We consider optical response induced by bound states in the continuum (BICs) in arrays of dielectric spheres. By combining quasi-mode expansion technique with coupled mode theory (CMT) we put forward a theory of the optical response by high-Q resonance surrounding BICs in momentum space. The central result are analytical expressions for the CMT parameters, which can be easily calculated from the eigenfrequencies and eigenvectors of the interaction matrix of the scattering systems. The results obtained are verified in comparison against exact numerical solutions to demonstrate that the CMT approximation is capable of reproducing Fano features in the spectral vicinity of the BIC. Based on the quasi-mode expansion technique we derived the asymptotic scaling law for the CMT parameters in the vicinity of the $Γ$-point. It is rigorously demonstrated that the line width in the CMT approximation exhibits different asymptotic behaviour depending on the symmetry of the BIC.
High refractive index dielectric particles present unique light scattering properties in the spectral range dominated by electric and magnetic dipolar resonances. These properties are absent in non-resonant low-index particles due to the strong overlap between dipolar and higher order multipolar contributions. Here we propose to induce duality and zero optical backscattering (first Kerker conditions) at multiple size parameter values on arbitrary dielectric spheres by illuminating with a tightly focused dipolar beam. As an illustrative example, we show that duality signatures, including topolo…
In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out, and also by getting absorbed within the medium. We analyze the leaky modes of solid dielectric spheres by examining solutions of Maxwell's equations for simple homogeneous, isotropic, linearly dispersive media that admit complex-valued oscillation frequencies. We show that, under appropriate circumstances, these leaky modes constitute a complete set into which an initial electromagnetic field distribution inside a dielectric sphere can be expanded. We provide the outline of a comple…
Controlling the electromagnetic helicity and directionality of the light scattered by dielectric particles is paramount to a variety of phenomenology of interest in all-dielectric optics and photonics. In this Letter, we show that the conservation of the electromagnetic helicity in the scattering by high-index dielectric Mie spheres can be used as a probe of pure-multipolar spectral regions, particularly, of dipolar nature, beyond its presumed spectral interval. This finding reveals that the dipolar behavior is not necessarily limited to small particles, in striking contrast to the current sta…
The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $γ$. Closed-form expressions were derived for the expansion coefficients of the scattered field phasors in terms of those of the incident field phasors. These expansion coefficients were used to obtain analytical expressions for the total scattering, extinction, forward scattering, and backscattering efficiencies of the sphere. Resonances exist for relatively low values of $γ$,…
We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces or arbitrary surface waves. A dielectric sphere is effectively an open system whose description requires the introduction of non-Hermitian operators characterized by complex eigenvalues and not normalizable e…
The sensitivity of a refractive index sensor based on an optical bound state in the continuum is considered. Applying Zel'dovich perturbation theory we derived an analytic expression for bulk sensitivity of an all-dielectic sensor utilizing symmetry protected in-$Γ$ optical bound states in a dielectric grating. The upper sensitivity limit is obtained. A recipe is proposed for obtaining the upper sensitivity limit by optimizing the design of the grating. The results are confirmed through direct numerical simulations.
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. 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 …
We consider light scattering by dielectric gratings supporting optical bound states in the continuum. Due to the presence of instantaneous Kerr nonlinearity the critical field enhancement in the spectral vicinity of the bound state triggers the effect of optical bistability. The onset of bistability is explained theoretically in the framework of the temporal coupled mode theory. As the central result we cast the problem into the form of a singly field-driven nonlinear oscillator. The theoretical results are verified in comparison against full-wave numerical simulations.
Recently, we showed that dielectric mesoscale spheres could support so-called super-resonance effect, i.e. high-order Mie resonance modes with giant field localization and enhancement. Due to the presence of the surrounding medium leads to a significant influence in the intensity of the field in the particle, based on Mie theory we show for the first time that this effect may be use to design refractive index sensor of medium. Using the example of air as an environment, we have shown that the sensitivity of the proposed sensor concept can reach from 10-6 to 10-8, depending on the accuracy of t…
The article reports on light enhancement by structural resonances in linear periodic arrays of identical dielectric elements. As the basic elements both spheres and rods with circular cross section have been considered. In either case, it has been demonstrated that high-$Q$ structural resonant modes originated from bound states in the continuum enable near-field amplitude enhancement by factor of $10$--$25$ in the red-to-near infrared range in lossy silicon. The asymptotic behavior of the $Q$-factor with the number of elements in the array is explained theoretically by analyzing quasi-bound st…
We consider propagating bound states in the continuum in dielectric gratings. The gratings consist of a slab with ridges periodically arranged ether on top or on the both sides of the slab. Based on the Fourier modal approach we recover the leaky zones above the line of light to identify the geometries of the gratings supporting Bloch bound states propagating in the direction perpendicular to the ridges. Most importantly, it is demonstrated that if a two-side grating possesses either mirror or glide symmetry the Bloch bound states are stable to variation of parameters as far as the above symme…
We consider bound states in the continuum (BICs) in low-contrast dielectric gratings (DGs). It is demonstrated that the BICs originate from the reduced guided modes on the effective dielectric slab with the permittivity equal to the average permittivity of the DG. In case of isolated resonances the positions of BICs can be found from two-wave dispersion relationships for guided leaky modes. In the case of the degeneracy between the two families of leaky modes the system exhibits an avoided crossing of resonances. In the spectral vicinity of the avoided crossing the transmittance as well as the…
We report bound states in the radiation continuum (BSCs) in a single infinitely long dielectric rod with periodically stepwise modulated permittivity alternating from $ε_1$ to $ε_2$. For $ε_2=1$ in air the rod is equivalent to a stack of dielectric discs with permittivity $ε_1$. Because of rotational and translational symmetries the BSCs are classified by orbital angular momentum $m$ and the Bloch wave vector $β$ directed along the rod. For $m=0$ and $β=0$ the symmetry protected BSCs have definite polarization and occur in a wide range of the radius of the rod and the dielectric permittivities…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the perfect spherical form the resonances change accordingly. In this thesis, a perturbation theory for the optical resonances of such a deformed sphere is developed. The optical resonances of such an open system are characterized by complex eigenvalues, where the real part relates to the frequency of the resonant light and the imaginary part to the energy leakage out…
The emerging all-dielectric platform exhibits high-quality ($Q$) resonances governed by the physics of bound states in the continuum (BIC) that drives highly efficient nonlinear optical processes. Here we demonstrate the robust enhancement of third-(THG) and fifth-harmonic generation (FHG) from all-dielectric metasurfaces composed of four silicon nanodisks. Through the symmetry breaking, the genuine BIC transforms into the high-$Q$ quasi-BIC resonance with tight field confinement for record high THG efficiency of $3.9\times10^{-4}$ W$^{-2}$ and FHG efficiency of $4.8\times10^{-10}$ W$^{-4}$ us…
High refractive index dielectric spheres present remarkable light-scattering properties in the spectral range dominated by dipolar modes. However, most of these properties are absent for larger spheres under plane wave illumination. Here, we propose to unravel dipolar regimes regardless of the sphere size and refractive index by illuminating with a pure dipolar field. This type of illumination ensures that the scattering response of the sphere is purely dipolar. In this scenario, we show that Kerker conditions are not only related to duality symmetry and a strong backward-to-forward asymmetric…
Recently emerged dielectric resonators and metasurfaces offer a low-loss platform for efficient manipulation of electromagnetic waves from microwave to visible. Such flat meta-optics can focus electromagnetic waves, generate structured beams and vortices, enhance local fields for sensing as well as provide additional functionalities for advanced MRI machinery. Recent advances are associated with exotic optical modes called bound states in the continuum, which can give rise to extremely large quality factors and supercavity lasing. Here, we experimentally demonstrate subwavelength active superc…
We consider E polarized bound states in the radiation continuum (BICs) in circular periodical arrays of $N$ infinitely long dielectric rods. We find that each true BIC which occurs in an infinite linear array has its counterpart in the circular array as a near-BIC with extremely large quality factor. We argue analytically as well as numerically that the quality factor of the symmetry protected near-BICs diverges as $e^{λN}$ where $λ$ is a material parameter dependent on the radius and the refraction index of the rods. By tuning of the radius of rods we also find numerically non-symmetry protec…
We investigate bound states in the continuum (BICs) in a planar dielectric waveguide structure consisting of a gold grating on a dielectric layer with a back layer of metal. In this structure, Friedrich-Wintgen (FW) BICs caused by the destructive interference between the radiations from two waveguide modes appear near the anti-crossing point of the dispersion curves. In this study, it is revealed that the branch at which the BIC appears changes according to the polarization of incident radiation. Based on a temporal coupled mode theory, it is shown that the BIC branch is determined by the sign…
Electrically small dielectric antennas are of great interest for modern technologies, since they can significantly reduce the physical size of electronic devices for processing and transmitting information. We investigate the influence of the resonance conditions of an electrically small dielectric spherical antenna with a high refractive index on its directivity and analyze the dependence of these resonances on the effectively excited modes of the dielectric sphere.
We present nonlinear optical four-wave mixing in a silicon nanodisk dimer metasurface. Under the oblique incident plane waves, the designed metasurface exhibits a multi-resonant feature with simultaneous excitations of three quasi-bound states in the continuum (BIC). Through employing these quasi-BICs with maximizing electric field energy at the input bump wavelengths, significant enhancement of third-order nonlinear processes including third-harmonic generation, degenerate and non-degenerate four-wave mixing are demonstrated, giving rise to ten new frequencies in the visible wavelengths. This…
The exact suppression of backscattering from rotationally symmetric objects requires dual symmetric materials where ${ε_r} = {μ_r}$. This prevents their design at many frequency bands, including the optical one, because magnetic materials are not available. Electromagnetically small non-magnetic spheres of large permittivity offer an alternative. They can be tailored to exhibit balanced electric and magnetic dipole polarizabilities, which result in approximate zero backscattering. In this case, the effect is inherently narrowband. Here, we put forward a different alternative that allows broadb…
True Bound States in the Continuum in Compact All-Dielectric Structures
Key Lab of Advanced Transducers and Intelligent Control System, Ministry of Education and Shanxi Province, College of Physics and Optoelectronics, Taiyuan University of Technology（先进换能器与智能控制系统教育部及山西省重点实验室，物理与光电工程学院，太原理工大学）
We investigate the diffraction of guided modes of a dielectric slab waveguide on a simple integrated structure consisting of a single dielectric ridge on the surface of the waveguide. Numerical simulations based on aperiodic rigorous coupled-wave analysis demonstrate the existence of sharp resonant features and bound states in the continuum (BICs) in the reflectance and the transmittance spectra occurring at oblique incidence of a TE-polarized guided mode on the ridge. Using the effective index method, we explain the resonances by the excitation of the cross-polarized modes of the ridge. The f…
Elusive features in photonic and electronic devices can be detected by means of advanced, time-domain spectroscopic techniques. In this letter we introduce a novel kind of modulation spectroscopy, based on the optomechanical interaction of photonic and mechanical modes. Applying the technique to a Si metasurface and its drum-like mechanical modes, we detect narrow-band quasi-Bound-State-in-the-Continuum (q-BIC) modes close to normal incidence, where their measurement can be hindered by a high symmetry protection and undesired background modes. Showing a visibility enhancement of more than one …
In this research, we report the experimental evidence of the directional Fano resonances at the scattering of a plane, linearly polarized electromagnetic wave by a homogeneous dielectric sphere with high refractive index and low losses. We observe a typical asymmetric Fano profile for the intensity scattered in, practically, any given direction, while the overall extinction cross section remains Lorentzian. The phenomenon is originated in the interference of the selectively excited electric dipolar and quadrupolar modes. The selectivity of the excitation is achieved by the proper choice of the…
General concept of Fano resonance is considered so that to show the possibility of this resonance in space. Using a recently found solution for a Bessel wave beam impinging a dielectric sphere, we analyze the electromagnetic fields near a microsphere with different optical size and permittivity values. We theoretically reveal a spatial Fano resonance when a resonant mode of the sphere interferes with {an amount of } non-resonant modes. This resonance results in a giant jump of the electric field behind the sphere impinged by the first-order Bessel beam. The local minimum of the electromagnetic…
Recent research has shown that coupling between point scatterers in a disordered medium by longitudinal electromagnetic fields is harmful for Anderson localization of light. However, it has been unclear if this feature is generic or specific for point scatterers. The present work demonstrates that the intensity of longitudinal field outside a spherical dielectric scatterer illuminated by monochromatic light exhibits a complicated, nonmonotonous dependence on the scatterer size. Moreover, the intensity is reduced for a hollow sphere, whereas one can adjust the parameters of a coated sphere to o…
In this paper, we examine the modification of specific nonclassical properties of the nonlinear coherent state on sphere upon perpendicular propagation through an absorptive and dispersive dielectric slab at finite temperature. For this purpose, by describing the dielectric dispersion of the slab by Lorentz model, the quadrature squeezing and the Mandel parameter are evaluated for the transmitted state. A generalization of single-mode nonlinear coherent state to the continuum-mode is considered. The degree of second-order coherence is instead calculated for a continuum nonlinear coherent state…
We discuss the recent advances in meta-optics and nanophotonics associated with the physics of bound states in the continuum (BICs). Such resonant states appear due to a strong coupling between leaky modes in optical guiding structures being supported by subwavelength high-index dielectric Mie-resonant nanoantennas or all-dielectric metasurfaces. First, we review briefly very recent developments in the BIC physics in application to isolated subwavelength particles. We pay a special attention to novel opportunities for nonlinear nanophotonics due to the large field enhancement inside the partic…
Quasi-Bound States in the Continuum-Induced Second Harmonic Generation Enhancement in High-$Q$ Triple Dielectric Nanoresonators
Institute for Advanced Study, Nanchang University（南昌大学高等研究院）；School of Education, Nanchang Institute of Science and Technology（南昌理工学院教育学院）；School of Optoelectronic Engineering, Guangdong Polytechnic Normal University（广东技术师范大学光电工程学院）；School of Information Engineering, Nanchang University（南昌大学信息工程学院）；School of Physics and Electronic Science, East China Normal University（华东师范大学物理与电子科学学院）
Dielectric metasurfaces supporting quasi-bound states in the continuum (quasi-BICs) exhibit very high quality factor resonances and electric field confinement. However, accessing the high-Q end of the quasi-BIC regime usually requires marginally distorting the metasurface design from a BIC condition, pushing the needed nanoscale fabrication precision to the limit. This work introduces a novel concept for generating high-Q quasi-BICs, which strongly relaxes this requirement by incorporating a relatively large perturbative element close to high-symmetry points of an undistorted BIC metasurface, …
Tailoring optical nonlinear effects (e.g. harmonic generation, sum-frequency mixing, etc.) in the recently emerging all-dielectric platform is important for both the fundamental science and industrial development of high-efficiency, ultrafast, and miniaturized photonic devices. In this work, we propose a novel paradigm for dynamically switchable high-harmonic generation in Silicon nanodimer metasurfaces by exploiting polarization-controlled dual bound states in the continuum (BIC). Owing to the high-quality factor of BIC resonances, efficient harmonic signals including the third-harmonic gener…
Bound states in the continuum (BICs) and exceptional points (EPs) have been the subjects of recent intensive research as they exhibit exotic phenomena that are significant for both fundamental physics and practical applications. We investigated the emergence of the Friedrich-Wintgen (FW) type BIC and the EP in a dielectric waveguide comprising a metal grating, focusing on their dependence on the grating thickness. The BIC emerges at a branch near the anti-crossing formed of the two waveguide modes, for a grating of any thickness. With the grating-thickness change, the anti-crossing gap varies …
Fano resonances induced by symmetry protected bound states in the continuum in dielectric metasurfaces: line-shape prediction by machine learning method
Optical coupling of two identical dielectric particles gives rise to bonding and anti-bonding 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 counter propagating Bessel beams. In the case of spheres we derive analytical expressions for the optical binding (OB) force which decreases as $1/L^2$ for large distance $L$ between the spheres and displays two periods of…
In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out (and also by getting absorbed within the medium). We analyze the leaky modes of a parallel-plate slab, a solid glass sphere, and a solid glass cylinder, by examining those solutions of Maxwell's equations (for dispersive as well as non-dispersive media) which admit of a complex-valued oscillation frequency. Under certain circumstances, these leaky modes constitute a complete set into which an arbitrary distribution of the electromagnetic field residing inside a dielectric body can be…
The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protected bound states in the continuum (BIC) and the magnetic dipole dominates these peculiar states. A smaller size of the defect in the broken-symmetry block gives rise to the resonance with a larger Q factor. Importantly, this relationship can be tuned by changing the structural parameter, resulting from the modulation of the topological configuration of BICs. Consequently, a Q facto…
Arrays of wavelength scale scatterers are a promising platform for designing optical elements with a compact footprint. The large number of degrees of freedom in this system allows for unique and plentiful functionalities. However, the many variables also create a complex design problem. While intuitive forward design methods work for simple optical elements, they often fail to produce complicated elements, especially those involving multiple elements. We present an inverse design methodology for large arrays of wavelength scale spheres based on both adjoint optimization or sensitivity analysi…
High index dielectric spherical particle supports the high-$Q$ resonant Mie modes that results in a regular series of sharp resonances in the radiation pressure. A presence of perfectly conducting metal surface transforms the Mie modes into the extremely high-$Q$ magnetic bonding or electric anti-bonding modes for close approaching of the sphere to the surface. We show that the electromagnetic plane wave with normal incidence results in repulsive or attractive resonant optical forces relative to metal for excitation of the electric bonding or magnetic anti-bonding resonant modes respectively. …
Substrate-engineered tunable bound states in the continuum and directional radiation in dielectric metasurfaces
Neijiang Normal University（内江师范学院）；Neijiang Optoelectronic Devices Engineering Research Center（内江光电器件工程研究中心）；Shenzhen University（深圳大学）；Great Bay University（大湾区大学）；Chongqing University（重庆大学）
