Recent progress in nanoscale optical physics is associated with the development of a new branch of nanophotonics exploring strong Mie resonances in dielectric nanoparticles with high refractive index. The high-index resonant dielectric nanostructures form building blocks for novel photonic metadevices with low losses and advanced functionalities. However, unlike extensively studied cavities in photonic crystals, such dielectric resonators demonstrate low quality factors (Q-factors). Here, we uncover a novel mechanism for achieving giant Q-factors of subwavelength nanoscale resonators by realizing the regime of bound states in the continuum. We reveal strong mode coupling and Fano resonances in high-index dielectric finite-length nanorods resulting in high-Q factors at the nanoscale. Thus, high-index dielectric resonators represent the simplest example of nanophotonic supercavities, expanding substantially the range of applications of all-dielectric resonant nanophotonics and meta-optics.Trapping of light in localized modes is extremely important for various applications in optics and photonics including lasing [1], sensing [2,3], harmonic generation [4,5], Raman scattering [6], and photovoltaics [7,8]. For many optical devices, it becomes critical to localize electromagnetic fields in small subwavelength volumes. Plasmonic structures based on metals allow subwavelength localization of light by means of surface plasmon polaritons [9]. However, metals impose inevitable losses and heating, which limit the device performance and efficiency. In contrast, dielectric nanoparticles with high refractive index offer a novel way for the subwavelength localization of light by employing the Mie resonances being limited only by the radiation damping [10]. Unlike metallic nanoscale structures, dielectric nanoparticles support both electric and magnetic Mie modes that expand substantially the applications of meta-optics [11]. Also, dielectric materials with high refractive index are available in a broad spectral range. At the same time, the standard Mie theory predicts relatively low values of the quality factor (Q ≈ 10) for nanoparticles made of conventional optical materials such as Si, Ge, and AlGaAs, both in the visible and near-infrared spectral ranges.However, for many applications of all-dielectric nanophotonics it is very desirable to achieve higher values of the Q factor. One way to enhance the Q factor is to increase the size of the resonator, for example by confining waves by cavities and defects in photonic crystals [12] or by exploiting modes with high angular momentum known as whispering gallery modes (WGM) [13]. Another way is to arrange several resonators in space and excite collective modes [14,15]. An alternative approach for enhancing the Q factors is to use the so-called anapole mode with the spectrally overlapped electric and toroidal dipole modes [16,17]. As a result, the Q factor of the anapole mode realized in a dielectric resonator may exceed 30 [18]. Here we suggest a novel approach based on bound stat...

The study of resonant dielectric nanostructures with high refractive index is a new research direction in nanoscale optics and metamaterial-inspired nanophotonics. Because of the unique opticallyinduced electric and magnetic Mie resonances, high-index nanoscale structures are expected to complement or even replace different plasmonic components in a range of potential applications. Here we study strong coupling between modes of a single subwavelength high-index dielectric resonator and analyse the mode transformation and Fano resonances when resonator's aspect ratio varies. We demonstrate that strong mode coupling results in resonances with high quality factors, which are related to the physics of bound states in the continuum when the radiative losses are almost suppressed due to the Friedrich-Wintgen scenario of destructive interference. We explain the physics of these states in terms of multipole decomposition and show that their appearance is accompanied by drastic change of the far-field radiation pattern. We reveal a fundamental link between the formation of the high-quality resonances and peculiarities of the Fano parameter in the scattering cross-section spectra. Our theoretical findings are confirmed by microwave experiments for the scattering of a high-index cylindrical resonators with a tunable aspect ratio. The proposed mechanism of the strong mode coupling in single subwavelength high-index resonators accompanied by resonances with high quality factor helps to extend substantially functionalities of all-dielectric nanophotonics that opens new horizons for active and passive nanoscale metadevices. arXiv:1805.09265v2 [physics.optics] 1 Dec 2018

We report the observation of a Fano resonance between continuum Mie scattering and a narrow Bragg band in synthetic opal photonic crystals. The resonance leads to a transmission spectrum exhibiting a Bragg dip with an asymmetric profile, which can be tunably reversed to a Bragg rise. The Fano asymmetry parameter is linked with the dielectric contrast between the permittivity of the filler and the specific value determined by the opal matrix. The existence of the Fano resonance is directly related to disorder due to non-uniformity of a-SiO2 opal spheres. Proposed theoretical "quasi-3D" model produces results in excellent agreement with the experimental data. PACS numbers: 42.70Qs, 42.25.Fx, 42.79.Fm Mie and Bragg scattering are key optical phenomena in photonic crystals (PhC) composed of spherical or nearly spherical particles. Light scattering by an isolated spherical particle can be described by Mie theory [1]. Considering PhC composed of a periodic array of such spheres, interference of scattered waves results in the transformation of Mie scattering into Bragg scattering and gives rise to formation of the photonic band structure [2]. The underlying Mie scattering is therefore hidden in perfectly ordered PhC and as a result, it has been insufficiently studied so that its role is clear only for the case of perfect structures. The resulting Bragg scattering, on the other hand, has been intensively examined, both experimentally and theoretically in great detail [2,3,4,5,6,7]. In particular, the multiple Bragg diffraction phenomenon in PhC, which occurs when two narrow Bragg bands demonstrate the avoided crossing effect [7,8,9, 10] has been thoroughly studied. Departing from this phenomenon and with intention to further deepen our understanding of light scattering in PhC, a number of challenging problems can be formulated: What can we expect if a spectrally narrow Bragg band interacts with a broad spectrum originating from certain scattering mechanisms such as Mie or Fabry-Perot scattering? Is it possible to observe the consequences of this interaction or simply Mie scattering experimentally? What are the effects of inherent disorder in the structural components of opal-based PhC, beyond the well-known broadening and degradation of stop bands [6,11,12,13,14,15]?If a narrow Bragg band interacts with the continuum spectrum through an interference effect constructively or destructively, we can expect an interaction of Fano-type [16], a phenomenon well-known across many different branches of physics. The Fano resonance between continuum and discrete states manifests as an asymmetric profile of narrow band in the transmission spectrum, which in general has the form:where Ω = (ω − ω B )/(γ B /2), ω B is the frequency, γ B is the width of the narrow band, and q is the Fano asymmetry parameter. It was shown theoretically that Fano-type asymmetric line shapes can be created in the response function of certain PhC. In general these systems consist of a waveguide with forward and backward propagating waves being indirectly...