We introduce a novel physical mechanism for achieving giant quality factors ($Q$-factors) in finite-length periodic arrays of subwavelength optical resonators. The underlying physics is based on interference between the band-edge mode and another standing mode in the array, and the formation of spatially localized states with dramatically suppressed radiative losses. We demonstrate this concept for an array of $N$ dipoles with simultaneous cancellation of multipoles up to $N$-th order and the $Q$ factor growing as $Q \propto N^α$, where $α\gtrsim 6.88$. Based on this finding, we propose a realistic array of Mie-resonant nanoparticles ($N \lesssim 29$) with a dramatic enhancement of the Purcell factor (up to $\sim $3400) achieved by tuning of the array parameters.
The aim of this review is to cover recent developments in the mathematical analysis of subwavelength resonators. The use of sophisticated mathematics in the field of metamaterials is reported, which provides a mathematical framework for focusing, trapping, and guiding of waves at subwavelength scales. Throughout this review, the power of layer potential techniques combined with asymptotic analysis for solving challenging wave propagation problems at subwavelength scales is demonstrated.
The ability to highly localize light with strong electric field enhancement is critical for enabling higher efficiency solar cells, light sources, and modulators. While deep subwavelength modes can be realized with plasmonic resonators, large losses in these metal structures preclude most practical applications. We developed an alternative approach to achieving subwavelength confinement that is not accompanied by inhibitive losses. We experimentally demonstrate a dielectric bowtie photonic crystal structure that supports mode volumes commensurate with plasmonic elements and quality factors tha…
Halide perovskites are promising materials with many significant applications in photovoltaics and optoelectronics. In this paper, we use integral methods to quantify the resonant properties of halide perovskite nano-particles. We prove that, for arbitrarily small particles, the subwavelength resonant frequencies can be expressed in terms of the eigenvalues of the Newtonian potential associated with its shape. We also characterize the hybridized subwavelength resonant frequencies of a dimer of two halide perovskite particles. Finally, we examine the specific case of spherical resonators and de…
Multiphoton processes of absorption photoluminescence have enabled a wide range of applications including three-dimensional microfabrication, data storage, and biological imaging. While the applications of two-photon and three-photon absorption and luminescence have matured considerably, higher-order photoluminescence processes remain more challenging to study due to their lower efficiency, particularly in subwavelength systems. Here we report the observation of it five-photon luminescence from a single subwavelength nanoantenna at room temperature enabled by the Mie resonances. We excite an A…
We report the enhanced transmission of electromagnetic waves through a single subwavelength aperture by making use of the resonance behavior of a split ring resonator (SRR) at microwave frequencies. By placing a single SRR at the near-field of the aperture, strongly localized electromagnetic fields are effectively coupled to the aperture with a radius that is twenty times smaller than the resonance wavelength. We obtained 740-fold transmission enhancement by exciting the electric resonance of SRR. A different coupling mechanism, through the magnetic resonance of SRR, is also verified to yield …
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 realiz…
Allowing a high quality factor (Q-factor) to a sub-wavelength dielectric resonator, quasi-bound states in the continuum (Q-BIC) has gained much interest. However, the Q-BIC resonance condition is too sensitive to the geometry of the resonator and its practical broadband generation on a single-wafer platform has been limited. Here, we present that employing the base angle as a structural degree of freedom, the truncated nano-cone resonator supports the Q-BIC resonance with a high Q-factor of >150 over a wide wavelength range of >100 nm. We expect our approach will boost the utilization of the Q…
We propose and demonstrate subwavelength grating (SWG) metamaterial waveguides and ring resonators on a silicon nitride platform for the first time. The SWG waveguide is engineered such that a large overlap of 53% of the Bloch mode with the top cladding material is achieved, demonstrating excellent potential for applications in evanescent field sensing and light amplification. The devices, which have critical dimensions greater than 100 nm, are fabricated using a commercial rapid turn-around silicon nitride prototyping foundry process using electron beam lithography. Experimental characterizat…
We consider a quantum-electrodynamic problem of the spontaneous emission from a two-dimensional (2D) emitter, such as a quantum well or a 2D semiconductor, placed in a quasi-2D waveguide or cavity with subwavelength confinement in one direction. We apply the Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. The Langevin noise operators that we introduce do not depend on any particular model of dissipative reservoir and can be applied to any dissipation mechanism. Moreover, our approac…
Electromagnetic response of dielectric resonators with high refractive index is governed by optically induced electric and magnetic Mie resonances facilitating confinement of light with the amplitude enhancement. However, strong subwavelength trapping of light was associated traditionally only with plasmonic or epsilon-near-zero structures which however suffer from losses. Recently, an alternative localization mechanism was proposed to trap light in individual subwavelength optical resonators with a high quality factor in the regime of a supercavity mode. Here, we present the experimental obse…
An ensemble of resonators arranged on a sub-wavelength scale is usually considered as a bulk effective medium, known as a metamaterial, and can offer unusual macroscopic properties. Here, we take a different approach and limit ourselves to the study of only a few number of such elementary components and demonstrate that it still offers uncommon opportunities. Typically, thanks to the multiple scattering and the phase shift that the resonances offer, we observe fields that vary at scales completely independent of the wavelength in freespace. By smartly tuning the resonance frequencies, we can d…
In the field of metamaterials, many intriguing phenomena arise from having a structure which is periodic in space. In time-dependent structures, conceptually similar properties can arise, which nevertheless have fundamentally different physical implications. In this work, we study time-dependent systems in the context of subwavelength metamaterials. The main result is a capacitance matrix characterization of the band structure, which generalizes previous recent work on static subwavelength metamaterials. This characterization provides both theoretical insight and efficient numerical methods to…
Comment on "Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances" [Phys.Rev.Lett. 96, 233901 (2006)]
When wave scattering systems are subject to certain symmetries, resonant states may decouple from the far-field continuum; they remain localized to the structure and cannot be excited by incident waves from the far field. In this work, we use layer-potential techniques to prove the existence of such states, known as bound states in the continuum, in systems of subwavelength resonators. When the symmetry is slightly broken, this resonant state can be excited from the far field. Remarkably, this may create asymmetric (Fano-type) scattering behaviour where the transmission is fundamentally differ…
Materials which possess a high local density of states varying at a subwavelength scale theoretically permit to focus waves onto focal spots much smaller than the free space wavelength. To do so metamaterials -manmade composite media exhibiting properties not available in nature- are usually considered. However this approach is limited to narrow bandwidths due to their resonant nature. Here, we prove that it is possible to use a fractal resonator alongside time reversal to focus microwaves onto $λ/15$ subwavelength focal spots from the far field, on extremely wide bandwidths. We first numerica…
Optical microresonators are of paramount importance in photonic circuits requiring fine spectral filtering or resonant light recirculation. Key performance metrics improve with increasing resonance quality factor (Q) across all applications. The performance of silicon photonic circuits is often hampered by the low-quality factor of planar silicon microresonators, typically of Q~10^4-10^5. On the other hand, bulk whispering gallery mode resonators provide a wide range of materials with intriguing optical properties and exceptionally high resonant quality factors Q>10^7. However, the efficient c…
The ability to control the laser modes within a subwavelength resonator is of key relevance in modern optoelectronics. This work deals with the theoretical research on optical properties of a PT--symmetric nano--scaled dimer formed by two dielectric wires, one is with loss and the other with gain, wrapped with graphene sheets. We show the existence of two non--radiating trapped modes which transform into radiating modes by increasing the gain--loss parameter. Moreover, these modes reach the lasing condition for suitable values of this parameter, a fact that makes these modes to achieve an ultr…
Mid-infrared photonic modes of a periodically patterned metal-dielectric-metal structure have been investigated theoretically and experimentally. We have observed an anticrossing behaviour between cavity modes localized in the double-metal regions and the surface plasmon polariton, signature of a hybridisation between the two modes.
Plasmonic bowtie antennas made of doped silicon can operate as plasmonic resonators at terahertz (THz) frequencies and provide large field enhancement close to their gap. We demonstrate both experimentally and theoretically that the field confinement close to the surface of the antenna enables the detection of ultrathin (100 nm) inorganic films, about 3750 times thinner than the free space wavelength. Based on model calculations, we conclude that the detection sensitivity and its variation with the thickness of the deposited layer are related to both the decay of the local THz field profile ar…
We analyze, by means of numerical simulations, transmission enhancements through sub- wavelength slits due to the presence of sets of plasmonic nanocylinders, placed near the exit of these apertures. Further, we extend this study to photonic crystals of dipolar plasmonic particles in front of an array of extraordinarily transmitting slits practiced in a metallic slab.
The high-Q {\it subwavelength} resonances in an isolated dielectric disk modes can be achieved by avoided crossing (anticrossing) of the nonorthogonal TE resonances under variation of the aspect ratio as it was reported by Rybin {\it et al} [Phys. Rev. Lett. 119, 243901 (2017)]. Traversing over two parameters, the aspect ratio and the distance between two disks, enhances the Q factor by several times compared to the case of the former case of one-parametric avoided crossing in the isolated disk. Therefore successive two-parametric avoided crossing gives multiplicative gain in the Q-factor as i…
Concentrating light within subwavelength spatial regions is a central topic in nanophotonics. In this letter, we introduce a general principle for the subwavelength localization and enhancement of electric fields in high-index resonators, based on the flux conservation of the displacement current density. We apply this design rule to a ring resonator by locally squeezing its section: since the flux is conserved, the electric field is necessarily enhanced to compensate the reduction of the section area. The introduced principle may constitute an important step toward the control of the displace…
We study, and illustrate with numerical calculations, transmission enhancement by subwavelength 2D slits due to the dominant role played by the excitation of the eigenmodes of plasmonic cylinders when they are placed at the aperture entrance; and also due to reinforced and highly localized energy in the slit as a consequence of the formation of a nanojet. We show that, providing the illumination is chosen such that an aperture transmitting eigenmode is generated, the phenomenon is independent of whether or not the slit alone produces extraordinary transmission; although in the former case this…
Electromagnetic scattering on subwavelength structures keeps attracting attention owing to abroad range of possible applications, where this phenomenon is in use. Fundamental limits of scattering cross-section, being well understood in spherical geometries, are overlooked in cases of low-symmetry resonators. Here, we revise the notion of superscattering and link this property with symmetry groups of the scattering potential. We demonstrate pathways to spectrally overlap several eigenmodes of a resonator in a way they interfere constructively and enhance the scattering cross-section. As a parti…
We introduce the resonant metalens, a cluster of coupled subwavelength resonators. Dispersion allows the conversion of subwavelength wavefields into temporal signatures while the Purcell effect permits an efficient radiation of this information in the far-field. The study of an array of resonant wires using microwaves provides a physical understanding of the underlying mechanism. We experimentally demonstrate imaging and focusing from the far-field with resolutions far below the diffraction limit. This concept is realizable at any frequency where subwavelength resonators can be designed.
Localized polymerization in subwavelength volumes using two photon dyes has now become a well-established method for fabrication of subwavelength structures. Unfortunately, the two photon absorption dyes used in such process are not only expensive but also proprietary. LTPO-L is an inexpensive, easily available single photon photoinitiator and has been used extensively for single photon absorption of UV light for polymerization. These polymerization volumes however are not localized and extend to micron size resolution having limited applications. We have exploited high quantum yield of radica…
Existing methods for the localization of light at the nanoscale use either a structure with negative permittivity, by exploiting subwavelength plasmonic resonances, or a dielectric structure with a high refractive index, which reduces the wavelength. In this paper, we provide an alternative to these two methods based on a modification of the modes of dielectric resonators by means of an active medium. We show that an active medium can promote subwavelength light localization in the dielectric structure. We consider a dielectric layer of size substantially smaller than a half-wavelength of ligh…
Transport of subwavelength electromagnetic (EM) energy has been achieved through near-field coupling of highly confined surface EM modes supported by plasmonic nanoparticles, in a configuration usually staying on a two-dimensional (2D) substrate. Vertical transport of similar modes along the third dimension, on the other hand, can bring more flexibility in designs of functional photonic devices, but this phenomenon has not been observed in reality. In this paper, designer (or spoof) surface plasmon resonators (plasmonic meta-atoms) are stacked in the direction vertical to their individual plan…
Subwavelength metallic resonators provide a route to achieving strong light-matter coupling by means of tight confinement of resonant electromagnetic fields. Investigation of such resonators however often presents experimental difficulties, particularly at terahertz (THz) frequencies. A single subwavelength resonator weakly interacts with THz beams, making it difficult to probe it using far-field methods; whereas arrays of resonators exhibit inter-resonator coupling, which affects the resonator spectral signature and field confinement. Here, traditional far-field THz spectroscopy is systematic…
In the context of continued spread of coronavirus disease 2019 (COVID-19) caused by SARS-CoV-2 and the emergence of new variants, the demand for rapid, accurate, and frequent detection is increasing. Besides, the new predominant strain, Omicron variant, manifests more similar clinical features to those of other common respiratory infections. The concurrent detection of multiple potential pathogens helps distinguish SARS-CoV-2 infection from other diseases with overlapping symptoms, which is significant for patients to receive tailored treatment and containing the outbreak. Here, we report a la…
Light transmission through bilayered thin metal films perforated with subwavelength hole arrays are numerically studied based on a full-vector finite-difference time-domain approach. A variety of transmission peaks originating from different physical mechanisms are observed. In addition to the direct tunnelling and Fabry-Pèrot resonances, generally possessed by idealized bilayered dielectric slabs, the near-field localized plasmon polaritons also play important roles. They not only influence the direct tunnelling in a destructive or constructive way, the interactions between these localized pl…
Enhanced transmissions through a gold film with arrays of subwavelength holes are theoretically studied, employing the rigid full vectorial three dimensional finite difference time domain method. Influence of air-holes shape to the transmission is firstly studied, which confirms two different resonances attributing to the enhanced transmission: the localized waveguide resonance and periodic surface plasmon resonances. For the film coated with dielectric layers, calculated results show that in the wavelength region of interest the localized waveguide resonant mode attributes to sensing rather t…
The interaction of light with the localized/delocalized system, i.e., a metal surface with rectangular cavities of finite depth, has been studied. Reflection spectrum has been measured in the optical frequencies and resonant minima have been observed. We have developed an analytical model, which agrees well with the experiment. The localized waveguide resonance and delocalized surface resonance have been identified and discussed. The results may be useful for manipulating the coupling between light and matters.
The existence of resonant enhanced transmission and collimation of light waves by subwavelength slits in metal films [for example, see T.W. Ebbesen et al., Nature (London) 391, 667 (1998) and H.J. Lezec et al., Science, 297, 820 (2002)] leads to the basic question: Can a light be enhanced and simultaneously localized in space and time by a subwavelength slit? To address this question, the spatial distribution of the energy flux of an ultrashort (femtosecond) wave-packet diffracted by a subwavelength (nanometer-size) slit was analyzed by using the conventional approach based on the Neerhoff and…
Being motivated by the recent prediction of high-$Q$ supercavity modes in subwavelength dielectric resonators, we study the second-harmonic generation from isolated subwavelength AlGaAs nanoantennas pumped by a structured light. We reveal that nonlinear effects at the nanoscale can be enhanced dramatically provided the resonator parameters are tuned to the regime of the bound state in the continuum. We predict a record-high conversion efficiency for nanoscale resonators that exceeds by two orders of magnitude the conversion efficiency observed at the conditions of magnetic dipole Mie resonance…
Subwavelength dielectric resonators assembled into metasurfaces have become a versatile tool for miniaturising optical components approaching the nanoscale. An important class of metasurface functionalities is associated with asymmetry in both generation and transmission of light with respect to reversals of the positions of emitters and receivers. Nonlinear light-matter interaction in metasurfaces offers a promising pathway towards miniaturisation of the asymmetric control of light. Here we demonstrate asymmetric parametric generation of light in nonlinear metasurfaces. We assemble dissimilar…
Topological photonic crystals (TPhCs) provide robust manipulation of light with built-in immunity to fabrication tolerances and disorder. Recently, it was shown that TPhCs based on weak topology with a dislocation inherit this robustness and further host topologically protected lower-dimensional localized modes. However, TPhCs with weak topology at optical frequencies have not been demonstrated so far. Here, we use scattering-type scanning near field optical microscopy to verify mid-bandgap zero-dimensional light localization close to 100 THz in a TPhC with nontrivial Zak phase and an edge dis…
In this paper, we investigate numerically the trapped modes with near zero group velocities supported in the ring array composed of dielectric nanorods, based on a two-dimensional model. Two sorts of trapped modes in the ring array have been identified: the BCR trapped modes which correspond to the bound modes below the light line at the edge of the first Brillouin zone in the corresponding planar structure (namely the infinite linear chain); the quasi-BIC trapped modes corresponding to the bound states in the continuum supported in the infinite linear chain. According to the whispering galler…
Open subwavelength cylindrical resonators of finite height are widely used in various photonics applications. Circular cylindrical resonators are particularly important in nanophotonics, since they are relatively easy to fabricate and can be designed to exhibit different resonance effects. In this paper, an efficient and robust numerical method is developed for computing resonant modes of circular cylinders which may have a few layers and may be embedded in a layered background. The resonant modes are complex-frequency outgoing solutions of the Maxwell's equations with no sources or incident w…
We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.
We study modulational instability in nonlinear arrays of subwavelength metallic nanoparticles, and analyze numerically nonlinear scenarios of the instability development. We demonstrate that modulational instability can lead to the formation of regular periodic or quasi-periodic modulations of the polarization. We reveal that such nonlinear nanoparticle arrays can support long-lived standing and moving oscillating nonlinear localized modes - plasmon oscillons.
We investigate the optical properties of microcavities with suspended subwavelength structured mirrors, such as high-contrast gratings or two-dimensional photonic crystals slabs, and focus in particular on the regime in which the microcavity free-spectral range is larger than the width of a Fano resonance of the highly reflecting structured mirror. In this unusual regime, the transmission spectrum of the microcavity essentially consists in a single mode, whose linewidth can be significantly narrower than both the Fano resonance linewidth and the linewidth of an equally short cavity without str…
We propose the generalization of the Fourier modal method aimed at calculating localized eigenmodes of integrated optical resonators. The method is based on constructing the analytic continuation of the structure's scattering matrix and calculating its poles. The method allows one to calculate the complex frequency of the localized mode and the corresponding field distribution. We use the proposed method to calculate the eigenmodes of rectangular dielectric block located on metal surface. We show that excitation of these modes by surface plasmon-polariton (SPP) results in resonant features in …
