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.

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

Singularities of the Poynting vector field subwavelength patterns in resonant light scattering by nanoparticles are discussed and classified. There are two generic types of the singularities, 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 proximity to the singular points. The connection of these types of singularities to the topology of the singular points, space dimension (3D vs.

Anapole: Its birth, life, and death.

Despite the recent extensive study of the nonradiating (anapole) mode in the resonant light scattering by nanoparticles, the key questions, about the dynamics of its excitation at the leading front of the incident pulse and collapse behind the trailing edge, still remain open. We answer the questions, first, by direct numerical integration of the complete set of the Maxwell equations, describing the scattering of a rectangular laser pulse by a dielectric cylinder. The simulation shows that while the excitation and the collapse periods, both have the same characteristic time-scale, the dynamics of these processes are qualitatively different.

Ultimate Absorption in Light Scattering by a Finite Obstacle.

Based on fundamental properties of the light scattering by a particle under a plane, linearly polarized wave illumination, we rigorously prove the existence of the ultimate upper limit for the light absorption by any partial mode and calculate this limit explicitly. The limit is a certain simple universal function of the incident light wave number, and the multipolarity of the corresponding partial mode solely. It does not depend on the optical constants of the scatterer, its size, or even its shape.

Laser heating of dielectric particles for medical and biological applications.

We consider the general problem of laser pulse heating of a spherical dielectric particle embedded in a liquid. The discussed range of the problem parameters is typical for medical and biological applications. We focus on the case, when the heat diffusivity in the particle is of the same order of magnitude as that in the fluid.

Small Dielectric Spheres with High Refractive Index as New Multifunctional Elements for Optical Devices.

The future of ultra-fast optical communication systems is inevitably connected with progress in optical circuits and nanoantennas. One of the key points of this progress is the creation of elementary components of optical devices with scattering diagrams tailored for redirecting the incident light in a desired manner. Here we demonstrate theoretically and experimentally that a small, simple, spatially homogeneous dielectric subwavelength sphere with a high refractive index and low losses (as some semiconductors in the visible or near infrared region) exhibits properties allowing to utilize it as a new multifunctional element for the mentioned devices.

Tuned Mullins-Sekerka instability: exact results.

Mullins-Sekerka's instability at 3D self-similar growth of a spherical seed crystal in an undercooled fluid is discussed. The exact solution of the linearized stability problem is obtained. It is quite different from the conventional results of the quasisteady approximation.

Beyond the hybridization effects in plasmonic nanoclusters: diffraction-induced enhanced absorption and scattering.

It is demonstrated herein both theoretically and experimentally that Young's interference can be observed in plasmonic structures when two or three nanoparticles with separation on the order of the wavelength are illuminated simultaneously by a plane wave. This effect leads to the formation of intermediate-field hybridized modes with a character distinct of those mediated by near-field and/or far-field radiative effects. The physical mechanism for the enhancement of absorption and scattering of light due to plasmonic Young's interference is revealed, which we explain through a redistribution of the Poynting vector field and the formation of near-field subwavelength optical vortices.

Link of microscopic and macroscopic fields in nematodynamics.

We have found an unusual and unexpected link between micro- (nematic director) and macro- (velocity) fields in nematodynamics, which exhibits itself in extended defects of a new type. In particular, we have shown that black lines (BLs) observed in electroconvection of a homeotropically aligned nematic layer are simultaneously Bloch's domain walls for the director field and lines of zero velocity intersecting a roll pattern for the convection. A detailed experimental study revealing the fine structure of BLs and their point defects is presented.

Patterns in dissipative systems with weakly broken continuous symmetry.

Patterns in dissipative systems with weakly broken symmetry are studied based upon the simplest canonical equation (generalized Nikolaevskiy model). A generic cubic dispersion equation governing stability of steady spatially periodic patterns is derived and analyzed. A domain of stable states in the space of the problem parameters (stability balloon) is obtained.

Light scattering by a finite obstacle and fano resonances.

The conditions for observing Fano resonances at elastic light scattering by a single finite-size obstacle are discussed. General arguments are illustrated by consideration of the scattering by a small (relative to the incident light wavelength) spherical obstacle based upon the exact Mie solution of the diffraction problem. The most attention is paid to recently discovered anomalous scattering.

Anomalous light scattering by small particles.

Light scattering by a small spherical particle with a low dissipation rate is discussed based upon the Mie theory. It is shown that if close to the plasmon (polariton) resonance frequencies the radiative damping prevails over dissipative losses, sharp giant resonances with very unusual properties may be observed. In particular, the resonance extinction cross section increases with an increase in the order of the resonance (dipole, quadrupole, etc.

General exact solution to the problem of the probability density for sums of random variables.

The exact explicit expression for the probability density p(N)(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands.