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We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic…
The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations. FMM groups…
The Transfer Matrix Method (TMM) is a widely used technique for modeling linear propagation of electromagnetic waves through stratified layered media. However, since its extension to inhomogeneous and nonlinear systems is not…
Hybrid nanophotonics based on metal-dielectric nanostructures unifies the advantages of plasmonics and all-dielectric nanophotonics providing strong localization of light, magnetic optical response and specifically designed scattering…
In this work, we utilize thin dielectric meta-atoms placed on a silver substrate to efficiently enhance and manipulate the third harmonic generation. We theoretically and experimentally reveal that when the structural symmetry of the…
Fluid-particle systems are highly sensitive to particle morphologies. While many attempts have been made on shape descriptors and coupling schemes, how to simulate the particle-particle and particle-fluid interactions with a balance between…
When the sizes of photonic nanoparticles are much smaller than the excitation wavelength, their optical response can be efficiently described with a series of polarizability tensors. Here, we propose a universal method to extract the…
Topologically-engineered mechanical frames are important model constructs for architecture, machine mechanisms, and metamaterials. Despite significant advances in macroscopically fashioned frames, realization and phonon imaging of…
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local…
In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one side they could look standard, since they are, real, symmetric…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
Advanced computational tools that describe the interaction of electrons with structured nanophotonic materials are crucial for theoretical predictions, specific design tasks, and the interpretation of experimental results. These tools open…
Metasurfaces have attracted extensive interests due to their ability to locally manipulate optical parameters of light and easy integration to complex optical systems. Particularly, metasurfaces can provide a novel platform for splitting…
We report a new experimental technique for quantifying the angular distribution of light scattered by single plasmonic and metamaterial nanoscatterers, based on Fourier microscopy in a dark field confocal set up. This new set up is a…
We propose a scheme for detecting and differentiating deeply subwavelength particles based on their spatial features. Our approach combines scattering from an ultrasonically modulated nanopatterend grating with heterodyne techniques to…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long range interactions, whose properties can be tailored by choice of injected laser powers, frequencies and polarizations. We use a…
While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupling to high-order quadratures for evaluating layer potentials…
In computational phase imaging with a microscope equipped with an array of light emitting diodes as illumination unit, conventional Fourier ptychographic microscopy achieves high resolution and wide-field reconstructions but is constrained…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…