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Probing optical excitations with nanometer resolution is important for understanding their dynamics and interactions down to the atomic scale. Electron microscopes currently offer the unparalleled ability of rendering spatially-resolved…
Photon splitting due to vacuum polarization in a laser field is considered. Using an operator technique, we derive the amplitudes for arbitrary strength, spectral content and polarization of the laser field. The case of a monochromatic…
This paper deals with the optimal synthesis of aperture fields for (radiating) near-field communications in obstructed environments. A physically consistent model based on knife-edge diffraction is used to formulate the problem as a…
Modern nanophotonic and meta-optical devices utilize a tremendous number of structural degrees of freedom to enhance light--matter interactions. A fundamental question is how large such enhancements can be. We develop an analytical…
One of the fundamental limits of classical optical microscopy is the diffraction limit of optical resolution. It results from the finite bandwidth of the optical transfer function (or OTF) of an optical microscope, which restricts the…
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting…
Direct observation of electric potential and field variation near local scatterers like grain boundaries, triple points and voids in thin platinum films studied by scanning tunneling potentiometry is presented. The field is highest at a…
Employing plasmonic antennas for subdiffraction focusing of light on recording media requires to take into account the complete structure of the medium, including dielectric cover layers. We find, with finite difference time domain…
The electron motion in a strong perpendicular magnetic field close to the impenetrable stripe is considered by making use of the singular integral equation technique. The energy spectrum is calculated and compared with the energy spectrum…
We put forward a theory on the optical force exerted upon a dipolar particle by a stationary and ergodic partially coherent light field. We show through a rigorous analysis that the ensemble averaged electromagnetic force is given in terms…
The space-time focusing of a (continuous) succession of localized X-shaped pulses is obtained by suitably integrating over their speed, i.e., over their axicon angle, thus generalizing a previous (discrete) approach. First, new Superluminal…
We consider eigenvalue problems for general elliptic operators of arbitrary order subject to homogeneous boundary conditions on open subsets of the euclidean N-dimensional space. We prove stability results for the dependence of the…
The Abbe diffraction limit, tied to the fundamental spatial bandwidth constraint imposed by any physical aperture, remains the primary barrier to achieving ultimate far-field optical resolution and precise light-matter interactions.…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
We discuss the dynamics of a charged nonrelativistic particle in electromagnetic field of a rotating magnetized celestial body. The equations of motion of the particle are obtained and some particular solutions are found. Effective…
Here, we demonstrate the radiative polarization of high-energy electron beams in collisions with ultrashort pulsed bi-chromatic laser fields. Employing a Boltzmann kinetic approach for the electron distribution allows us to simulate the…
In strong field laser physics it is a common practice to use the high-order harmonic cutoff to estimate the laser intensity of the pulse that generates the harmonic radiation. Based on the semiclassical arguments it is possible to find a…
We give an upper bound on the maximal eigenvalue of the adjacency matrix of a connected graph in terms of its maximum degree, diameter and order. This bound is best possible up to a constant factor and improves prevoius results of…
We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide…
The possibility of the precise measurement of the electron beam energy using absorption of radiation by electrons in a static and homogeneous magnetic field in a range up to a few hundred GeV energies, was considered in [1]. With the…