonlinear eigenvalue analysis. We attempt to find input images for which the output of a black-box denoiser is proportional to the input. We…
We report on the design, realization and experimental investigation by spatially resolved monochromated electron energy loss spectroscopy (EELS) of high quality factor cavities with modal volumes smaller than $\lambda^3$, with $\lambda$ the…
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.
The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same…
The quantum entanglement between two excitons in two-dimensional materials, embedded in an optical microcavity, was investigated. The energy eigenstates of a Jaynes-Cummings like Hamiltonian for two qubits coupled to a single cavity mode…
We demonstrate tunable frequency-converted light mediated by a chi-(2) nonlinear photonic crystal nanocavity. The wavelength-scale InP-based cavity supports two closely-spaced localized modes near 1550 nm which are resonantly excited by a…
We present a comprehensive study of internal quality factors in superconducting stub-geometry 3-dimensional cavities made of aluminum. We use wet etching, annealing and electrochemichal polishing to improve the as machined quality factor.…
We propose an iterative method to find pointwise growth exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates capture pointwise stability and instability in extended systems…
We prove the existence and the uniqueness of a local maximal solution to an $H^1$-critical stochastic wave equation with multiplicative noise on a smooth bounded domain $\mathcal{D} \subset \mathbb{R}^2$ with exponential nonlinearity.…
We present the results of theoretical and experimental studies of dispersively coupled (or "membrane in the middle") optomechanical systems. We calculate the linear optical properties of a high finesse cavity containing a thin dielectric…
We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system…
Demonstrating and exploiting the quantum nature of larger, more macroscopic mechanical objects would help us to directly investigate the limitations of quantum-based measurements and quantum information protocols, as well as test long…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…
This works deals with one dimensional infinite perturbation - namely line defects - in periodic media. In optics, such defects are created to construct an (open) waveguide that concentrates light. The existence and the computation of the…
We studied the interaction of a two-level atom with a frequency modulated cavity mode in an ideal optical cavity. The system, described by a Jaynes-Cumming Hamiltonian, gave rise to a set of stiff nonlinear first order equations solved…
The amplification of disk oscillations resulting from nonlinear resonant couplings between the oscillations and a disk deformation is examined. The disk is geometrically thin and general relativistic with a non-rotating central source. A…
We introduce a numerical procedure which permits to drastically accelerate the design of multimode photonic crystal resonators. Specifically, we demonstrate that the optical response of an important class of such nanoscale structures is…
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…