arXiv subjects

Vladimir Igoshin

Publications and source records attributed to Vladimir Igoshin.

7 recordsLinked to original sources

arXiv2026

Mie Optical Computing

Optical computing is emerging as a promising paradigm for next-generation information processing. Diffractive optical processors rely on spatially distributed trainable degrees of freedom, leading to extended architectures. Here, we propose a compact neuromorphic optical-computing approach where the entire trainable transformation is implemented by a single Mie scatterer. By formulating computation in vector spherical harmonics basis, trainable modal couplings can be concentrated within a finite object through its T-matrix. Since available T-matrix parameters scale as the fourth power of maximal multipole order, this architecture can overcome trainable-parameter-density limitations of conventional spatially distributed diffractive processors. We demonstrate classification of phase-encoded MNIST images using scattered-field intensity. At a particle size parameter of $ka = 15$, the trained T-matrix reaches approximately 90% test accuracy, comparable to a single-layer artificial neural network. Similar performance can be achieved using near-fields, enabling on-chip integration. We show how reciprocity, passivity, and particle symmetry constrain performance: passivity reduces the accessible operator space while improving robustness, whereas symmetry reduces the number of independent parameters. Finally, we inverse-design a non-absorbing dielectric scatterer that realizes the classification task with 84% accuracy. These results demonstrate that nontrivial neuromorphic transformations can be encoded within the multipolar response of a single compact scatterer.

physics.optics↗

arXiv2026

Optical Theorem for Measuring the Acoustic Extinction Cross Section of Helmholtz Resonators

The optical theorem is a powerful tool of scattering theory that directly relates the extinction cross section of a scatterer to its forward scattering amplitude. While widely used in electromagnetism and optics, its application in acoustics has remained limited, primarily due to experimental challenges. These include the finite size of practical sound sources and the stringent requirements for detecting weak scattered signals. In this work, we analyze these limitations and develop a robust methodology for measuring the acoustic extinction cross section under realistic conditions, including non-ideal anechoic environments. The approach is applied experimentally to a Helmholtz resonator in an imperfect anechoic environment with standing-wave resonances. The retrieved extinction cross section exhibits a single pronounced resonance near 2000 Hz. The resonance position, peak magnitude, and spectral lineshape are consistent with full-wave numerical simulations. The results demonstrate that, when combined with appropriate data processing, the optical theorem provides a simple and reliable tool for characterizing acoustic resonators, opening new opportunities for quantitative analysis of acoustic scattering and absorption phenomena.

physics.class-ph↗

arXiv2026

Resonant state expansion for acoustic resonators. Part I. Eigenvalue problem

Resonant-state expansion (RSE) is a powerful modal framework for the perturbative analysis of open resonant systems, providing direct access to complex eigenfrequencies and eigenmodes. While RSE is well developed in electromagnetism, a comparably systematic formulation for acoustics remains less established. Here, we develop a general Green-function-based formalism for acoustic RSE and illustrate it for a class of two-dimensional acoustic resonators. Using the resonant states of an analytically solvable cylindrical reference system as a basis, we derive explicit perturbation matrix elements for uniform, radial, and sectoral variations of density and compressibility, representing homogeneous tuning, graded profiles, and symmetry-induced modal coupling. The resulting complex eigenfrequencies and eigenmodes are validated against exact analytical solutions and finite-element simulations, showing excellent quantitative agreement. The framework provides a systematic and physically transparent approach for analyzing perturbed open acoustic resonators and establishes a basis for resonant-state methods in acoustic metamaterials and non-Hermitian acoustics.

physics.comp-ph↗

arXiv2026

Resonant state expansion for acoustic resonators. Part II. Scattering problem

We develop a resonant-state expansion formulation for acoustic scattering by individual resonators. The scattered pressure and particle-velocity fields are expanded over the resonant states of the system, with excitation amplitudes determined by overlap integrals between the incident field and the resonant states over the resonator volume. Using the acoustic energy flux, we derive expressions for the extinction, scattering, and absorption cross-sections and show that the extinction spectrum can be resolved into contributions from individual resonant states. The formulation is first validated for a homogeneous two-dimensional cylinder, where it reproduces the analytical Mie-theory solution. We then consider a sectorally perturbed cylinder with coupled azimuthal modes and demonstrate agreement with finite-element simulations. Finally, we combine the eigenvalue and scattering formulations for a material-programmed hard-wall annular metaatom and reproduce its scattering spectra and near fields. The developed framework provides a physically transparent modal approach to acoustic scattering by open resonators with reduced symmetry and spatially structured material parameters.

physics.comp-ph↗

arXiv2024

Inverse design of Mie resonators with minimal backscattering

Manipulation and engineering of light scattering by resonant nanostructures is one of the central problems in optics and photonics. In this work, we theoretically study the effect of suppressed back-scattering of dielectric nanoantenna. We employed covariance matrix adaptation evolution strategy to identify the geometries of circular dielectric structures with minimized backward scattering cross section. Zero back-scattering is achieved due to generalized Kerker effect and multipole cancellation condition. We found a set of geometries and shapes of the nanoantenna having back-scattering intensity close to zero. With help of clustering algorithms, all the found geometries fall separated into several groups according to their multipolar content. While the optical properties of scatterers in each group were similar due to similar multipolar content, their shapes can be significantly different which stresses the ambiguity of free-form optimization problem. We believe that the obtained results and found possible classes on generalized Kerker nanoantenna can help in designing nanophotonic structures such as antireflective metasurfaces.

physics.optics↗

arXiv2023

Exceptional points in single open acoustic resonator due to the symmetry breaking

Exceptional points (EPs) have been widely studied in quantum mechanics, condensed matter physics, optics and photonics. However, their potential in acoustics has only recently been recognized due to the rapid development of acoustic metamaterials. This paper proposes a method for achieving EP conditions in acoustic resonators by lowering their symmetry and enabling resonant mode interaction. The formation of EPs is predicted through direct numerical simulation supported by coupled mode theory and resonant state expansion. These findings have significant implications for the design and optimization of acoustic metamaterials for applications such as acoustic sensing and noise reduction.

physics.class-ph↗

arXiv2021

Acoustic resonators: symmetry classification and multipolar content of the eigenmodes

Acoustics recently became a versatile platform for discovering novel physical effects and concepts at a relatively simple technological level. On this way, single resonators and the structure of their resonant modes play a central role and define the properties of complex acoustic systems such as acoustic metamaterials, phononic crystals, and topological structures. In this paper, we present a powerful method allowing a qualitative analysis of eigenmodes of resonators in the linear monochromatic acoustic domain based on multipole classification of eigenmodes. Using the apparatus of group theory, we explain and predict the structure of the scattered field knowing only the symmetry group of the resonator by connecting the multipolar content of incident and scattered fields. Such an approach can be utilized for developing resonators with predesigned properties avoiding time-consuming simulations. We have performed full multipole symmetry classification for a number of resonators geometries, and tightened it with scattering spectra profiles.

physics.class-ph↗