# Новые публикации

## Bound states in the continuum in dielectric resonators embedded into metallic waveguide

https://doi.org/10.1016/B978-0-32-395195-1.00012-0

We consider dielectric cavities whose radiation space is restricted by two parallel metallic planes. The TE solutions of the Maxwell's equations of the system are equivalent to the solutions of periodical arrays of dielectric cavities. The system readily allows to achieve bound states in the continuum (BICs) of any type, including topological BICs that depends on the position and orientation of the cavities relative to the planes. This facilitates experimental studies immensely compared to infinite arrays of the cavities. We show the effect of merging topologically protected BICs, which pushes the square asymptotic of the *Q*-factor to the power degree of 4 or even 6.

## Lattice distortion generates bound states in the continuum

https://doi.org/10.1007/s11433-023-2282-8

High-Q optical cavity is an indispensable component of many photonic devices, such as lasers, sensors, harmonic generation and photon emission, and chiral dichroism. Conventional way of realizing ultrahigh Q-factor relies on Fabry-Pérot resonators, photonic crystal nanocavities fabricated by a CMOS-compatible process, or whispering gallery modes.

## Exceptional points in periodic array of silicon rods

https://doi.org/10.1063/5.0173550

We find numerically the complex eigenvalues in grating composed of infinitely long silicon rods of rectangular cross section and show existence of exceptional points (EPs) in parametric space of structural scales and wave vector along the rods. The EPs have sufficiently small imaginary parts due to their proximity to bound states in the continuum. This enables to trace the resonant frequencies in the transmission around the EP and, accordingly, to identify the EP by bifurcation of the transmission. We present generic coupled mode theory to elucidate this effect. We also show that structural fluctuations of grating preserve EP but obscures their observation because of inhomogeneous broadening of transmission peaks.

## Acoustic resonances in non-Hermitian open systems

https://doi.org/10.1038/s42254-023-00659-z

Acoustic resonances in open systems, which are usually associated with resonant modes characterized by complex eigenfrequencies, play a fundamental role in manipulating acoustic wave radiation and propagation. Notably, they are accompanied by considerable field enhancement, boosting interactions between waves and matter, and leading to various exciting applications. In the past two decades, acoustic metamaterials have enabled a high degree of control over tailoring acoustic resonances over a range of frequencies. Here, we provide an overview of recent advances in the area of acoustic resonances in non-Hermitian open systems, including Helmholtz resonators, metamaterials and metasurfaces, and discuss their applications in various acoustic devices, including sound absorbers, acoustic sources, vortex beam generation and imaging. We also discuss bound states in the continuum and their applications in boosting acoustic wave–matter interactions, active phononics and non-Hermitian acoustic resonances, including phononic topological insulators and the acoustic skin effect.

## Size-selective optical trapping of nanoparticles with bound states in the continuum

https://doi.org/10.1016/j.optlaseng.2023.107797

We consider a waveguide with a symmetrically integrated silicon cylinder. This design supports a symmetry protected bound state in the continuum (BIC) with *Q*-factor controlled by slight displacement of the cylinder. When excited by a TE_{10} electromagnetic wave, the BIC leads to giant optical forces near the cylinder. These forces have a strong impact on nanoparticles being dragged by liquid flow over the waveguide as they approach the cylinder. At the same time, the nanoparticles perturb the resonant frequency of the BIC with a value proportional to their volume and proximity to the cylinder. Therefore, the interplay between the resonant width of the BIC and the nanoparticle frequency perturbation determines the positions of the nanoparticles trapped around the cylinder. This paradigm demonstrates resonant self-trapping and sorting of nanoparticles by size through BIC excitation. We highlight the extreme sensitivity of these effects to the frequency of the injected TE wave. Additionally, we show that these results remain valid when considering the finite conductivity of metal

## A Series of Avoided Crossings of Resonances in the System of Several Different Dielectric Resonators Results in Giant Q-Factors

https://doi.org/10.3390/photonics10090973

On an example of a system of three/four/five/six different coupled coaxial silicon disks, we realize a series of avoided crossings of resonances (ACRs) with respect to the different morphologies for the different scales of each disk. Each next step of ACR accompanied by the optimization processes of all previous ACRs contributes almost one order of magnitude to the Q-factor. As a result, we achieve unprecedented values for the Q-factors: 6.66.6·104104 for three, 4.8·1064.8·106 for four, 8.5·1078.5·107 for five and several billions for six free standing silicon disks. Comparisons to such prominent methods as whispering gallery modes or quasi bound states in the continuum to boost the Q-factor demonstrate the tremendous advantage of the present approach not only in terms of Q-factor values but also in terms of mode volumes. Multipole analysis of the final hybridized resonant mode explains such extremely large Q-factor values. The analysis shows a strong redistribution of radiation owing to the almost-exact destructive interference of the dominating complex multipole radiation amplitudes.

## Super-bound states in the continuum through merging in grating

https://doi.org/10.48550/arXiv.2306.13313

Bound states in the continuum (BICs) in gratings composed of infinitely long silicon rods of rectangular cross-section are considered. We reveal merging off-Γ Friedrich-Wintgen BIC with symmetry protected BIC. We present CMT and multipole decomposition theory complementary each other to analyze the merging phenomenon. The theories show a crossover of the behavior of Q-factor from standard inverse square law k−2x,z towards to extremely fast boosting law k−6x,z in momentum space. In turn that crossover gives rise to another crossover from Q∼N2 to Q∼N3 for symmetry protected quasi BIC in finite grating of N rods owing to suppression of radiation leakage of quasi BIC mode from surface of grating. As a result the Q-factor of quasi BIC is determined by residual leakage from ends of grating. We show numerically that this leakage also can be suppressed considerably if to stretch grating from the ends.

## Size-selective optical trapping of nanoparticles with bound states in the continuum

https://doi.org/10.1016/j.optlaseng.2023.107797

We consider a waveguide with a symmetrically integrated silicon cylinder. This design supports a symmetry protected bound state in the continuum (BIC) with *Q*-factor controlled by slight displacement of the cylinder. When excited by a TE_{10} electromagnetic wave, the BIC leads to giant optical forces near the cylinder. These forces have a strong impact on nanoparticles being dragged by liquid flow over the waveguide as they approach the cylinder. At the same time, the nanoparticles perturb the resonant frequency of the BIC with a value proportional to their volume and proximity to the cylinder. Therefore, the interplay between the resonant width of the BIC and the nanoparticle frequency perturbation determines the positions of the nanoparticles trapped around the cylinder. This paradigm demonstrates resonant self-trapping and sorting of nanoparticles by size through BIC excitation. We highlight the extreme sensitivity of these effects to the frequency of the injected TE wave. Additionally, we show that these results remain valid when considering the finite conductivity of metal waveguides.

## Super Quasibound State in the Continuum

DOI: https://doi.org/10.1103/PhysRevApplied.20.L011003

Avoided crossing of resonances and merging multiple bound states in the continuum (BICs) are parallel means for tailoring the physical properties of BICs. Herein, we introduce a concept of super quasi-BIC for photonic crystal (PhC) systems where its quality (Q) factor is boosted in both parametric and momentum spaces. A super quasi-BIC with substantial enhancement of Q factor can be achieved in a finite PhC by combining avoided crossing of two symmetry-protected (SP) quasi-BICs in parametric space and merging BICs in momentum space simultaneously. Of note, analytical theory shows that the proposed mechanism results in the transition of asymptotic behavior of the Q factor over the numbers of resonators from N2 to exclusive N3 for SP BICs, which is highly significant for realizing quasi-BICs in a compact PhC. Microwave experiments are performed to validate the theoretical results. Our results provide a paradigm shift for manipulating the physical properties quasi-BICs in finite PhC structures, which can also be generalized to the two-dimensional PhC slab case. It would facilitate various applications, including but not limited to low-threshold lasing and high figure-of-merit sensing, etc

## Bound States in the Continuum Protected by Reduced Symmetry of Three-Dimensional Open Acoustic Resonators

https://doi.org/10.1103/PhysRevApplied.19.054001

Bound states in the continuum (BICs) have been demonstrated as a powerful tool for trapping acoustic fields in an acoustic resonator. It has been widely recognized that symmetry-protected (SP) BICs result from symmetry incompatibility of some eigenmodes of a resonator with propagating modes of waveguides. The most typical example of SP BIC is the odd eigenmode of the resonator with the eigenfrequency embedded into the propagating band of even propagating eigenmodes of the waveguide. In this work, we consider a more sophisticated case of an acoustic cuboid resonator that is opened by the attachment of two cylindrical waveguides. We show that BICs can be sustained in an open acoustic resonator with reduced symmetry. For symmetrical positions of waveguides, the eigenmodes of the cuboid can also be classified as SP BICs and show different stability against the shifts of waveguides from the positions of symmetry of the cuboid. We fabricate a series of coupled waveguide resonators and experimentally verify the existence of these BICs by identifying the vanished linewidth of Fano resonance in transmission spectra. Besides, we also show that evanescent modes of waveguides play a role in the formation of BICs in a nonaxisymmetric waveguide-resonator system by tuning the angle *θ* between two waveguides. Consequently, the eigenmodes remain SP BICs for *θ *= 0° and *θ *= 180° but convert into accidental BICs at *θ *≈ 85°or *θ *≈ 275°. Such accidental BICs are also experimentally verified. Our results enrich the understanding of SP BICs and accidental BICs, and provide alternative methods of routing acoustic waves and designing acoustic devices requiring fine spectrum features, such as filters and sensors.

## General Framework of Bound States in the Continuum in an Open Acoustic Resonator

https://doi.org/10.1103/PhysRevApplied.18.054021

Bound states in the continuum (BICs) provide a viable way of achieving high-Q resonances in both photonics and acoustics. In this work, we propose a general method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a coupled acoustic waveguide-resonator system. We demonstrate that FW BICs can be achieved with arbitrary two degenerate resonances in a closed resonator, regardless of whether they have the same or opposite parity. Moreover, their eigenmode profiles can be arbitrarily engineered by adjusting the position of the attached waveguide. This suggests an effective way of continuously switching the nature of the BICs from FW BICs to symmetry-protected BICs or accidental BICs. Also, such BICs are sustained in the coupled waveguide-resonator system with shapes such as rectangles, ellipses, and rhomboids. These interesting phenomena are well explained by the two-level effective non-Hermitian Hamiltonian, where two strongly coupled degenerate modes play a major role in forming such FW BICs. Additionally, we find that such an open system also supports accidental BICs in geometry space instead of momentum space via tuning the position of the attached waveguide, which is attributed to the quenched coupling between the waveguide and eigenmodes of the closed cavity. Finally, we fabricate a series of three-dimensional coupled resonator waveguides and experimentally verify the existence of FW BICs and accidental BICs by measuring the transmission spectra. Our results complement the current BIC library in acoustics and provide nice routes for designing acoustic devices, such as acoustic absorbers, filters, and sensors.

## Self-trapping of nanoparticles by bound states in the continuum

https://doi.org/10.1103/PhysRevB.106.165430

In the first tutorial part of the paper, we show that equilibrium positions of small dielectric particles inside the Fabry-Perot resonator (FPR) are sensitive to a frequency of incident electromagnetic wave and size of particle. That elucidates basic principles of resonant trapping of nanoparticles by excitation of high-Q resonances of FPR. In the second part, we consider a long dielectric cylinder with submicron radius (primary cylinder) integrated into a metallic waveguide which supports symmetry-protected bound states in the continuum (BICs). We consider the case of a slightly shifted cylinder relative to the axis of symmetry of a waveguide that controls the Q factor of quasi-BIC. Then, the extra nanoparticle perturbs quasi-BIC as dependent on the size of the nanoparticle and position relative to the primary cylinder. An interplay between the resonant width of quasi-BIC and a degree of frequency perturbation defines whether a dragging nanoparticle is terminated at a surface of the primary cylinder for an ultrasmall size of nanoparticles or at the definite distances from the cylinder for the larger size of nanoparticles. Thereby, we demonstrate a paradigm of resonant self-trapping and sorting of nanoparticles by use of quasi-BICs. We also show extremal sensitivity of self-trapping to the frequency of an electromagnetic (EM) wave propagating over waveguide.

## Desktop laboratory of bound states in the continuum in metallic waveguide with dielectric cavities

DOI: 10.1103/PhysRevB.106.075304

We consider dielectric cavities whose radiation space is restricted by two parallel metallic planes. The TM solutions of the Maxwell equations of the system are equivalent to the solutions of periodical arrays of dielectric cavities. The system readily allows to achieve bound states in the continuum (BICs) of any type including topological BICs as dependent on position and orientation of the cavities relative to the planes and that extremely facilitates experimental studies in comparison to infinite arrays of the cavities. We show the effect of merging of topologically protected BICs that pushes the square asymptotic of the Q factor into the power degree 4 or even 6.

## Degenerate bound states in the continuum in square and triangular open acoustic resonators

https://doi.org/10.1103/PhysRevB.106.085404

We consider square and equilateral triangular open acoustic resonators with the C4v and C3v symmetries, respectively. There is a unique property of square and triangular resonators of accidental number fourfold degeneracy of eigenstates that gives rise to twofold-degenerate Friedrich-Wintgen (FW) bound states in the continuum (BICs). Compared to usual FW BICs, the degenerate FW BICs maintain high Q factor in wide range of the size of resonators. That removes the fabrication difficulties of the proper choice of resonator. The presence of degenerate BICs in triangular resonators is extremely sensitive to switch output flows by small perturbations with 100% efficiency.

## Exceptional Points through Variation of Distances between Four Coaxial Dielectric Disks

https://doi.org/10.3390/photonics8110460

By variation of a refractive index and aspect ratio of the isolated disk, we achieved exceptional points (EPs) at which the resonant frequencies and resonant modes coalesce. However, in practice, that kind of variation presents a technological problem. We considered the method to avoid the problem by substitution of two disk’s dimers. In each dimer, variation of the distance between disks was equivalent to a variation of the aspect ratio of the dimer. Moreover, the variation of the distance between dimers provides the second parameter that gives rise to a vast number of EPs. We recovered the initial resonant eigenmode by encircling multiple EPs two, three, and four times in the two-dimensional parametric space of distances.

## Ultrahigh-Q system of a few coaxial disks

https://doi.org/10.1515/nanoph-2021-0345

Resonant modes of high contrast dielectric disk have finite *Q*-factors in the subwavelength range due to radiation leakage into the surrounding space. That leakage can be reduced considerably (a few times) by exploiting of the mechanism of destructive interference of two modes for avoided crossing of resonances (ACR) (Rybin et al. M. V. Rybin, K. L. Koshelev, Z. F. Sadrieva, et al., “High-Q Supercavity Modes in Subwavelength Dielectric Resonators,” *Phys. Rev. Lett.*, vol. 119, p. 243901, 2017.). In the present paper we report suppression of radiation leakage by a few orders in magnitude via the ACR in the structure of three and four different coaxial disks. For fine multi-scale tuning of disks we reveal the ultrahigh-*Q* resonances of order 10^{5} for the case of three disks and of order 10^{6} for the case of four coaxial disks of equal radii.

## Exceptional points in a dielectric spheroid

DOI:https://doi.org/10.1103/PhysRevA.104.053507

Evolution of resonant frequencies and resonant modes as dependent on the aspect ratio is considered in a dielectric high index spheroid. Because of rotational symmetry of the spheroid the solutions are separated by the azimuthal index m. By the two-parametric variation of a refractive index and the aspect ratio we achieve exceptional points at which the resonant frequencies and resonant modes are coalesced in the sector m=0.

## Resonant binding of dielectric particles to a metal surface without plasmonics

A high index dielectric spherical particle supports the high-Q resonant Mie modes that result in a regular series of sharp resonances in the radiation pressure. The presence of a perfectly conducting metal surface transforms the Mie modes into extremely high-Q magnetic bonding or electric antibonding modes for the close approach of a sphere to a surface. We show that an electromagnetic plane wave with normal incidence results in repulsive or attractive resonant optical forces relative to a metal for the excitation of electric bonding or magnetic antibonding resonant modes, respectively. A magnitude of resonant optical forces reaches the order of 1 nN of magnitude for micron-sized silicon particles and a power of light 1mW/μm2 that exceeds the gravitational force by four orders. However, what is the most remarkable is there are steady positions for a sphere between the pulling and pushing forces that give rise to the resonant binding of the sphere to a metal surface.

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.L051501

## Interference traps waves in an open system: bound states in the continuum

I review the four mechanisms of bound states in the continuum (BICs) in the application of microwave and acoustic cavities open to directional waveguides. The most simple are symmetry-protected BICs, which are localized inside the cavity because of the orthogonality of the eigenmodes to the propagating modes of waveguides. However, the most general and interesting is the Friedrich–Wintgen mechanism, when the BICs are the result of the fully destructive interference of outgoing resonant modes. The third type of BICs, Fabry–Perot BICs, occurs in a double resonator system when each resonator can serve as an ideal mirror. Finally, the accidental BICs can be realized in the open cavities with no symmetry like the open Sinai billiard in which the eigenmode of the resonator can become orthogonal to the continuum of the waveguide accidentally due to a smooth deformation of the eigenmode. We also review the one-dimensional systems in which the BICs occur owing to the fully destructive interference of two waves separated by spin or polarization or by paths in the Aharonov–Bohm rings. We make broad use of the method of effective non-Hermitian Hamiltonian equivalent to the coupled mode theory, which detects BICs by finding zero-width resonances.

## Mie Resonance Engineering in Two Disks

## Resonant bending of silicon nanowires by incident light

Coupling of two dielectric wires with a rectangular cross section gives rise to bonding and anti-bonding resonances. The latter is featured by extremal narrowing of the resonant width for variation of the aspect ratio of the cross section and distance between wires. A plane wave resonant to this anti-bonding resonance gives rise to unprecedent enhancement of the optical forces up to several nano Newtons per micrometer length of the wires. The forces oscillate with the angle of incidence of the plane wave but always try to repel the wires. If the wires are fixed at the ends, the light power.5mW/µm2 bends wires with length 50 µm by order 100 nm.

## Giant resonant enhancement of optical binding of dielectric particles

Optical coupling of two identical dielectric particles gives rise to bonding and antibonding resonances. The latter is featured by significant narrowing of the resonant width and strong enhancement of the Q factor for the high-index micron-size particles in subwavelength range. We consider particles shaped as spheres and disks under coaxial illumination of dual incoherent counterpropagating Bessel beams. In the case of spheres we derive analytical expressions for the optical binding (OB) force which decays and displays two periods of oscillations. For close distances the OB force enormously increases in the resonant regime. The case of two coaxial disks is featured by extremal enhancement of the Q factor owing to the twofold variation over the distance between disks and the aspect ratio of each disk compared to the case of two spheres. In that case we demonstrate enhancement of the OB force up to several tens of nanonewtons. We show that the magnitude and sign of the OB force strongly depend on the longitudinal wave vector of the Bessel beams.

## Giant resonant enhancement of optical binding of dielectric disks

Two-fold variation over the aspect ratio of each disk and distance between disks gives rise to numerous events of avoided crossing of resonances of individual disks. For these events, the hybridized anti-bonding resonant modes can acquire a morphology close to the Mie resonant mode with the high orbital momentum of an equivalent sphere. The 𝑄Q factor of such resonance can exceed the 𝑄Q factor of an isolated disk by two orders of magnitude. We show that dual incoherent counterpropagating coaxial Bessel beams with power 1mW/µm21mW/µm2 with frequency resonant to such anti-bonding Mie-like modes result in unprecedented optical binding forces up to tens of nano-Newtons for silicon micrometer-sized disks. We show also that the magnitude and sign of optical forces depend strongly on the longitudinal wave vector of the Bessel beams.

## Bound states in the continuum in open spherical resonator

We consider the bound states in the continuum (BICs) or embedded trapped modes in an open spherical acoustic resonator. The eigenfrequencies of closed resonator are2l+1<i-fold degenerated, wherelis the orbital index. An attachment of two cylindrical waveguides lifts this degeneracy and transforms the eigenfrequencies into resonances whose real parts depend on the position of the waveguides. When the waveguides are angled by pi<i, variation over that angle gives rise to avoided crossings of resonant modes with differentlto result in the Friedrich-Wintgen BICs. For = pi there might be only the symmetry protected BICs. When three waveguides are connected to the spherical resonator the Friedrich-Wintgen BICs occur due to the avoided crossings of resonant modes with the samelbut different azimuthal indices-l <= m <= l.

## Interaction between dielectric particles enhances the Q factor

We study behavior of resonant modes with a distance between two identical dielectric cylinders and disks. We reveal two basic scenarios of evolution of resonances with the distance between the cylinders. For larger distances and respectively weaker interaction of particles the resonances are bound around the Mie resonances and evolve by spiral way. For shorter distances and respectively stronger interaction the resonances bypass the Mie resonances. Both scenarios demonstrate considerable enhancement of the Q factor compared to the case of isolated particle.

## One-dimensional photonic bound states in the continuum

In 1985 Fridriech and Wintgen proposed a mechanism for bound states in the continuum based on full destructive interference of two resonances which can be easily applied to the two- and three-dimensional wave systems. Here we explicitly show that this mechanism can be realized in one-dimensional quantum potential well, owing to destructive interference of electron paths with different spin in tilted magnetic field. Due to one-by-one correspondence between the spin of the electron and the polarization state of light, we have found numerous bound states in the continuum in the one-dimensional photonic system and experimentally confirmed them. The experimental set-up consists of the one-dimensional photonic crystal conjugated with a liquid-crystalline anisotropic defect layer and covered by metal film.

## Interaction between dielectric particles enhances the Q-factor

We study behavior of resonant modes with a distance between two dielectric resonators shaped as cylinders and disks. We reveal two basic scenarios of evolution of resonances with the distance between the cylinders. For larger distances and respectively weaker interaction of particles the resonances are bound around the resonances of isolated resonators and evolve by spiral way. For shorter distances and respectively stronger interaction the resonances bypass the isolated resonances. Both scenarios demonstrate considerable enhancement of the Q factor compared to the case of isolated particle.

## Generation of vortex waves in non-coaxial cylindrical waveguides

A non-coaxial waveguide composed of a cylindrical resonator of radius R and cylindrical waveguides with the radii r1 and r2, respectively, is considered. The radii satisfy the inequality r1 < r2 < R. The conversion from the channel with zero orbital angular momentum (OAM) into the channels with non-zero OAM is achieved by shifting the center lines of the waveguides relative to the center line of the cylindrical resonator. The center lines of input and output waveguides are shifted relative to each other by the angle D/ in order to twist the output acoustic wave. The conversion efficiency of the input wave with zero OAM into the output wave with non-zero OAM as dependent on the frequency, length of the resonator, and D/ is considered, and the domains where the efficiency can reach almost 100% are found. (C) 2019 Acoustical Society of America.

## Evolution of the resonances of two parallel dielectric cylinders with distance between them

We study evolution of resonant modes by traversing over the distance between two parallel dielectric cylinders. The processes of mutual scattering of Mie resonant modes by cylinders result in an interaction between the cylinders which lifts a degeneracy of resonances of the isolated cylinders. There are two basic scenarios of evolution. For strong interaction of cylinders resonances bypass the Mie resonances with increase of the distance. That scenario is typical for low-lying resonances (monopole and dipole). For weak interaction of cylinders the resonances are bound around the Mie resonances of isolated cylinders that form the second scenario. Both scenarios demonstrate a significant enhancement of the Q factor compared to the case of an isolated cylinder

## Interaction between coaxial dielectric disks enhances the Q factor

We study the behavior of resonant modes under variation of the distance between two coaxial dielectric disks and show an avoided crossing of resonances because of the interaction between the disks. Owing to coaxial arrangement of disks, the resonant modes are specified by the azimuthal index m=0,1,2,…. In the present paper, we consider the case m=0. At a long enough distance, the modes are symmetric and antisymmetric hybridizations of the resonant modes of the isolated disk. With decreasing the distance, the interaction becomes stronger, giving rise to avoided crossings of different resonances of the isolated disk. This in turn enhances the Q factor of the two disks by one order in magnitude compared to the Q factor of the isolated disk.

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