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The analytical expressions for the electromagnetic potential generated from a focusing charged particle beam are indispensable in various beam physics problems. In this article, we review the theory in detail and point out the necessary…
We theoretically investigate the optical force exerted on an isotropic particle illuminated by a superposition of plane waves. We derive explicit analytical expressions for the exerted force up to quadrupolar polarizabilities. Based on…
When a convex perfectly conducting inclusion is closely spaced to the boundary of the matrix domain, a bigger convex domain containing the inclusion, the electric field can be arbitrary large. We establish both the pointwise upper bound and…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
We show that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations and provide a simple equation to find how the field evolves over time. Multiple 3D fields can be realized at different times by superposing with…
The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3…
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…
We use numerical optimization to study the properties of (1) the class of one-dimensional potential energy functions and (2) systems of point charges in two-dimensions that yield the largest hyperpolarizabilities, which we find to be within…
A method is presented to investigate diffraction of an electromagnetic plane wave by an infinitely thin infinitely conducting circular cylinder with longitudinal slots. It is based on the use of the combined boundary conditions method that…
We revisit in the framework of the classical theory the problem of the accelerated motion of an electron, taking into account the effect of the radiation emission. We present results for the momentum and energy of the electromagnetic field…
A new, fully-localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known…
Ultrashort light pulses are ubiquitous in modern research, but the electromagnetic field of the optical cycles is usually not easy to obtain as a function of time. Field-resolved pulse characterization requires either a nonlinear-optical…
In this article, the optimal control problem for a harmonic oscillator with an inequality constraint is considered. The applied energy of the oscillator during a fixed final time period is used as the performance criterion. The analytical…
Due to quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general…
The linearized problem of plasma oscillations in layer (particularly, in thin films) in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the…
The emerging field of free-electron quantum optics enables electron-photon entanglement and holds the potential for generating nontrivial photon states for quantum information processing. Although recent experimental studies have entered…
The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a…
The propagation of free electromagnetic radiation in the field of a plane gravitational wave is investigated. A solution is found one order of approximation beyond the limit of geometrical optics in both transverse--traceless (TT) gauge and…
Possibility of magnetic energy accumulation inside silicon nanoparticles at the conditions of resonant optical responses is investigated theoretically. The magnetic field distributions inside silicon nanocylinders with and without coaxial…
Ellipsometry is a powerful and well-established optical technique used in the characterisation of materials. It works by combining the components of elliptically polarized light in order to draw information about the optical system. We…