Effect of Energy Conservation Law, Space Dimension, and Problem Symmetry on the Poynting Vector Field Singularities

A brief review is given of the author recent achievements in classifying singular points of the Poynting vector patterns in electromagnetic fields of complex configuration. The deep connection between the topological structure of the force lines pattern and the law of energy conservation, the symmetry of the problem, and the dimension of the space has been unveiledComment: 12 pages, 8 figure

Nonlinear Pattern Selection in Binary Mixture Convection with Through-Flow

The pattern selection problem in binary-mixture convection in an extended channel with a lateral through-flow is presented. The through-flow breaks left--right parity and changes pattern dynamics dramatically. The problem is studied based on computer simulation of the complete set of hydrodynamic equations (Oberbeck-Boussinesq approximation) in the two-dimensional rectangular channel with aspect ratio $\Gamma = 12$ and convection-suppressing lateral boundary conditions. A wide variety of new dynamical patterns is obtained, discussed and classified.Comment: 9 pages and 2 figure

The Poynting vector field generic singularities in resonant scattering of plane linearly polarized electromagnetic waves by subwavelength particles

We present the results of a study of the Poynting vector field generic singularities at the resonant light scattering of a plane monochromatic linearly polarized electromagnetic wave by a subwavelength particle. We reveal the impact of the problem symmetry, the spatial dimension, and the energy conservation law on the properties of the singularities. We show that, in the cases when the problem symmetry results in the existence of an invariant plane for the Poynting vector field lines, a formation of a standing wave in the immediate vicinity of a singularity gives rise to a saddle-type singular point. All other types of singularities are associated with vanishing at the singular points, either (i) magnetic field, for the polarization plane parallel to the invariant plane, or (ii) electric field, at the perpendicular orientation of the polarization plane. We also show that in the case of two-dimensional problems (scattering by a cylinder), the energy conservation law restricts the types of possible singularities only to saddles and centers in the non-dissipative media and to saddles, foci, and nodes in dissipative. Finally, we show that dissipation affects the (i)-type singularities much stronger than the (ii)-type. The same conclusions are valid for the imaginary part of the Poynting vector in problems where the latter is regarded as a complex quantity. The singular points associated with the formation of standing waves are different for real and imaginary parts of this complex vector field, while all other singularities are common. We illustrate the general discussion by analyzing singularities at light scattering by a subwavelength Germanium cylinder with the actual dispersion of its refractive index.Comment: 20 pages, 3 figures, 2 table

Nature of the Poynting Vector Field Singularities in Resonant Light Scattering by Nanoparticles

Singularities of the Poynting vector field at resonant light scattering by nanoparticles are discussed and classified. It is shown that there are two generic types of them, namely (i) the singularities related to the vanishing of the magnetic (and/or electric) field at the singular points and (ii) the singularities related to the formation of standing waves in the proximity of the singular points. The connection of these types of singularities to the topology of the singular points and the space dimension (3D vs. 2D) is revealed.Comment: 9 pages, 4 figure