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In general relativity, when two black holes merge they produce a rotating (Kerr) black hole remnant. According to perturbation theory, the remnant emits "ringdown" radiation: a superposition of exponentials with characteristic complex…
The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is…
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…
We give a geometrical theory of resonances in Maxwell's equations that generalizes Mie formulae for spheres to any dielectric or metallic particle without sharp edges. We show that the electromagnetic response of a particle is given by a…
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…
Applications of cavity optomechanics span from gravitational wave detection to the study of quantum motion states in mesoscopic mechanical systems. The engineering of resonators supporting strongly interacting mechanical and optical modes…
The spectral numerical mode-matching (SNMM) method is developed to simulate the 3D layered multi-region structures. The SNMM method is a semi-analytical solver having the properties of dimensionality reduction to reduce computational costs;…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
Full-wave numerical methods based on quasinormal modes (QNMs) offer valuable physical insights and computational efficiency for analyzing electromagnetic resonators. However, despite their advantages, many researchers in electromagnetism…
Resonances are omnipresent in physics and essential for the description of wave phenomena. We present an approach for computing eigenfrequency sensitivities of resonances. The theory is based on Riesz projections and the approach can be…
Superconducting microwave resonators are reliable circuits widely used for detection and as test devices for material research. A reliable determination of their external and internal quality factors is crucial for many modern applications,…
We propose a fundamentally new method for the design of metamaterial arrays, valid for any waves modeled by the Helmholtz equation, including scalar optics and acoustics. The design and analysis of these devices is based on eigenvalue and…
We present a high-sensitivity measurement technique for mechanical nanoresonators. Due to intrinsic nonlinear effects, different flexural modes of a nanobeam can be coupled while driving each of them on resonance. This mode-coupling scheme…
We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show…
All-dielectric optical nano-resonators, exhibiting exotic near-field distributions upon excitations, have emerged as low-loss, versatile and highly adaptable components in nanophotonic structures for manipulating electromagnetic waves and…
We demonstrate the use of machine learning through convolutional neural networks to solve inverse design problems of optical resonator engineering. The neural network finds a harmonic modulation of a spherical mirror to generate a resonator…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close…
We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for higher order eigenmodes. The…
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…
The Minneart resonance is a low frequency resonance in which the wavelength is much larger than the size of the resonators. It is interesting to study the interaction between two adjacent bubbles when they are brought close together.…