arXiv subjects

Michael I. Tribelsky

Publications and source records attributed to Michael I. Tribelsky.

At least 19 recordsLinked to original sources

arXiv2026

Surface-pinned nonsingular topologically charged defects in nanoplasmonics

We discuss surface-pinned, topologically charged, nonsingular defects (SD) in light scattering by a plasmonic object. They follow from exact Maxwell boundary conditions and are purely topological---unaffected by surface forces. At optical frequencies, in (quasi) 2D, they appear in the electric and Poynting vector fields for $H^{(z)}$ polarization, not for $E^{(z)}$. Exact solutions for a circular cylinder reveal topological charge-conserving bifurcations involving SDs with bulk singularities or SDs alone, and contraction of defect regions under loss.

physics.optics↗

arXiv2025

The Eckhaus instability: from initial to final stages

A systematic analysis of the Eckhaus instability in the one-dimensional Ginzburg-Landau equation is presented. The analysis is based on numerical integration of the equation in a large (xt)-domain. The initial conditions correspond to a stationary, unstable spatially periodic solution perturbed by "noise." The latter consists of a set of spatially periodic modes with small amplitudes and random phases. The evolution of the solution is examined by analyzing and comparing the dynamics of three key characteristics: the solution itself, its spatial spectrum, and the value of the Lyapunov functional. All calculations exhibit four distinct, mutually agreed, well-defined regimes: (i) rapid decay of stable perturbations; (ii) latent changes, when the solution and the Lyapunov functional undergo minimal alterations while the Fourier spectrum concentrates around the most unstable perturbations; (iii) a phase-slip period, characterized by a sharp decrease in the Lyapunov functional; (iv) slow relaxation to a final stable state.

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arXiv2024

The Poynting vector field singularities: Effects of symmetry and its violation

The phenomenological theory revealing the generic effects of the problem symmetry, its violation, and energy conservation law on the singularities of the Poynting vector field is presented. The bifurcation scenario of their formation (annihilation) under variations of the problem parameters is elucidated. The results describe the singularities in scattering a linearly polarized plane electromagnetic wave. However, they are valid for any configuration of the incident beam at its scattering by a subwavelength particle. The author shows that topological changes in the pattern of the Poynting vector field occur through a finite number of pitchfork bifurcations. It means that the patterns are topologically stable under variations of the problem parameter(s) that lie between the bifurcation values. The latter ensures that the discussed topological properties of the problem are robust to weak symmetry violation, which is inevitable in any actual experiment. The general consideration is illustrated by a detailed study of singularities in scattering by an infinite right circular germanium cylinder. The results open the possibility of fitting and controlling radiation patterns on subwavelength scales important for various nanotechnologies.

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arXiv2023

Fall of a Particle to the Center of a Singular Potential: Classical vs. Quantum Exact Solutions

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.

quant-ph↗

arXiv2023

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 unveiled

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arXiv2022

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.

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arXiv2022

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.

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arXiv2021

Two tractable models of non-stationary light scattering by subwavelength particles and their application to Fano resonances

We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on generalization of the temporal coupled-mode theory, and the other employs the normal mode approach. 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. To exhibit the power of the models, we apply them to explain the dynamic light scattering of a square-envelope pulse by an infinite circular cylinder made of $GaP$, when the pulse carrier frequency lies in the vicinity of the destructive interference at the Fano resonances. 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 electromagnetic energy released in the particle at the previous scattering stages. The accuracy of the models is checked against their comparison with results of the direct numerical integration of the complete set of Maxwell's equations and occurs very high. The models' advantages and disadvantages are revealed, and the ways to apply them to other types of dynamic resonant scattering are discussed.

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arXiv2021

Fall of Quantum Particle to the Center: Exact results

The fall of a particle to the center of a singular potential U(r) is one of a few fundamental problems of quantum mechanics. Nonetheless, its solution is not complete yet. The known results just indicate that if U(r) decays fast enough at r tends to zero, the spectrum of the Schrodinger equation is not bounded from below. However, the wave functions of the problem are singular at r = 0 and do not admit the limiting transition to the wave function of the ground state. Therefore, the unboundedness of the spectrum is only the necessary condition. To prove that a quantum particle indeed can fall to the center, a wave function describing the fall should be obtained explicitly. This is done in the present paper. Specifically, an exact solution of the time-dependent Schrodinger equation describing the fall to the center is obtained and analyzed. The law describing the collapse to a single point of the region of the wave function localization is obtained explicitly, as well as the temporal dependences of the average kinetic and potential energy of the falling particle and its momentum. It is shown that the known necessary conditions for the particle to fall simultaneously are sufficient.

quant-ph↗

arXiv2020

Resonant scattering of electromagnetic waves by small metal particles

The review is devoted to a discussion of new (and often unexpected) aspects of the old problem of elastic light scattering by small metal particles, whose size is comparable to or smaller than the thickness of the skin layer. The main focus is put on elucidating the physical grounds for these new aspects. It is shown that, in many practically important cases, the scattering of light by such particles, despite their smallness, may have almost nothing in common with the Rayleigh one. The so-called, anomalous scattering and absorption, as well as Fano resonances, including unconventional (associated with the excitation of longitudinal electromagnetic oscillations) and directional Fano resonances, observed only in a small solid angle, are discussed in detail. The review contains a Mathematical Supplement, which includes a summary of the main results of the Mie theory and a discussion of some general properties of the scattering coefficients. In addition to purely academic interest, the phenomena considered in this review can find wide applications in biology, medicine, pharmacology, genetic engineering, imaging of ultra-small objects, ultra-high-resolution spectroscopy, information transmission, recording, and processing, and many other applications and technologies. The reported study was funded by RFBR, project number 19-11-00001 and the project of the Russian Science Foundation No. 19-72-30012, within the framework of which all the original calculations given in this publication were performed.

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arXiv2020

Universal tractable model of dynamic resonances and its application to light scattering by small particles

If the duration of the input pulse resonantly interacting with a system is comparable or smaller than the time required for the system to achieve the steady state, transient effects become important. For complex systems, a quantitative description of these effects may be a very difficult problem. We suggest a simple tractable model to describe these phenomena. The model is based on approximation of the actual Fourier spectrum of the system by that composed of the superposition of the spectra of uncoupled harmonic oscillators (normal modes). The physical nature of the underlying system is employed to select the proper approximation. This reduces the dynamics of the system to tractable dynamics of just a few driven oscillators. The method is simple and may be applied to many types of resonances. As an illustration, the approach is employed to describe the sharp intensive spikes observed in the recent numerical simulation of short light pulses scattered by a cylinder in the proximity of destructive Fano interference [Phys. Rev. A., vol. 100, 053824 (2019)] and exhibits excellent agreement with the numerics.

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arXiv2019

Paradox of multiple plasmonic resonances at light scattering by a cylinder of infinitesimal radius

The paradox of the divergence of the resonant scattering cross section of a cylinder with the permittivity equals minus unity and vanishing radius (R) irradiated by a monochromatic electromagnetic wave is discussed. Within the framework of the exact solution of the Maxwell equations, the divergence at the specified conditions is caused by the overlap of all but one multipolar resonances. It is shown that the paradox is caused by the too straightforward analysis of the expression for the cross section, which has a singularity at this point. To resolve the singularity, one must, first, generalize the problem formulation, taking into account the final linewidth of the incident wave, and then perform the correct sequence of limit transitions. The application of this approach gives rise to the vanishing cross section at the vanishing R. It ruins the expectations to employ such a cylinder as a superscatterer but simultaneously open a door to counterintuitive effects both in far and near field zones related to unusual size dependences of the scattered fields at small but finite R.

physics.optics↗

arXiv2018

Dynamic Fano resonances: From toy model to resonant Mie scattering

Based on the substantial difference in the response time for the resonant and background partitions at stepwise variations of the exiting signal, a simple exactly integrable model describing the dynamic Fano resonance (DFRs) is proposed. The model does not have any fitting parameters, may include any number of resonant partitions and exhibits high accuracy. It is shown that at the point of the destructive interference any sharp variation of the amplitude of the excitation (no matter an increase or a decrease) gives rise to pronounced "flashes" in the intensity of the output signal. In particular, the flash should appear behind the trailing edge of the exciting pulse, when the excitation is already over. The model is applied to explain the DFRs at the light scattering by a dielectric cylinder with two resonant modes excited simultaneously and exhibits the excellent agreement with the results of the direct numerical integration of the Maxwell equations.

physics.optics↗

arXiv2017

Transient effects at resonant light scattering by particles: Anapole as a storage for "frozen light"?

Transient effects at excitation of high-Q resonant modes at a leading front of a laser pulse and their decomposition at its trailing edge during the pulse scattering by a particle are discussed. The main attention is paid to the nonradiating (anapole) mode excited in a high-index cylinder. The problem is studied both analytically and numerically. It is shown that the anapole is a steady but essentially nonequilibrium mode, which can exist if and only if the host particle is irradiated by a continuous incident wave. As soon as the incident wave is switched off the anapole becomes a radiating mode and collapses very fast owing to extensive radiative losses. It ruins the hopes to employ the anapole-like excitations as storages for the "frozen light."

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arXiv2016

Directional Fano Resonances at Light Scattering by a High Refractive Index Dielectric Sphere

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 originated 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 extends the conventional Fano approach to the case when both interfering partitions are resonant. The perfect agreement between the experiment and the theory is demonstrated.

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arXiv2016

The ultimate absorption at light scattering by a single obstacle

Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric spherical or infinite cylindrical structure of an arbitrary radius. Then, we generalize it to an arbitrary finite obstacle. Importantly, the result is true for any polarization, any angle of incidence of the plane wave and any type of the structure (homogeneous, stratified, or with smoothly variable refractive index). The corresponding maximal partial cross- section is a universal quantity, which does not depend on the optical constants of the scatterer its radius, and even its shape.

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arXiv2011

Laser Pulse Heating of Spherical Metal Particles

We consider a general problem of laser pulse heating of spherical metal particles with the sizes ranging from nanometers to millimeters. We employ the exact Mie solutions of the diffraction problem and solve heat-transfer equations to determine the maximum temperature at the particle surface as a function of optical and thermometric parameters of the problem. The main attention is paid to the case when the thermometric conductivity of the particle is much larger than that of the environment, as it is in the case of metal particles in fluids. We show that in this case at any given finite duration of the laser pulse the maximum temperature rise as a function of the particle size reaches an absolute maximum at a certain finite size of the particle, and we suggest simple approximate analytical expressions for this dependence which covers the entire range of variations of the problem parameters and agree well with direct numerical simulations.

physics.optics↗

arXiv2009

Anomalous Light Absorption by Small Particles

A new type of resonant light absorption by a small particle (nanocluster) is reported. The problem cannot be described within the commonly used dipole scattering approximation and should be studied with methods based upon the exact Mie solution. It is shown that the absorption cross-section has giant maxima realized at small values of the imaginary part of the complex dielectric permittivity of the particle. The maxima are situated in the vicinity of the plasmon (polariton) resonances and correspond to the regions where the dissipative damping equals the radiative one. The case is similar to the recently introduced anomalous scattering [PRL vol. 97, 263902 (2006)] and exhibits similar peculiarities.

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