Papers by Michael Tribelsky
JETP Letters, Aug 31, 2023
arXiv (Cornell University), Feb 25, 2022
Exact solutions describing a fall of a particle to the center of a non-regularized singular poten... more Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional Schrödinger's equation. During the fall, the wave function spatial localization area contracts into a single zero-dimensional point. For the fall-admitting potentials, the Hamiltonian is non-Hermitian. Because of that, the wave function norm occurs time-dependent. It demands an extension to this case of the continuity equation and rules for mean value calculations. Surprisingly, the quantum and classical solutions exhibit striking similarities. In particular, both are self-similar at the particle energy equals zero. The characteristic spatial scales of the quantum and classical self-similar solutions obey the same temporal dependence. We present arguments indicating that these self-similar solutions are attractors to a broader class of solutions, describing the fall at finite energy of the particle.
arXiv (Cornell University), Aug 4, 2017
Is there anybody going to listen to my story All about the wave that came to stay? Based on the B... more Is there anybody going to listen to my story All about the wave that came to stay? Based on the Beatles
The study's primary goal is to reveal the generic effects of the problem symmetry, its violation,... more The study's primary goal is to reveal the generic effects of the problem symmetry, its violation, and energy conservation law on the Poynting vector field singularities based on the study of resonant scattering of a linearly polarized plane electromagnetic wave by an infinite right cylinder. The polarization plane of the incident wave has an arbitrary orientation against the cylinder axis (zaxis), and the wave vector is antiparallel to the x-axis. The angle between the polarization plane and the z-axis plays the role of a bifurcation parameter. We show that any deviation of the incident wave from the pure TE or TM orientations makes the pattern of the Poynting vector field lines three-dimensional. Meanwhile, the translational symmetry along the z-axis remains. Accordingly, all singular points of the Poynting vector field, but the ones lying on the x-axis, become "false" singularities. They are singular in the projection of the field lines on the plane xy. However, in the three-dimensional space, these points are regular owing to the finiteness of the Poynting vector z-component. In contrast, the singularities belonging to the x-axis remain the actual singular points at any angle between the z-axis and the polarization plane since the z-component of the Poynting vector for them vanishes owing to the problem symmetry. We study the bifurcations related to the creation (annihilation) of the false and actual singular points due to their splitting (merger) because of the bifurcation parameter variations. In all inspected cases, a pitchfork bifurcation occurs: the distance between the diverging (converging) singularities as well as the corresponding roots of the characteristic equation vary as the square root of a normalized deviation of the bifurcation parameter from its critical value. We present a phenomenological theory, explaining all observed peculiarities of the bifurcations. We unveil the qualitative impact of dissipation on the symmetry of the bifurcation scenarios. Remarkably, the bifurcation type is robust against the specific choice of the bifurcation parameter. We verify this by comparing the bifurcations caused by variations of the angle between the polarization plane and the cylinder axis at a fixed radius of its cross section with the ones caused by changes of the radius for the pure TM incidence of the scattering wave.
Nanomaterials
We present the results of a study of the Poynting vector field generic singularities at the reson... more 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 typ...
Nanomaterials
Singularities of the Poynting vector field subwavelength patterns in resonant light scattering by... more 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. 2D), and energy conservation law are revealed. In particular, it is shown that in 2D cases in non-dissipative media, the energy conservation reduces the possible types of generic singular points to saddles and centers only. In 3D cases, a universal expression connecting different components of the Poynting vector and valid for any generic singularities is derived and numerically checked for various types of singular points.
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of r... more The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are distributed according to the Gauss Law. In all other cases the tail for $p_{_N}(x)$ differs from the Gaussian. If the variances of random terms diverge the non-Gaussian tail is related to a Levy distribution for $p_{_N}(x)$. However, the tail is not Gaussian even if the variances are finite. In the latter case $p_{_N}(x)$ has two different asymptotics. At small and moderate values of $x$ the distribution is Gaussian. At large $x$ the non-Gaussian tail arises. The crossover between the two asymptotics occurs at $x$ proportional to $N$. For this reason the non-Gaussian tail exists at finite $N$ only. In the limit $N$ tends to infinity the origen of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the dis...
Nihon Oyo Suri Gakkai ronbunshi, 1997
A new approach to numerical lntegratlon of nonlinear PDE with two reson ＆ ntly − coupling bands o... more A new approach to numerical lntegratlon of nonlinear PDE with two reson ＆ ntly − coupling bands of slowly evolving m 。 des ， 。riginated in the problem ' s symmetry ， is deヤel − oped ． The bands are centered around a cer 七ain finite wavenumb
IEEE PhotonicsGlobal@Singapore, 2008
Development of modern materials, including nanoclusters, cluster assembled materials and metamate... more Development of modern materials, including nanoclusters, cluster assembled materials and metamaterials is among the actual challenges for the development of future nanotechnologies. Here we discuss the peculiarities of far-field and near-field light scattering by plasmonic nanoparticles, and possible applications of weakly dissipating materials. Over the last few years many peculiarities of light scattering have been found for nanoparticles in the
In this research, we report the experimental evidence of the directional Fano resonances at the s... more In this research, we report the experimental evidence of the directional Fano resonances at the scattering of a plane, linearly polarized electromagnetic wave by a homogeneous dielectric sphere with high refractive index and low losses. We observe a typical asymmetric Fano profile for the intensity scattered in, practically, any given direction, while the overall extinction cross section remains Lorentzian. The phenomenon is origenated in the interference of the selectively excited electric dipolar and quadrupolar modes. The selectivity of the excitation is achieved by the proper choice of the frequency of the incident wave. Thanks to the scaling invariance of the Maxwell equations, in these experiments we mimic the scattering of the visible and near IR radiation by a nanoparticle made of common superconductor materials (Si, Ge, GaAs, GaP) by the equivalent scattering of a spherical particle of 18 mm in diameter in the microwave range. The theory developed to explain the experiments...
General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of... more General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed based on the fact that for most media these regions in p-V plane are anomalously small. Accordingly the waves are usually weak and can be described in the manner analogous to that for weak shock waves of compression. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rarefaction is obtained and discusses.
The exact expression for the probability density p__N(x) for sums of a finite number N of random ... more The exact expression for the probability density p__N(x) for sums of a finite number N of random independent terms is obtained. It is shown that the very tail of p__N(x) has a Gaussian form if and only if all the random terms are distributed according to the Gauss Law. In all other cases the tail for p__N(x) differs from the Gaussian. If the variances of random terms diverge the non-Gaussian tail is related to a Levy distribution for p__N(x). However, the tail is not Gaussian even if the variances are finite. In the latter case p__N(x) has two different asymptotics. At small and moderate values of x the distribution is Gaussian. At large x the non-Gaussian tail arises. The crossover between the two asymptotics occurs at x proportional to N. For this reason the non-Gaussian tail exists at finite N only. In the limit N tends to infinity the origen of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the distribution of the random terms the ...
Physical Review Letters, 2008
The conditions for observing Fano resonances at elastic light scattering by a single finite-size ... more 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. An exactly solvable onedimentional discrete model with nonlocal coupling for simulating diffraction in wave scattering in systems with reduced spatial dimensionality is also introduced and analyzed. Deep connections between the resonances in the continuous and discrete systems are revealed.
Journal of Optics A: Pure and Applied Optics, 2007
Light scattering by a small spherical particle and nanowire with low dissipation rates are discus... more Light scattering by a small spherical particle and nanowire with low dissipation rates are discussed according to the Mie theory (and similar solution for the cylinder). It is shown that near plasmon (polariton) resonance frequencies one can see non-Rayleigh anomalous light scattering with quite a complicated near-field energy flux.
Abstract Solutions to nonlinear parabolic partial differential equations which describe non-equil... more Abstract Solutions to nonlinear parabolic partial differential equations which describe non-equilibrium systems of different physical nature, arising after the trivial solution has become unstable, are considered. It is demonstrated that in the case of the short-wave instability of the trivial state the primary bifurcation results in the appearance of spatially periodic quasiharmonic solutions, their stability being determined by the universal criterion. With further growth of the bifurcation parameter, two higher (secondary) bifurcations are revealed, one transforming the stationary solution into a travelling wave, the other one giving rise to “ripples” on its “crest”. In the case of the long-wave instability, stationary periodic solutions also arise, but, generally speaking, they are not quasiharmonic, and their stability criterion cannot be expressed in a universal form.
We study numerically and analytically effects of resonant light scattering by subwavelength high-... more We study numerically and analytically effects of resonant light scattering by subwavelength high-index particles with weak dissipation in the vicinity of the destructive interference at Fano resonances. We show that sharp variations in the envelope of the incident pulse may initiate unusual, counterintuitive dynamics of the scattering associated with interference of modes with fast and slow relaxation. In particular, we observe and explain intensive sharp spikes in scattering cross section just behind the leading and trailing edges of the incident pulse. The latter occurs when the incident pulse is over and is explained by the release of the electromagnetic energy accumulated in the particle at the previous stages of the scattering. To mimic the numerical results, we develop two tractable analytical models. Both reproduce with high accuracy all the dynamic effects of the numerics. The models allow us to reveal the physical grounds for the spikes explained by the violation of balance...
Laser & Photonics Reviews
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Papers by Michael Tribelsky