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Metasurfaces enable powerful control of electromagnetic waves using subwavelength planar structures, but their deeply subwavelength periodicity typically suppresses propagating diffraction orders, which limits the number of available…
We study the fundamental limit on the localization precision for a subwavelength scatterer embedded in a strongly scattering environment, using the external degrees of freedom provided by wavefront shaping. For a weakly scattering target,…
The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are…
In this paper an analytical approach for calculating scattering matrix elements for the case of normal incidence of the plane electromagnetic waves on the square patch-type Frequency Selective Surface (FSS), which is placed at the interface…
A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…
Previous work developed a K-matrix formalism applicable to positive energies for the scattering between two $s$-wave interacting particles with two internal states, isotropic spin-orbit coupling and vanishing center-of-mass momentum [H.…
While controlling particle diffusion in a confined geometry is a popular approach taken by both natural and artificial systems, it has not been widely adopted for controlling light transport in random media, where wave interference effects…
Speckle patterns produced by disordered scattering systems exhibit a sensitivity to addition of individual particles which can be used for sensing applications. Using a coupled dipole model we investigate how multiple scattering can enhance…
Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity.
Modeling the propagation of light through disordered media is central to understanding and controlling wave transport in diverse optical and mesoscopic applications. Here, we present a random matrix simulation framework for modeling the…
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…
The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable…
This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…
We study wave propagation through a one-dimensional array of subwavelength resonators with periodically time-modulated material parameters. Focusing on a high-contrast regime, we use a scattering framework based on Fourier expansions and…
In an ultrasonic array system, increasing the aperture size to achieve a high resolution requires more transmit and receive channels, thus making it essential to have an analysis technique that can reconstruct the shape and physical…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density,…
Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in…
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…