Dielectric perturbations: anomalous resonance frequency shifts in optical resonators
Farhan Azeem, Luke S. Trainor, Patrick A. Devane, Daniel S. Norman, Alfredo Rueda, Nicholas J. Lambert, Madhuri Kumari, Matthew R. Foreman, Harald G. L. Schwefel
Small perturbations in the dielectric environment around a high quality whispering gallery mode resonator usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations of strong frequency shifts that can be opposite and even exceed the contribution of the perturbations' polarizability. The mode frequencies of a lithium niobate whispering gallery mode resonator are shifted using substrates of refractive indices ranging from 1.50 to 4.22. Both blue- and red-shifts are observed, as well as an increase in mode linewidth, when substrates are moved into the evanescent field of the whispering gallery mode. We compare the experimental results to a theoretical model by Foreman et al. and provide an additional intuitive explanation based on the Goos-Hänchen shift for the optical domain.
Metamaterials comprising assemblies of dielectric resonators have attracted much attention due to their low intrinsic loss and isotropic optical response. In particular, metasurfaces made from silicon dielectric resonators have shown desirable behaviors such as efficient nonlinear optical conversion, spectral filtering and advanced wave-front engineering. To further explore the potential of dielectric metamaterials, we present all-dielectric metamaterials fabricated from epitaxially grown III-V semiconductors that can exploit the high second-order optical susceptibilities of III-V semiconducto…
In this paper, we derive a model from Maxwell equations for the magnetic resonance of split-ring resonators. Using this model we revisit the scaling of split-ring resonators. Inspired by our model, we propose a new type of split-hybrid metal-dielectric ring resonator, of which the ring is made composed of moderately high index dielectric material (e.g. SiC, TiO2, ZnS) (for the major portion), while and metal (e.g. Ag) fills the gap. Such a new magnetic metamaterial is able to overcome the saturation problem of split-ring resonatorssaturation-free and therefore is able to operate at short wavel…
We demonstrate, for the first time, an all-dielectric metamaterial resonator in the mid-wave infrared based on high-index tellurium cubic inclusions. Dielectric resonators are desirable compared to conventional metallo-dielectric metamaterials at optical frequencies as they are largely angular invariant, free of ohmic loss, and easily integrated into three-dimensional volumes. With these low-loss, isotropic elements, disruptive optical metamaterial designs, such as wide-angle lenses and cloaks, can be more easily realized.
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…
We introduce a practical dielectric metasurface design for microwave frequencies. The metasurface is made of an array of dielectric resonators held together by dielectric connections thus avoiding the need of a mechanical support in the form of a dielectric slab and the spurious multiple reflections that such a slab would generate. The proposed design can be used either for broadband metasurface applications or monochromatic wave transformations. The capabilities of the concept to manipulate the transmission phase and amplitude of the metasurface are supported by numerical and experimental res…
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…
Nanometer-resolution 3D Tomographic and Vectorial Near-field Imaging in Dielectric Optical Resonators
State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室、微纳光子结构教育部重点实验室和物理系）；Shanghai Key Laboratory of Metasurfaces for Light Manipulation, Fudan University（复旦大学光调控超材料上海市重点实验室）
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.
In this paper, we propose a novel design of dielectric laser-driven accelerator (DLA) utilizing evanescent electric field of racetrack ring resonator structures. Driven by laser light with the correctly designed optical phase window, sustained acceleration of electrons with controlled deflection is shown. Based on this design, we calculate an acceleration from 30 keV to 148.312 keV in 104.655 μm using a cascaded 11-stage racetrack ring resonators. This new idea poses a solution for on-chip integration of many DLA stages, while maintains high average accelerating gradients, providing a potentia…
The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective…
In this study, we used parallel plane mirror resonator analogy to design all-dielectric optical resonator that is performed with the objective-first inverse design algorithm. Confinement of the light is succeeded via predefined objective function to create symmetric mirror regions for the fundamental transverse-electric polarization mode. The algorithm creates bandgap in random structure to obtain resonance peak at the desired wavelength without any intuitive scanning of the parameter space. The first order mode is confined on the cavity region at pre-defined wavelength. The obtained structure…
The study of invisibility of an infinite dielectric rod with high refractive index is based on the two-dimensional Mie scattering problem, and it suggests strong suppression of scattering due to the Fano interference between spectrally broad nonresonant waves and narrow Mie-resonant modes. However, when the dielectric rod has a finite extension, it becomes a resonator supporting the Fabry-Perot modes which introduce additional scattering and eventually destroy the invisibility. Here we reveal that for shorter rods with modest values of the aspect ratio r/L (where r and L are the radius and len…
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…
Molecular optomechanics stems from the description of Raman scattering in the presence of an optical resonator using a cavity optomechanics formalism. We extend the molecular optomechanics formalism to the case of hybrid dielectric-plasmonic resonators, with multiple optical resonances and with both free-space and waveguide addressing. We demonstrate how the Raman enhancement is the product of a pump enhancement and a modified LDOS, that simply depend on the complex response functions of the hybrid system. The Fano lineshapes that result from hybridization of a broadband and narrowband modes a…
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…
We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination…
The ultimate limits of performance for any classical optical system are set by sub-wavelength fluctuations within the host material, that may be frozen-in or even dynamically induced. The most common manifestation of such sub-wavelength disorder is Rayleigh light scattering, which is observed in nearly all wave-guiding technologies today and can lead to both irreversible radiative losses as well as undesirable intermodal coupling. While it has been shown that backscattering from disorder can be suppressed by breaking time-reversal symmetry in magneto-optic and topological insulator materials, …
We present a new approach to dielectric metasurface design that relies on a single resonator per unit cell and produces robust, high quality-factor Fano resonances. Our approach utilizes symmetry breaking of highly symmetric resonator geoemetries, such as cubes, to induce couplings between the otherwise orthogonal resonator modes. In particular, we design perturbations that couple "bright" dipole modes to "dark" dipole modes whose radiative decay is suppressed by local field effects in the array. Our approach is widely scalable from the near-infrared to radio frequencies. We first unravel the …
Printing technology based on plasmonic structures has many advantages over pigment based color printing such as high resolution, ultra-compact size and low power consumption. However, due to high losses and broad resonance behavior of metals in the visible spectrum, it becomes challenging to produce well-defined colors. Here, we investigate cross-shaped dielectric nanoresonators which enable high quality resonance in the visible spectral regime and, hence, high quality colors. We numerically predict and experimentally demonstrate that the proposed all-dielectric nanostructures exhibit high qua…
In the Terahertz (THz) domain, we investigate both numerically and experimentally the directional emission of whispering gallery mode resonators that are perturbed by a small scatterer in the vicinity of the resonators rim. We determine quality factor degradation, the modal structure and the emission direction for various geometries. We find that scatterers do allow for directional emission without destroying the resonator's quality factor. This finding allows for new geometries and outcoupling scenarios for active whispering gallery mode structures such as quantum cascade lasers and passive r…
Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry breaking mechanism in electrodynamics occurs between counter-propagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counter-propagating light in bi-directionally pumped microresonators finds application in the realisation of optical non-reciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counter-propagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinea…
Open dielectric resonators of different shapes are widely used for the manufacture of microlasers. A precise determination of their resonance frequencies and widths is crucial for their design. Most microlasers have a flat cylindrical geometry, and a two-dimensional approximation, the so-called method of the effective index of refraction, is commonly employed for numerical calculations. Our aim has been an experimental test of the precision and applicability of a model based on this approximation. We performed very thorough and accurate measurements of the resonance frequencies and widths of t…
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 study long-lived resonances (lowest-loss modes) in hexagonally shaped dielectric resonators in order to gain insight into the physics of a class of microcrystal lasers. Numerical results on resonance positions and lifetimes, near-field intensity patterns, far-field emission patterns, and effects of rounding of corners are presented. Most features are explained by a semiclassical approximation based on pseudointegrable ray dynamics and boundary waves. The semiclassical model is also relevant for other microlasers of polygonal geometry.
We show that global lower bounds to the mode volume of a dielectric resonator can be computed via Lagrangian duality. State-of-the-art designs rely on sharp tips, but such structures appear to be highly sub-optimal at nanometer-scale feature sizes, and we demonstrate that computational inverse design offers orders-of-magnitude possible improvements. Our bound can be applied for geometries that are simultaneously resonant at multiple frequencies, for high-efficiency nonlinear-optics applications, and we identify the unavoidable penalties that must accompany such multiresonant structures.
A leaky-wave antenna at optical frequencies is designed and integrated with a ring resonator at 1550 nm wavelength. The leaky wave is generated by using periodic perturbations in the integrated dielectric waveguide that excite the -1 spatial harmonic. The antenna consists of a dielectric waveguides with semiconductor corrugations, and it is compatible with CMOS fabrication technology. We show that integrating the leaky wave antenna in an optical ring resonator that is fed by directional couplers, we can improve the electronic control of the radiation through carrier injection into the semicond…
Traditionally, photonic crystal slabs can support resonances that are strongly confined to the slab but also couple to external radiation. However, when a photonic crystal slab is placed on a substrate, the resonance modes become less confined, and as the index contrast between slab and substrate decreases, they eventually disappear. Using the scale structure of the Dione juno butterfly wing as an inspiration, we present a low-index zigzag surface structure that supports resonance modes even without index contrast with the substrate. The zigzag structure supports resonances that are contained …
We study numerically, analytically and experimentally the resonant transmission of light in a waveguide formed by a periodic array of high-index dielectric nanoparticles with a side-coupled resonator. We demonstrate that a resonator with high enough Q-factor provides the conditions for the Fano-type interference allowing to control the resonant transmission of light. We suggest a practical realization of this resonant effect based on the quadrupole resonance of a dielectric particle and demonstrate it experimentally for ceramic spheres at microwaves.
We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good qualitative agreement between the experimental data and the predictions of the trace formula. Deviations could be attributed to missing resonances in the measured spectra in accordance with previous experiments [Phys. Rev. E 81, 066215 (2010)]. The investigation of the numerical length spectrum showed good qualitative and reasonable quantitative agreement wi…
Ensembles of nitrogen-vacancy (NV) color centers in diamond hold promise of ultraprecise magnetometery competing with SQUID detectors. By utilizing advantages of dielectric materials such as very low losses for electromagnetic field and therefore possibility to create high quality factor resonators with strong concentration of the field in it we implemented a dielectric resonator antenna for coherent manipulation of large ensemble of NV centers in diamond. We reached average Rabi frequency of 10 MHz in the volume of 7 cubic millimeters with standard deviation less than 1% at moderate pump powe…
It is proposed and demonstrated that Q-factor of optical resonators can be significantly enhanced by introducing an extra anisotropic cladding. We study the optical resonances of all-dielectric core-shell nanoresonators and reveal that radially anisotropic claddings can be employed to squeeze more energy into the core area, leading to stronger light confinement and thus significant Q-factor enhancement. We further show that the required homogenous claddings of unusual anisotropy parameters can be realized through all-dielectric multi-layered isotropic structures, which offers realistic extra f…
Creation of correlated photon pairs is one of the key topics in contemporary quantum optics. Here, we theoretically describe the generation of photon pairs in the process of spontaneous parametric down-conversion in a resonant spherical nanoparticle made of a dielectric material with bulk $χ^{(2)}$ nonlinearity. We pick the nanoparticle size that satisfies the condition of resonant eigenmodes described by Mie theory. We reveal that highly directional photon-pair generation can be observed utilising the nonlinear Kerker-type effect, and that this regime provides useful polarisation correlations…
Optical whispering gallery mode (WGM) resonators are a powerful and versatile tool used in many branches of science. Fine tuning of the central frequency and line width of individual resonances is however desirable in a number of applications including frequency conversion, optical communications and efficient light-matter coupling. To this end we present a detailed theoretical analysis of dielectric tuning of WGMs supported in axisymmetric resonators. Using the Bethe-Schwinger equation and adopting an angular spectrum field representation we study the resonance shift and mode broadening of hi…
In this paper we describe a methodology for tailoring the design of metamaterial dielectric resonators, which represent a promising path toward low-loss metamaterials at optical frequencies. We first describe a procedure to decompose the far field scattered by subwavelength resonators in terms of multipolar field components, providing explicit expressions for the multipolar far fields. We apply this formulation to confirm that an isolated high-permittivity cube resonator possesses frequency separated electric and magnetic dipole resonances, as well as a magnetic quadrupole resonance in close p…
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…
Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the requirements needed to maintain total internal reflection of the internal electromagnetic fields, matched to exponentially decaying evanescent waves outside the cavity. Two-dimensional electromagnetics is considered, with no dependence on the coordinate perpendicular to the cross section; hence, independent transverse electric (TE) and transverse magnetic (…
The authors report on observation of Bragg confined mode in a hollow cylindrical dielectric cavity. A resonance was observed at 13.4 $GHz$ with an unloaded Q-factor of order $2\times10^5$, which is more than a factor of 6 above the dielectric loss limit. Previously such modes have only been realized from pure Transverse Electric modes with no azimuthal variations and only the $E_ϕ$ component. From rigorous numeric simulations it is shown that the mode is a hybrid mode with non-zero azimuthal variations and with dominant $E_r$ and $E_ϕ$ electric field components and $H_z$ magnetic field compone…
Optomechanical crystals provide coupling between phonons and photons by confining them to commensurate wavelength-scale dimensions. We present a new concept for designing optomechanical crystals capable of achieving unprecedented coupling rates by confining optical and mechanical waves to deep sub-wavelength dimensions. Our design is based on a dielectric bowtie unit cell with an effective optical/mechanical mode volume of $7.6 \times 10^{-3} {(λ/n_{\textrm{Si}})}^3$/$ 1.2 \times 10^{-3} {λ_{\textrm{mech}}}^3$. We present results from numerical modeling, indicating a single-photon optomechanic…
The vast majority of resonant systems show a red-shift for the resonance frequency when a perturbation, e.g. losses, are introduced to the system. In contrast, here we report for the first time the experimental demonstration of both red- and anomalous blue-shifting of whispering-gallery modes (WGMs) using dielectric and metallic substrates. The maximum blue-shift is more than three times as large as the expected red-shift, proving that the anomalous blue-shift is more than a peculiar curiosity. The experiments are performed in the terahertz (THz) frequency range with coherent continuous-wave s…
We show how the recently found quasi-bound state in the continuum optical states in dielectric antennae can be utilized to engineer pillar microcavities design with the substantially optimized quality factor to mode volume ratio.
Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial structure, and cannot be classified through mode indices which would require additional constants of motion in the ray dynamics. Understanding and controlling the emission properties of such resonators requires the investigation of the correspondence between classical phase space structures of the ray motion inside the resonator and resonant solutions of the …
We propose a novel scheme for enhancing the quality factor of coupled resonators optical waveguides (CROWs) when operating near a degenerate band edge (DBE). A DBE is a four-mode exceptional point of degeneracy (EPD) occurring when four Bloch eigenmodes coalesce providing a resonance condition with a giant enhancement in fields. We report an unprecedented scaling law of quality factor of CROWs when operating at the DBE, even in the presence of losses and structural perturbations. Remarkably, the Q factor of the proposed CROW can be engineered to exceed that of a single ring resonator having a …
The problem of pattern formation in resonantly-enhanced near-field lithography by the use of dielectric or plasmonic planar resonators is investigated. Sub-diffraction-limited bright or dark spots can be produced by taking advantage of the rotational invariance of planar resonators. To increase the spatial bandwidth of the resonant enhancement, an array of coupled planar resonators can open up a band of Bloch resonances, analogous to coupled-resonator optical waveguides.
We consider light-induced binding and motion of dielectric microparticles in an optical waveguide that gives rise to a back-action effect such as light transmission oscillating with time. Modeling the particles by dielectric slabs allows us to solve the problem analytically and obtain a rich variety of dynamical regimes both for Newtonian and damped motion. This variety is clearly reflected in temporal oscillations of the light transmission. The characteristic frequencies of the oscillations are within the ultrasound range of the order of $10^{5}$ Hz for micron size particles and injected powe…
Metasurfaces are engineered thin surfaces comprising two dimensional (2D) arrays of sub-wavelength spaced and sub-wavelength sized resonators. Metasurfaces can locally manipulate the amplitude, phase and polarization of light with high spatial resolution. In this study, we report numerical and experimental results of a vortex-beam-generating metasurface fabricated specifically for infrared (IR) and terahertz (THz) wavelengths. The designed metasurface consisted of a 2D array of dielectric cross-shaped resonators with spatially varying length, thereby providing desired spatially varying phase s…
