arXiv subjects

Kristina Frizyuk

Publications and source records attributed to Kristina Frizyuk.

At least 19 recordsLinked to original sources

arXiv2026

Geometric Phases and Holonomy in Structured Optical Fields

Geometric phases are widely used in modern optics, yet their meaning and underlying geometry depend on the actual physical settings, which can substantially differ from one another. This tutorial article introduces geometric phases in nanophotonic systems, focusing on the interaction of structured light with nanostructures or metaatoms. We compare the present setting with the conventional geometric phases of structured-light optics and clarify how the underlying geometries are genuinely different. Our aim is to provide a pedagogical bridge between the mathematical language of geometric phases and experimentally relevant examples from nanophotonics.

physics.optics↗

arXiv2026

Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm

The transition matrix (T-matrix) is a complete description of an object's linear scattering response. As such, it has found wide adoption for the theoretical and computational description of multiple-scattering phenomena. In its original form, the T-matrix describes the interaction of a scatterer with a monochromatic source. In practice, however, information about the T-matrix is usually needed in an extended spectral domain. To access the frequency-dispersion, one might naively sample T-matrices over a finely resolved set of discrete frequencies and store one T-matrix per frequency. This approach has multiple drawbacks: it is computationally expensive, requires excessive memory, and it disregards the physical origin of the spectral features, weakening physical interpretability. To overcome these major limitations, we leverage a pole-expansion technique to represent the T-matrix with arbitrary frequency resolution within a selected frequency domain via a set of resonant contributions. A matrix-valued variant of the recently established adaptive Antoulas-Anderson (AAA) algorithm for rational approximation enables us to compute the pole-expansion at minimal computational cost using only a small number of direct evaluations. We demonstrate the benefits of such a representation with examples ranging from semi-analytically accessible scatterers to quasi-dual bound states in the continuum. To allow the wider community to capitalize on these findings, we provide open-source tools to perform the presented pole-expansion of the T-matrix.

physics.optics↗

arXiv2026

Tensor-driven geometric phase in nonlinear AlGaAs metasurfaces

Dielectric metasurfaces provide a unique platform for efficient harmonic generation and optical wavefront manipulation at the nanoscale. While several approaches are available for performing wavefront shaping, the one exploiting geometric phase streamlines significantly the design and fabrication process. It has been recently shown that, in III-V semiconductor alloys, the rotation of the crystal axes affects the phase and amplitude of second-harmonic generation (SHG) induced by circularly polarized light [1]. Based on this notion, we fabricated and characterized two aluminum gallium arsenide metasurfaces displaying the versatility of the geometric phase design approach through nonlinear beam steering and structured-light generation on the harmonic field.

physics.optics↗

arXiv2026

Symmetry analysis and multipole classification of eigenmodes in electromagnetic resonators for engineering their optical properties

The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode structure and multipole content which determines the linear and non-linear response of the resonator. Here, we develop the algorithm for the classification of eigenmodes in resonators of the simplest shapes depending on their symmetry group. For each type of mode, we find its multipole content. As an illustrative example, we apply the developed formalism to the analysis of dielectric triangular prism and demonstrate the formation of high-Q resonances originated due to suppression of the scattering through the main multipole channel. The developed approach one to engineer, predict, and explain scattering phenomena and optical properties of resonators and meta-atoms basing only on their symmetry without the need for numerical simulations and it can be used for the design of new photonic and microwave devices.

physics.optics↗

arXiv2025

Near-infrared polarimetric imaging with nonlinear flat-optics

A compact and broadband polarimetric imaging platform is presented, based on second-harmonic generation (SHG) in nonlinear flat-optics. The system employs periodic all-dielectric AlGaAs gratings to induce polarization-dependent SH emission, enabling pixel by pixel direct retrieval of the full Stokes vector from an input intensity distribution in the near-infrared range. By engineering the geometry and orientation of the polarimetric units, sensitivity to linear and circular polarization components is achieved. A superpixel design comprising four polarimetric structures allows accurate reconstruction of the polarization state without moving parts or sequential measurements. This approach offers a scalable, passive, and cost-effective solution for polarimetric imaging, particularly suited for near-infrared applications.

physics.optics↗

arXiv2024

Light structuring via nonlinear total angular momentum addition with flat optics

Shaping the structure of light with flat optical devices has driven significant advancements in our fundamental understanding of light and light-matter interactions, and enabled a broad range of applications, from image processing and microscopy to optical communication, quantum information processing, and the manipulation of microparticles. Yet, pushing the boundaries of structured light beyond the linear optical regime remains an open challenge. Nonlinear optical interactions, such as wave mixing in nonlinear flat optics, offer a powerful platform to unlock new degrees of freedom and functionalities for generating and detecting structured light. In this study, we experimentally demonstrate the non-trivial structuring of third-harmonic light enabled by the addition of total angular momentum projection in a nonlinear, isotropic flat optics element -- a single thin film of amorphous silicon. We identify the total angular momentum projection and helicity as the most critical properties for analyzing the experimental results. The theoretical model we propose, supported by numerical simulations, offers quantitative predictions for light structuring through nonlinear wave mixing under various pumping conditions, including vectorial and non-paraxial pump light. Notably, we reveal that the shape of third-harmonic light is highly sensitive to the polarization state of the pump. Our findings demonstrate that harnessing the addition of total angular momentum projection in nonlinear wave mixing can be a powerful strategy for generating and detecting precisely controlled structured light.

physics.optics↗

arXiv2024

Achiral nanostructures: perturbative harmonic generation and dichroism under vortex and vector beams illumination

In this study, we investigate the nonlinear optical phenomena emerging from the interaction of vortex and vector beams with achiral nanoparticles or nanostructures. We reveal the conditions under which linear or nonlinear dichroism can be observed. Despite the achiral symmetry of the nanostructure, the interplay between the symmetries of the vortex beam, the nanostructure, and the crystalline lattice of the nanostructure material may result in circular dichroism in the nonlinear regime. We derive a formula that describes the conditions for the appearance of circular dichroism across a broad range of scenarios, taking into account all the symmetries. Building on these findings, we have determined the conditions for both linear and nonlinear dichroism when illuminated by vector beams. We believe that this work provides important insights that can enhance the design of chiral sensors and optical traps, making them more versatile and effective.

physics.optics↗

arXiv2023

Fast simulation of light scattering and harmonic generation in axially symmetric structures in COMSOL

In the field of optics and nanophotonics, simulation of electromagnetic scattering plays a major role in the study of complex nanostructures and optical devices. The numerical analysis of scattering spectra, even for nanocavities with simple geometry, is associated with significant computational difficulties. However, when the system exhibits certain symmetries, it becomes possible to simplify the problem through the process of separation of variables, which leads to a decrease in its dimension. In this paper, we aim to provide a practical guide to a fast simulation of linear and non-linear scattering problems in COMSOL Multiphysics for axisymmetric objects including computation of scattering cross-section as well as its multipolar decomposition, optical forces, and second harmonic generation. We also accompany the provided guide with the ready-to-run COMSOL models.

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↗

arXiv2022

When does nonlinear circular dichroism appear in achiral dielectric nanoparticles?

Sometimes it appears, sometimes it does not. We present a theoretical study of circular dichroism in the second-harmonic signal of single dielectric nanostructures with different symmetries and noncentrosymmetric materials. We show that this effect is not fully identified only by macroscopic and lattice symmetries, but their relative orientation as well. Based on the cumbersome symmetry and modal analysis, we provide a general and very simple formula to determine whether the dichroism exists, and a table with the most significant cases.

physics.optics↗

arXiv2022

Nonlinearity-induced optical torque

Optically-induced mechanical torque leading to the rotation of small objects requires the presence of absorption or breaking cylindrical symmetry of a scatterer. A spherical non-absorbing particle cannot rotate due to the conservation of the angular momentum of light upon scattering. Here, we suggest a novel physical mechanism for the angular momentum transfer to non-absorbing particles via nonlinear light scattering. The breaking of symmetry occurs at the microscopic level manifested in nonlinear negative optical torque due to the excitation of resonant states at the harmonic frequency with higher projection of angular momentum. The proposed physical mechanism can be verified with resonant dielectric nanostructures, and we suggest some specific realizations.

physics.optics↗

arXiv2022

Multipolar theory of bianisotropic response

Bianisotropy of metaatoms is usually associated with their nonlocal response and the mutual coupling between electric and magnetic dipole moments induced by the incident field. In this work, we generalize the theory of bianisotropy beyond the dipole response to the cases of arbitrary high-order multipole resonances. We demonstrate that bianisotropy is exclusively caused by the absence of the inversion symmetry of metaatoms. The strength of the bianisotropy response is normally increased with the size of a meta-atom but its origin is fully connected to the symmetry of the structure. As an important example of bianisotropic particle, we consider a triangular prism and show how accounting for the higher-order multipoles prevents the violation of the Onsager-Casimir conditions for kinetic coefficients appearing in the dipole approximation. The developed theory is an important step towards a deeper insight into the scattering properties of nanoantennas and meta-atoms.

physics.optics↗

arXiv2022

Bound States in the Continuum in Multipolar Lattices

We develop a theory of bound states in the continuum (BICs) in multipolar lattices -- periodic arrays of resonant multipoles. We predict that BICs are completely robust to changes in lattice parameters remaining pinned to specific directions in the $k$-space. The lack of radiation for BICs in such structures is protected by the symmetry of multipoles forming the lattice. We also show that some multipolar lattices can host BICs forming a continuous line in the $k$-space and such BICs carry zero topological charge. The developed approach sets a direct fundamental relation between the topological charge of BIC and the asymptotic behavior of the Q-factor in its vicinity. We believe that our theory is a significant step towards gaining deeper insight into the physics of BICs and the engineering of high-Q states in all-dielectric metasurfaces.

physics.optics↗

arXiv2022

Thermo-optical reshaping of SHG emission from dimerall-dielectric nanoresonators

In recent years resonant semiconductor and all-dielectric nanophotonics offered a lot of possibilities for thermally-induced light manipulation at the nanoscale. Owing to high-quality resonant states, such nanostructures allow for efficient light-to-heat conversion supported by various temperature detection approaches based on thermally sensitive intrinsic optical responses (photoluminescence, Raman scattering, thermorefraction etc.). In this work, we study theoretically a phenomenon of the photothermal reshaping of the radiation pattern of second-harmonic generation (SHG) that occurs in resonant all-dielectric systems. In the suggested geometry near-IR pulsed laser is utilized for excitation of SHG while simultaneous continuous wave visible laser heats the structure. The thermooptical switching of the resonant optical states in the nanostructures governs the reconfiguration of the emission pattern, without significant loss in the magnitude of the SHG. We believe, that our findings will pave the way for subwavelength-size near-IR thermally switchable nonlinear optical devices.

physics.optics↗

arXiv2022

Second-harmonic generation tuning by stretching arrays of GaAs nanowires

We present a wearable device with III-V nanowires in a flexible polymer, which is used for active mechanical tuning of the second-harmonic generation intensity. An array of vertical GaAs nanowires was grown with metalorganic vapour-phase epitaxy, then embedded in polydimethylsiloxane and detached from the rigid substrate with mechanical peel off. Experimental results show a tunability of the second-harmonic generation intensity by a factor of two for 30% stretching which matches the simulations including the distribution of sizes. We studied the impact of different parameters on the band dispersion and tunability of the second-harmonic generation, such as the pitch, the length, and the diameter. We predict at least three orders of magnitude active mechanical tuning of the nonlinear signal intensity for nanowire arrays. The flexibility of the array together with the resonant wavelength engineering make such structures perspective platforms for future bendable or stretchable nanophotonic devices as light sources or sensors.

physics.optics↗

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↗

arXiv2021

Nonlinear circular dichroism in Mie-resonant nanoparticle dimers

We study nonlinear response of a dimer composed of two identical Mie-resonant dielectric nanoparticles illuminated normally by a circularly polarized light. We develop a general theory describing hybridization of multipolar modes of the coupled nanoparticles, and reveal nonvanishing nonlinear circular dichroism (CD) in the second-harmonic generation (SHG) signal enhanced by the multipolar resonances in the dimer provided its axis is oriented under an angle to the crystalline lattice of the dielectric material. We present experimental results for this SHG-CD effect obtained for the AlGaAs dimers placed on an engineered substrate which confirm the basic prediction of our general multipolar hybridization theory.

physics.optics↗

arXiv2020

Directional emission of down-converted photons from a dielectric nano-resonator

Creation of correlated photon pairs is one of the key topics in contemporary quantum optics. Here, we theoretically describe the generation of photon pairs in the process of spontaneous parametric down-conversion in a resonant spherical nanoparticle made of a dielectric material with bulk $χ^{(2)}$ nonlinearity. We pick the nanoparticle size that satisfies the condition of resonant eigenmodes described by Mie theory. We reveal that highly directional photon-pair generation can be observed utilising the nonlinear Kerker-type effect, and that this regime provides useful polarisation correlations.

physics.optics↗