- I'm a professor of Theoretical Physics, Head of Lab at Lomonosov Moscow State University. My present interests lie in nanooptics, nanophotonics, etc.edit
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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... 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...
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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... 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.
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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... 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 origin of the tail is shifted to infinity, i. e., the tail vanishes. Depending on the particular type of the dis...
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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... 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
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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.... 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 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...
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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... 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.
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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... 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 origin 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 ...
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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... 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.
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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... 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...
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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 coupledmode theory, and the other employs the normal... more
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 coupledmode 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 th...
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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... more
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 o...
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We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on a generalization of the temporal coupled-mode theory, and the other employs the... more
We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on a 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-sections 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...
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The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically, the problem is reduced to the calculation of the “energy” of the ground state in the... more
The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically, the problem is reduced to the calculation of the “energy” of the ground state in the Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.
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We carry out a systematic study of a different type of chaos at onset ''soft-mode turbulence''based on numerical integration of the simplest one-dimensional model. The chaos is characterized by a smooth interplay of... more
We carry out a systematic study of a different type of chaos at onset ''soft-mode turbulence''based on numerical integration of the simplest one-dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and ...
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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... more
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. First, we obtain this result for the scattering by a spherical particle. Then, we generalize it to an arbitrary finite obstacle. The results are valid for any polarization of the incident wave, any angle of its incidence, and any type of the scatterer (homogeneous, stratified, or with smoothly variable refractive index). We also prove that the maximal partial absorption cross section for any finite scatterer cannot exceed the corresponding value for a homogeneous sphere in 3D and circul...
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The steady-state process of melting of highly absorbing media by a laser pulse of long duration is considered theoretically. The shape of the free surface of the melt, deformed by the reactive pressure of the vapor from the specimen, is... more
The steady-state process of melting of highly absorbing media by a laser pulse of long duration is considered theoretically. The shape of the free surface of the melt, deformed by the reactive pressure of the vapor from the specimen, is determined, the equation of the surface being obtained in the explicit form z = z(r). All the parameters entering into it are expressed in terms of the laser-beam parameters and the thermophysical properties of the melt. The connection between the deformation of the free melt surface and the phenomenon of deep-penetration (dagger-like) melting of the specimen is explained. It is shown that this phenomenon involves a threshold and analytical expressions are found for the magnitude of this threshold, good agreement with experiment being obtained. It is shown that there is also a threshold of the laser-radiation intensity for the transition to the intense-evaporation regime, and the magnitude of this threshold is found in the case when the heat conduction cannot be considered as one-dimensional because the laser pulse is of long duration. It is shown that the relationship between the magnitudes of these two thresholds can be arbitrary and is mainly determined by the properties of the material being processed. A study is made of the free oscillations of the melt surface, which appear after the end of the laser pulse. It is shown that the first harmonic always has the maximum amplitude.
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An experimental and theoretical investigation was made of the interaction of flashlamp radiation with an absorbing liquid. The experimental conditions corresponded to liquid cooling of flashlamps used for laser pumping. Such special... more
An experimental and theoretical investigation was made of the interaction of flashlamp radiation with an absorbing liquid. The experimental conditions corresponded to liquid cooling of flashlamps used for laser pumping. Such special effects in the liquid as a phase transition and a supercritical state were observed in the liquid. A method was developed for obtaining an analytic solution of the