Related papers: Mode Recognition by Shape Morphing for Maxwell's E…

The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the…

This paper describes how resonance spectra and mode profiles can be used to characterize and quantify the mode-shaping effects in open-access plano-concave optical microcavities. The presented semi-analytic theory is based on the…

We present a detailed experimental characterization of the spectral and spatial structure of the confined optical modes for oxide-apertured micropillar cavities, showing good-quality Hermite-Gaussian profiles, easily mode-matched to…

We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the…

We develop a theoretical predictive model for an all-pass ring resonator that enables the most complete description of linear coupling regimes. The model is based on eigenmode decomposition of Maxwell's equations with full account of the…

Let f be a newform, as specified by its Hecke eigenvalues, on a Shimura curve X. We describe a method for evaluating f. The most interesting case is when X arises as a compact quotient of the hyperbolic plane, so that classical q-expansions…

We present a method for finding the eigenmodes of the Laplace operator acting on any compact manifold. The procedure can be used to simulate cosmic microwave background fluctuations in multi-connected cosmological models. Other applications…

Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…

We use a spatially resolved cavity ring-down technique to show that the 2D eigenmode of an unstable optical cavity has a fractal pattern, i.e. it looks the same at different length scales. In agreement with theory, we find that this pattern…

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

Capsule networks are constrained by the parameter-expensive nature of their layers, and the general lack of provable equivariance guarantees. We present a variation of capsule networks that aims to remedy this. We identify that learning all…

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…

``Can one hear the shape of a drum?'' was a question posed (and made famous) by mathematician Mark Kac in the mid-1960s. It addresses whether a deeper connection exists between the resonance modes (eigenmodes) of a drum and its shape. Here…

We propose a modular, data-driven framework for jointly learning unknown functional mappings and discovering the underlying one-parameter symmetry subgroup governing the data. Unlike conventional geometric deep learning methods that assume…

We experimentally show an all-optical multipolar decomposition of the lowest-order Eigenmodes of a single gold nanoprism using azimuthally and radially polarized cylindrical vector beams. By scanning the particle through these tailored…

In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…

Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…

In this work we investigate a combination of classical PDE constrained optimization methods and a rounding strategy based on shape optimization for the identification of interfaces. The goal is to identify radioactive regions in a…

Optical microcavities confine light to wavelength-scale volumes and are a key component for manipulating and enhancing the interaction of light, vacuum states, and matter. Current microcavities are constrained to a small number of spatial…

We present an oxide aperture microcavity with embedded quantum dots that utilizes a three contact design to independently tune the quantum dot wavelength and birefringence of the cavity modes. A polarization splitting tuning of $\sim$5 GHz…