Related papers: Time-Harmonic Optical Chirality in Inhomogeneous S…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…
Optical analog computing enables powerful functionalities, including spatial differentiation, image processing, and ultrafast linear operations. Yet, most existing approaches rely on resonant or periodic structures, whose performance is…
Geometrical chirality is a property of objects that describes three-dimensional mirror-symmetry violation and therefore it requires a non-vanishing spatial extent. In contrary, optical chirality describes only the local handedness of…
A fully implicit numerical approach based on the space-time finite element method is implemented for the semilinear wave equation in 1(space) + 1(time) and 2 + 1 dimensions to explore critical collapse and search for self-similar solutions.…
The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear…
The interaction of chirped femtosecond laser pulses with hybrid materials - materials comprised of plasmon sustaining structures and resonant molecules - is scrutinized using a self-consistent model of coupled Maxwell-Bloch equations. The…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
The ability to manipulate phonon waveforms in continuous media has attracted significant research interest and is crucial for practical applications ranging from biological imaging to material characterization. Although several spatial…
Structured light enables the characterization of chirality of optically small nanoparticles by taking advantage of the helicity maximization concept recently introduced in[1]. By referring to fields with nonzero helicity density as chiral…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is…
Recent advances in the physics of resonant optical metasurfaces allowed to realize the so-called maximum chirality of planar structures by engineering their geometric parameters. Here we employ bilayer membrane metasurfaces with a square…
We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain…
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always…
Achieving intrinsic optical chirality requires breaking all mirror symmetries of an object, and maximum chirality, which allows interaction with only one helicity of light, is particularly promising for applications such as chiral sensing,…
The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of…
Scattering media, being ubiquitous in nature and critically important for assessments (e.g., biological tissues), are often considered as nuisance in optics. Here we show that it is not always the case and scattering media could be…