Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution

Plasmonic skyrmions are an optical manifestation of topological defects in a continuous vector field. Identifying them requires characterization of the vector structure of the electromagnetic near field on thin metal films. Here we introduce time-resolved vector microscopy that creates movies of the electric field vectors of surface plasmons with subfemtosecond time steps and a 10-nanometer spatial scale. We image complete time sequences of propagating surface plasmons as well as plasmonic skyrmions, resolving all vector components of the electric field and their time dynamics, thus demonstrating dynamic spin-momentum coupling as well as the time-varying skyrmion number. The ability to image linear optical effects in the spin and phase structures of light in the single-nanometer range will allow for entirely novel microscopy and metrology applications.

Remarks on a semilinear system in ℝn motivated by difference equations

We study some conditions of solvability of a semilinear system in ℝn, where the linear part is represented by an n × n matrix with one-dimensional kernel and the nonlinear term is a sublinear, continuous vector field.

Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems

The anisotropic perfectly matched layer (APML) defines a continuous vector field outside a rectangle domain and performs the complex coordinate stretching along the vector field. Inspired by [Z. Chen et al., Inverse Probl. Imag., 7, (2013):663–678] and based on the idea of the shortest distance, we propose a new approach to construct the vector field which still allows us to prove the exponential decay of the stretched Green function without the constraint on the thickness of the PML layer. Moreover, by using the reflection argument, we prove the stability of the PML problem in the PML layer and the convergence of the PML method. Numerical experiments are also included.

On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes

Let X = {Xt: t ≥ 0} be a stationary piecewise continuous Rd-valued process that moves between jumps along the integral curves of a given continuous vector field, and let S ⊂ Rd be a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings of S by X to the distribution of X0. Our result is illustrated by examples relating to queueing networks and stress release network models.

On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes

LetX= {Xt:t≥ 0} be a stationary piecewise continuousRd-valued process that moves between jumps along the integral curves of a given continuous vector field, and letS⊂Rdbe a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings ofSbyXto the distribution ofX0. Our result is illustrated by examples relating to queueing networks and stress release network models.