Reflection and refraction of the electromagnetic field in a semi-infinite plasma

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite (half-space) plasma, as well as the reflection coefficient, by using a general procedure based on equations of motion and electromagnetic potentials. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in plasma is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

Proca and electromagnetic fields

In the framework of the proper orthochronous Lorentz group, the old connection is revived between the electromagnetic field characterized by a self-dual tensor and a traceless second-rank spinor obeying the Proca equation. The relationship between this spinor and the Hertz potential also considered as a self-dual tensor is emphasized. The extension of this formalism to meet the covariance under the full Lorentz group is also discussed.     

Response of a semi-infinite cubic lattice to uniform electric fields

Self-consistent field equations for the dipole moments of point polarizable atoms in slabs of cubic lattices with a uniform applied electric field are constructed. Results of Toeplitz operator theory are used to characterize the ranges of atomic polarizability for which there are unique solutions to the equations. A normal mode analysis of the frequency spectrum of the coupled dipole lattice is given and is used in the interpretation of the results for the simple cubic lattice. Approximate solutions of the self-consistent field equations for the semi-infinite lattice are constructed which display the exponential approach of the atomic dipoles to their infinite lattice value with increasing penetration into the lattice.     

Gravitational and electromagnetic fields of a charged tachyon

An axially symmetric exact solution of the Einstein-Maxwell equations is obtained and is interpreted to give the gravitational and electromagnetic fields of a charged tachyon. Switching off the charge parameter yields the solution for the uncharged tachyon which was earlier obtained by Vaidya. The null surfaces for the charged tachyon are discussed.     

Mapping electromagnetic fields near a subwavelength hole

We study, both experimentally and theoretically, the scattering of electromagnetic waves by a subwavelength hole fabricated in a thin metallic film. We employ the scanning near-field optical microscopy in order to reconstruct experimentally the full three-dimensional structure of the electromagnetic fields in the vicinity of the hole. We observe an interference of all excited waves with an incident laser beam which allows us to gain the information about the wave phases. Along with the well-known surface plasmon polaritons propagating primarily in the direction of the incident beam polarization, we observe the free-space radiation diffracted by the hole. We compare the experimental results with the fields of pure electric and pure magnetic dipoles as well as with direct numerical simulations. We confirm that a single hole in a thin metallic film excited at the normal incidence manifests itself as an effective magnetic dipole in the visible spectral range.     

Pauli equation for a particle in metric and electromagnetic fields

A Pauli theory (Pauli equation and definition of probability current and density) for a particle in weak metric and arbitrary electromagnetic fields is treated. To formulate non-relativistic quantum mechanical problems in arbitrary electromagnetic fields and weak metrics (non-inertial systems, gravitational fields which are distant fields of arbitrary distribution of masses, gravitational waves) it is not necessary to make use of the general-relativistic Dirac equation. Close analogies to the known Pauli theory with electromagnetic fields exist. For different metric fields the corresponding Hamiltonians are given. For quantum systems (H-atoms) which are disturbed by a homogeneous gravitational field and a gravitational wave the resulting shift of energy levels and the transition probability is calculated.     

Radiation from a charge in nonuniform orthogonal electromagnetic fields

It is shown by the methods of classical electrodynamics that, with defined conditions in arbitrary nonuniform fields, depending on two Cartesian coordinates, harmonic motion of a charge can be achieved over a plane trajectory. The radiation from the charge has specific singularities, which are conditioned by the magnitude and nature of the nonuniformity of external fields in the region of the trajectory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 101–107, July, 1973.     

Rectilinear motion of a charged magneton in electromagnetic fields

Uniform and rectilinear motion of a classical spin particle, a charged magneton, is considered in external electromagnetic fields of special type. The equations of motion are solved in both the vector and tensor methods of describing the spin. The rectilinear motion of a hyperbolically accelerated magneton is also considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 62–65, April, 1980.It is a pleasant duty to thank Professor V. G. Bagrov for suggesting the problem and discussing the results of the paper.     

Gravitational and electromagnetic fields near a de Sitter-like infinity

We present a characterization of general gravitational and electromagnetic fields near de Sitter-like conformal infinity which supplements the standard peeling behavior. This is based on an explicit evaluation of the dependence of the radiative component of the fields on the null direction from which infinity is approached. It is shown that the directional pattern of radiation has a universal character that is determined by the algebraic (Petrov) type of the spacetime. Specifically, the radiation field vanishes along directions opposite to principal null directions.     

Neutrinos in electromagnetic fields and moving media

The history of the development of the theory of neutrino-flavor and neutrino-spin oscillations in electromagnetic fields and in a medium is briefly surveyed. A new Lorentz-invariant approach to describing neutrino oscillations in a medium is formulated in such a way that it makes it possible to consider the motion of a medium at an arbitrary velocity, including relativistic ones. This approach permits studying neutrinospin oscillations under the effect of an arbitrary external electromagnetic field. In particular, it is predicted that, in the field of an electromagnetic wave, new resonances may exist in neutrino oscillations. In the case of spin oscillations in various electromagnetic fields, the concept of a critical magnetic-field-component strength is introduced above which the oscillations become sizable. In considering neutrino oscillations in moving matter, it is shown within the Lorentz-invariant formalism that the relativistic motion of matter significantly affects the character of neutrino oscillations and can radically change the conditions under which the oscillations are resonantly enhanced. Possible new effects in neutrino oscillations are discussed for the case of neutrino propagation in relativistic fluxes of matter.     

The motion of a charged particle in magnetostatic and electromagnetic fields

The exact solutions are given of the relativistic equations of motion for both the momentum and displacement of a charged particle which is injected into an arbitrary number of intense electromagnetic waves of any polarization and frequency, including zero, all of which propagate parallel to a uniform magnetostatic field with the speed of light. The solutions are implicit in time.     

Electron in crossed constant electromagnetic fields and a plane wave field

The Dirac equation for an electron interacting with constant homogeneous orthogonal magnetic and electric fields (E = H) and with the field of a plane wave being propagated in a direction perpendicular sto E and H is solved exactly. The plane wave field is hence considered either classically or in a quantized manner, or as the field of a wave consisting of classical and quantized parts.     

Stationary electromagnetic fields around a rotating black hole

The general stationary solution of Maxwell's equations in the Kerr background geometry is given. Future applications are outlined.     

Four component electromagnetic fields and electrodynamics

Dirac-Maxwell equations with magnetic monopoles are generalized to electromagnetic fields by introducing fourth components to the fields and their solutions are obtained. The formalism is presented into tensor, dyonic as well as quaternionic forms and conservation theorems for the field energy and momenta are obtained involving the new contribution from the mutual interaction of the fields and currents. The generation of the standard modeste, tm andtem ofem waves is also obtained in the formalism.