arXiv subjects

Alexey A. Shcherbakov

Publications and source records attributed to Alexey A. Shcherbakov.

14 recordsLinked to original sources

arXiv2026

Efficient calculation of inductive coupling for arrays of wire ring resonators

Generalization of the inductance to the case of non-quasistatic electromagnetic field oscillations appears to be fruitful when considering wireless power transfer and RF metamaterials consisting of thin wire loop meta-atoms. When dealing with large systems of interacting loops carrying currents, efficiency and precision of calculation in the presence of retardation is crucial. In this work, we derive a series expansion of such generalized inductance and propose a way for its efficient numerical approximation. Illustrative examples are provided both for inductance convergence of a pair of two loops and extinction efficiency for scattering by metamaterial samples.

physics.comp-ph↗

arXiv2025

Electromagnetics of deeply subwavelength metamaterial particles

This article discusses electromagnetic properties of volumetric metamaterial samples with essentially discrete structure, that is, assembled as a periodic array of electromagnetic resonators. We develop an efficient numerical procedure for calculating quasi-static electromagnetic response precisely to analyse samples containing several million meta-atoms. We demonstrate that, contrary to a common belief, even million-``atoms'' samples with sharp edges are still quite different from uniform (``homogenised'') materials, and their properties are critically sensitive to their shape and boundary structure. We also compare our results with calculations based on the discrete dipole approximation as well as with an integral model for continuous particles, and analyse distinctions and similarities between the different approaches. In particular, discrete metamaterials present themselves as a stringent platform for assessing continuous models developed for finite objects with sharp edges. Overall, the reported results should be important for understanding mesoscopic systems with strongly interacting elements.

physics.app-ph↗

arXiv2025

Logarithmically complex rigorous Fourier space solution to the 1D grating diffraction problem

The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography masks. Fourier space methods, such as the Fourier Modal Method, are established tools for the analysis of the electromagnetic properties of periodic structures, but are too computationally demanding to be directly applied to large and multiscale optical structures. This work focuses on pushing the limits of rigorous computations of periodic electromagnetic structures by adapting a powerful tensor compression technique called the Tensor Train decomposition. We have found that the millions and billions of numbers produced by standard discretization schemes are inherently excessive for storing the information about diffraction problems required for computations with a given accuracy, and we show how to adapt the TT algorithms to have a logarithmically growing amount of information to be sufficient for reliable rigorous solution of the Maxwell's equations on an example of large period multiscale 1D grating structures.

physics.comp-ph↗

arXiv2024

Intuitive understanding of extinction of small particles in absorbing and active host media within the MLWA

In an absorbing or an active host medium characterized by a complex refractive index $n_2=n_2'+{\rm i}n_2''$, our previously developed modified dipole long-wave approximation (MLWA) is shown to essentially overly with the exact Mie theory results for spherical nanoparticle with radius $a\lesssim 25$ nm ($a\lesssim 20$ nm) in the case of Ag and Au (Al and Mg) nanoparticles. The agreement for Au and Ag (Al and Mg) nanoparticles, slightly better in the case of Au than Ag, continues to be acceptable up to $a\sim 50$ nm ($a\sim 40$ nm), and can be used, at least qualitatively, up to $a\sim 70$~nm ($a\sim 50$ nm) correspondingly. A first order analytic perturbation theory (PT) in a normalized extinction coefficient, $\barκ=n_2''/n_2'$, around a nonabsorbing host is developed within the dipole MLWA and its properties are investigated. It is shown that, in a suitable parameter range, the PT can reliably capture the effect of host absorption or gain on the extinction efficiency of various plasmonic nanoparticles.

physics.optics↗

arXiv2024

Generation of nearly pure and highly directional magnetic light in fluorescence of rare earth ions

A thorough analysis of the emission via the magnetic dipole (MD) transition, called magnetic light below, of trivalent rare-earth ions in or near dielectric homogeneous spheres has been performed. In the search for enhancement of fluorescence from magnetic light, one faces the difficult task of identifying the regions where the combined fluorescence due to multiple electric dipole (ED) transitions becomes negligible compared to the fluorescence of the MD transition. We have succeeded in identifying a number of configurations with dielectric sphere parameters and a radial position of a trivalent rare-earth emitter wherein the branching ratio of the MD transition approaches its limit of one, implying that transitions from a given initial level (e.g., $^5$D$_0$-level of Eu$^{3+}$) are completely dominated by the MD transition. The dimensionless directivity of the MD emission, the radiative decay rates, and the fluorescence of the magnetic light can be increased by a factor of more than $25$, $10^3$, and $10^4$, respectively.

physics.optics↗

arXiv2023

Transporting Particles with Vortex Rings

Due to their long-lived nature, vortex rings are highly promising for non-contact transportation of colloidal microparticles. However, they are complex structures, and their description using rigorous, closed-form mathematical expressions is challenging, particularly in the presence of strongly inhomogeneous colloidal suspensions. This study presents straightforward analytical approximations that reveal the dynamics of vortex rings transporting microparticles. Our results were validated using comprehensive simulations and experimental measurements.

cond-mat.soft↗

arXiv2023

Numerical simulation of the electromagnetic wave reflection from 2D random semi-infinite strongly scattering media

Light scattering in disordered media plays an important role in various areas of applied science from biophysics to astronomy. In this paper we study two approaches to calculate scattering properties of semi-infinite densely packed media with high contrast and wavelength scale inhomogeneities by combining the Fourier Modal Method and the super-cell approach. Our work reveals capabilities to attain ensemble averaged solutions for the Maxwell's equations in complex media, and demonstrated numerical convergence supports the consistency of the considered approaches.

physics.comp-ph↗

arXiv2022

Reformulated Fourier Modal Method with improved near field computations

In this paper we propose a new formulation of the Fourier Modal Method based on an alternative treatment of interface conditions allowing us to overcome the effect of the Gibbs phenomenon. Explicit consideration of the interface conditions for the discontinuous part of the field leads to an equation for the eigenvalue problem, which can be written in an inversion-free form. The results of the method are in good agreement with the results for the classical approach based on the Li factorization rules both for dielectric and metallic gratings. Moreover, the developed method allows calculating the near field much more accurately, and may find its applications in sensing and nonlinear optics.

physics.optics↗

arXiv2019

Curvilinear coordinate Generalized Source Method for gratings with sharp edges

High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed Generalized Source Method in the curvilinear coordinates, which has theoretical $O\left(N\log N\right)$ asymptotic numerical complexity, a new method formulation is developed for gratings with sharp edges. It is shown that corrugation corners can be treated as effective medium interfaces within the rationale of the method. Moreover, the given formulation is demonstrated to allow for application of the same derivation as one used in classical electrodynamics to derive the interface conditions. This yields continuous combinations of the fields and metric tensor components, which can be directly Fourier factorized. Together with an efficient algorithm the new formulation is demonstrated to substantially increase the computation accuracy for given computer resources.

physics.comp-ph↗

arXiv2019

Calculation of the electromagnetic scattering by non-spherical particles based on the volume integral equation in the spherical wave function basis

The paper presents a method for calculation of non-spherical particle T-matrices based on the volume integral equation and the spherical vector wave function basis, and relies on the Generalized Source Method rationale. The developed method appears to be close to the invariant imbedding approach, and the derivations aims at intuitive demonstration of the calculation scheme. In parallel calculation of single columns of T-matrix is considered in detail, and it is shown that this way not only has a promising potential of parallelization but also yields an almost zero power balance for purely dielectric particles.

physics.comp-ph↗

arXiv2018

Direct S-matrix calculation for diffractive structures and metasurfaces

The paper presents a derivation of analytical components of S-matrices for arbitrary planar diffractive structures and metasurfaces in the Fourier domain. Attained general formulas for S-matrix components can be applied within both formulations in the Cartesian and curvilinear metric. A numerical method based on these results can benefit from all previous improvements of the Fourier domain methods. In addition, we provide expressions for S-matrix calculation in case of periodically corrugated layers of 2D materials, which are valid for arbitrary corrugation depth-to-period ratios. As an example the derived equations are used to simulate resonant grating excitation of graphene plasmons and an impact of silica interlayer on corresponding reflection curves.

physics.optics↗

arXiv2017

Concurrency of anisotropy and spatial dispersion in low refractive index dielectric composites

The article demonstrates uncommon manifestation of spatial dispersion in low refractive index contrast 3D periodic dielectric composites with periods of about one tenth of the wavelength. First principles simulations by the well established plane wave method reveal that spatial dispersion leads to appearance of additional optical axes and can compensate anisotropy in certain directions.

physics.optics↗

arXiv2017

General analytical solution for the electromagnetic grating diffraction problem

Implementing the modal method in the electromagnetic grating diffraction problem delivered by the curvilinear coordinate transformation yields a general analytical solution to the 1D grating diffraction problem in a form of a T-matrix. Simultaneously it is shown that the validity of the Rayleigh expansion is defined by the validity of the modal expansion in a transformed medium delivered by the coordinate transformation.

physics.class-ph↗

arXiv2015

3D periodic dielectric composite homogenization based on the Generalized Source Method

The article encloses a new Fourier space method for rigorous optical simulation of 3D periodic dielectric structures. The method relies upon rigorous solution of Maxwell's equations in complex composite structures by the Generalized Source Method. Extremely fast GPU enabled calculations provide a possibility for an efficient search of eigenmodes in 3D periodic complex structures on the basis of rigorously obtained resonant electromagnetic response. The method is applied to the homogenization problem demonstrating a complete anisotropic dielectric tensor retrieval.

physics.comp-ph↗