# Новые публикации

## 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.

## Multi-channel bound states in the continuum in coaxial cylindrical waveguide

Bound states in the continuum (BICs) or embedded trapped modes are widely studied in different physical systems. The studies are restricted to a single open scattering channel. In the present paper we consider BICs embedded into several continua in a cylindrical resonator opened by two coaxially attached cylindrical waveguides with different radii. We demonstrate that engineering the BICs requires a degeneracy of three eigenmodeds of the closed resonator. That is achieved by variation of both the length and the radius of the resonator.

## Experimental observation of a symmetry-protected bound state in the continuum in a chain of dielectric disks

The existence of bound states in the continuum (BIC) manifests a general wave phenomenon first predicted in quantum mechanics by John von Neumann and Eugene Wigner [J. von Neumann and E. Wigner, Phys. Z. 30, 465 (1929)]. Today it is being actively explored in photonics, radiophysics, acoustics, and hydrodynamics. We report an experimental observation of an electromagnetic bound state in the radiation continuum in a one-dimensional array of dielectric particles. By measurement of the transmission spectra of the ceramic disk chain at GHz frequencies, we demonstrate how a resonant state in the vicinity of the center of the Brillouin zone turns into a symmetry-protected BIC with increase in the number of the disks. We estimate a number of the disks when the radiation losses become negligible in comparison to material absorption and, therefore, the chain could be considered practically as infinite. The presented analysis is supplemented by measurements of the near fields of the symmetry-protected BIC. All measurements are in a good agreement with the results of the numerical simulation and analytical model based on a tight-binding approximation. The obtained results provide useful guidelines for practical implementations of structures with bound states in the continuum that opens up horizons for the development of optical and radio-frequency metadevices.

## High-Q resonant modes in a finite array of dielectric particles

We trace the Q factor of the resonant modes which are limited to bound states in the continuum (BICs) for N=∞ in the finite array of N dielectric spheres and disks. For the symmetry-protected BICs we observe the quadratic dependence of the Q factor on N for high-refractive-index particles, while for low-refractive-index particles there is an interplay between the quadratic and cubic dependencies. The Q factor of accidental BICs grows cubically with N. We show that a plane wave can excite these quasi-BICs for tuning of the angle of incidence.

## Bound states with orbital angular momentum in the continuum of cylindrical non-axisymmetric waveguide

We consider acoustic wave transmission in a non-axisymmetric waveguide which consists of a cylindrical resonator of radius and length and two cylindrical waveguides of radius whose axes are shifted relative to the axis of the resonator and relative to each other by azimuthal angle . We find multiple bound states in the continuum (trapped modes) with nonzero orbital angular momentum under variation of due to full destructive interference of resonant modes leaking into waveguides. For we find the degenerate bound states in the continuum whose contribution into the scattering wave function is complex and supports giant vortical acoustic intensity spinning inside the resonator.

## Goos-Hanchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab

We consider reflection of the Laguerre–Gaussian light beams by a dielectric slab. In view of the unified operator approach, the higher-order Laguerre–Gaussian beams represent a parametric family with the transverse beam profile given by an arbitrary generating parameter. Relying on the Fourier expansion in the focal plane of the beam, we compute the Goos–Hänchen and the Imbert–Fedorov shifts for light beams with non-zero order and azimuthal index. It is demonstrated that both shifts exhibit resonant behavior as functions of the angle of incidence due to the interference between the waves reflected from the upper and lower interfaces. The centroid shifts strongly depend on the order and azimuthal index of the beam. Most interestingly, it is found that the generating parameter of the higher-order beam families strongly affects the shifts. Thus, reshaping of the incident wavefront with fixed order and azimuthal index changes the linear Goos–Hänchen shift up to one half of the beam radius, both negative and positive.

## Fibers based on propagating bound states in the continuum

We show that a circular periodic array of silicon dielectric cylinders supports nearly bound states in the continuum (BICs) propagating along the cylinders. These propagating nearly BICs with extremely large-Q factors are surrounded by resonant modes weakly leaking into the radiation continuum. We present leaky zones in the form of dispersion curves for complex eigenfrequencies dependent on propagation constant kz, with the wave vector directed along the cylinders in the vicinity of different types of BICs. Symmetry-protected nearly BICs have the resonant width proportional to squared propagation constant Γ∼k2z; the widths of non-symmetry-protected nearly BICs behave as Γ∼(kz−kc)2, where kc and non-symmetry-protected nearly BICs have the resonant width proportional to k4z. The latter propagating nearly BICs can serve for the transmission of a electromagnetic signal paving a way to a different type of optical fiber. We also demonstrate weakly leaking resonant modes which carry orbital angular momentum.

## Scattering plane waves by a dielectric cylinder with periodically modulated permittivity at oblique incidence

For scattering of electromagnetic waves by a dielectric cylinder with periodically modulated permittivity we focus on the vicinity of the frequency of the wave with regard to the eigenfrequencies of bound states in the continuum. Then response of the cylinder becomes extremely sensitive to the angle of incidence and polarization of the plane wave. The cross section of the scattering of electromagnetic waves with mixed polarization undergoes crucial change from the Bragg shape to the Fano shape by rotation of the polarization that paves a way to tuning of Fano resonances by an external source.

## Trapped modes in a non-axisymmetric cylindrical waveguide

We consider acoustic wave transmission in a non-axisymmetric waveguide which consists of a cylindrical resonator and two cylindrical waveguides whose axes are shifted relatively to each other by an azimuthal angle . Under variation of the resonator's length and fixed we find bound states in the continuum (trapped modes) due to full destructive interference of resonant modes leaking into the waveguides. Rotation of the waveguide adds complex phases to the coupling strengths of the resonator eigenmodes with the propagating modes of the waveguides tuning Fano resonances to give rise to a wave faucet. Under variation of with fixed resonator's length we find symmetry protected trapped modes. For these trapped modes contribute to the scattering function supporting high vortical acoustic intensity spinning inside the resonator. The waveguide rotation brings an important feature to the scattering and provides an instrument for control of acoustic transmittance and wave trapping.

## Optical defect mode with tunable Q factor in a one-dimensional anisotropic photonic crystal

We consider a one-dimensional photonic crystal composed of alternating layers of isotropic and anisotropic dielectric materials. Such a system has different band structures for different polarizations of light. We demonstrate that if a defect layer is inserted into the structure, the crystal can support a polarized optical defect mode that is a bound state in the continuum (BIC). In the case of an anisotropic defect layer, by tilting the principle dielectric axes of the defect layer relative to those of the photonic crystal the BIC is transformed to a quasi-BIC. We derive an analytical expression for the decay rate of the resonance. An experimental setup with a liquid crystal defect layer is proposed to tune the Q factor of the quasi-BIC through applying an external electric field. We speculate that the setup provides a simple and robust platform for observing optical bound states in the continuum in the form of resonances with tunable Q factor.

## Propagating Bloch bound states with orbital angular momentum above the light line in the array of dielectric spheres

We present propagating Bloch bound states in the radiation continuum with orbital angular momentum in an infinite linear periodical array of dielectric spheres. The bound states in the continuum demonstrate a giant Poynting vector spiraling around the array. They can be excited by a plane wave with incident linear polarization with a small tilt relative to the axis of the array.

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