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 gallery condition, the BCR trapped modes can be supported in the ring array only when the number of dielectric elements N is even, while the quasi-BIC ones always exist no matter whether N is odd or even. For both two kind of trapped modes, the lowest one of each kind possesses the highest Q factor, which are ~105 for BCR kind and ~1011 for quasi-BIC kind with N=16 respectively, and the radiation loss increases dramatically as the structural resonance increases. Finally, the behavior of the Q factor with N is explained numerically for the lowest one of each kind of trapped modes. The Q factor scales as Q~exp(0.662N) for the quasi-BIC trapped mode and Q~exp(0.325N) for the BCR one. Intriguingly, the Q factor of the quasi-BIC trapped mode can be as large as ~105 even at N=8. Compared to the finite linear chain, the structure of ring array exhibits overwhelming advantage in Q factor with the same N because there is no array-edge radiation loss in the ring array. We note that the principles can certainly be extended to particles of other shapes (such as nanospheres, nanodisks, and many other experimentally feasible geometries).
Metallic nano-structured lens has the potential applications of transporting subwavelength imaging information and it is achieved by manipulating the length of the nanorod and the periodicity of the rod array. In this paper, we demonstrate the impact of filling ratio on the subwavelength imaging capabilities of such a lens. Through full-wave electromagnetic simulation, we have demonstrated that the imaging performance of silver (Ag) nanorod array does not only depend on the length and periodicity but also on the filling ratios or the radius of the wire medium. We have investigated two differen…
Systems of closely-spaced resonators can be strongly coupled by interactions mediated by scattered electromagnetic fields. In large systems the resulting response has been shown to be more sensitive to these collective interactions than to the detailed structure of individual resonators. Attempts to describe such systems have resulted in point-dipole approximations to resonators that are computationally efficient for large resonator ensembles. Here we provide a detailed study for the validity of point dipole approximations in small systems of strongly coupled plasmonic nanorods, including the …
Strong Stokes and anti-Stokes one-photon luminescence from single gold nanorods is measured in experiments. It is found that the intensity and polarization of the Stokes and anti-Stokes emissions are in strong correlation. Our experimental observation discovered a coherent process in light emission from single gold nanorods. We present a theoretical mode, based on the concept of cavity resonance, for consistently understanding both Stokes and anti-Stokes photoluminescence. Our theory is in good agreement of all our measurements.
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…
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…
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.
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…
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…
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…
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…
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…
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…
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 real…
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…
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…
The polarizability $α$ determines the absorption, extinction and scattering by small particles. Beyond being purely set by scatterer size and material, in fact polarizability can be affected by backaction: the influence of the photonic environment on the scatterer. As such, controlling the strength of backaction provides a tool to tailor the (radiative) properties of nanoparticles. Here, we control the backaction between broadband scatterers and a single mode of a high-quality cavity. We demonstrate that backaction from a microtoroid ring resonator significantly alters the polarizability of an…
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…
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.
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…
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…
The radiation dynamics of optical emitters can be manipulated by properly designed material structures providing high local density of photonic states, a phenomenon often referred to as the Purcell effect. Plasmonic nanorod metamaterials with hyperbolic dispersion of electromagnetic modes are believed to deliver a significant Purcell enhancement with both broadband and non-resonant nature. Here, we have investigated finite-size cavities formed by nanorod metamaterials and shown that the main mechanism of the Purcell effect in these hyperbolic resonators originates from the cavity hyperbolic mo…
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…
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 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…
We describe how the finite-difference time-domain (FDTD) technique can be used to compute the quasinormal mode (QNM) for metallic nano-resonators, which is important for describing and understanding light-matter interactions in nanoplasmonics. We use the QNM to model the enhanced spontaneous emission rate for dipole emitters near a gold nanorod dimer structure using a newly developed QNM expansion technique. Significant enhanced photon emission factors of around 1500 are obtained with large output $β$-factors of about $60\%$.
Among various plasmonic waveguides, the metal-insulator-metal (MIM) type is the most promising for true subwavelength photonic integration. To date, many photonic devices based on MIM waveguides have been investigated, including resonators. However, most of the reported MIM ring resonators suffer from low extinction ratios. In this paper, we present a comprehensive analysis of the intrinsic reasons for the low performance of MIM ring resonators, and give the analytical transmission relation for a universal all-pass ring resonator which has coupling loss. Based on the analysis we propose the pl…
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…
We measure strong magnetic field intensities in a subwavelength gap separating two dielectric resonators. This dimer magnetic antenna is characterized in the GHz spectral regime when considering three conditions of illumination. We detail the different magneto-electric couplings involved in the enhancement of the near magnetic field and derive the analytical expression of the magnetic field intensities. The results reported here in the GHz domain can be extended to other spectral domains since they are obtained with a dielectric permittivity 16 that can be observed in a very broad spectrum ran…
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…
We experimentally demonstrate the effect of anomalous breakdown of the effective medium approximation in all-dielectric deeply subwavelength thickness ($d \simλ/160-λ/30$) multilayers, as recently predicted theoretically [H.H. Sheinfux et al., Phys. Rev. Lett. 113, 243901 (2014)]. Multilayer stacks are composed of alternating alumina and titania layers fabricated using atomic layer deposition. For light incident on such multilayers at angles near the total internal reflection we observe pronounced differences in the reflectance spectra for structures with 10-nm versus 20-nm thick layers, as we…
We study the transfer of electromagnetic energy across a subwavelength gap separating two co-axial metal nanorodes. The absence of spacer in the gap separating the rods the system exhibits the strong coupling between longitudinal plasmons in the two rods. The nature and magnitude of this coupling is studied by varying various geometrical parameters. When the length of one rod is varied this mode spectrum exhibits the familiar anti-crossing behavior that depends on the coupling strength determined by the gap width. As a function of frequency the transmission is dominated by a splitted longitudi…
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…
We develop and implement a new mathematical and computational framework for designing photonic elements with one or more high-$Q$ scattering resonances. The approach relies on solving for the poles of the scattering matrix, which mathematically amounts to minimizing the determinant of the Fredholm integral operator of the electric field with respect to the permittivity profile of the scattering element. We apply the method to design subwavelength gradient-permittivity structures with multiple scattering resonances and quality factors exceeding 500. We also find the spectral scattering cross se…
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…
Understanding light-matter interactions using localized surface plasmons (LSPs) is of fundamental interest in classical and quantum plasmonics and has a wide range of applications. In order to understand the spatial properties of LSPs, electron energy loss spectroscopy (EELS) is a common and powerful method of spatially resolving the extreme localized fields that can be obtained with metal resonators. However, modelling EELS for general shaped resonators presents a major challenge in computational electrodynamics, requiring the full photon Green function as a function of two space points and f…
We analyze a whispering gallery mode biosensor with a metallic nanorod bound to its surface. It is found that a localized surface plasmon resonance in the nanorod can reduce the optical mode volume of the resonator by as much as four orders of magnitude via a local enhancement of the electric field, thus improving the detection sensitivity. Optical frequency shifts as large as 15 MHz are predicted for typical proteins and, for typical experimental parameters, the biosensor is predicted to be limited by laser frequency noise, leading to a minimum detectable polarizability on the order of 10 cub…
Nano particle-plasmons are attributed to quasi-static oscillation with no wave propagation due to their subwavelength size. However, when located within a band-gap medium (even in air if the particle is small enough), the particle interfaces are acting as wave-mirrors, incurring small negative retardation. The latter when compensated by a respective (short) propagation within the particle substantiates a full-fledged resonator based on constructive interference. This unusual wave interference in the deep subwavelength regime (modal-volume<0.001lambda^3) significantly enhances the Q-factor, e.g…
