Toroidal Resonance Research Articles

On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities

Plasmonics is expected to play a key role in nanotechnology, leading to intriguing routes in many engineering and biological applications. Recently, it has been realized that toroidal resonances could be an alternative to electric and magnetic resonances, which have governed the innovation of plasmonic applications so far. In a previous contribution, we proved the existence of toroidal moments in an oligomeric void-plasmonic structure [1]. In this article, we investigate the role of topology and symmetry in decomposing the various dipolar, quadrupolar, and toroidal moments, using energy-filtering transmission electron microscopy supported by three-dimensional finite-difference time-domain method simulations. The consequences of changing the topology on the toroidal character are discussed by comparing results obtained from nanoholes forming heptamer and hexamer nanocavity systems that were drilled into a thin silver film.

Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials

The toroidal dipole is a peculiar electromagnetic excitation that can not be presented in terms of standard electric and magnetic multipoles. A static toroidal dipole has been shown to lead to violation of parity in atomic spectra and many other unusual electromagnetic phenomena. The existence of electromagnetic resonances of toroidal nature was experimentally demonstrated only recently, first in the microwave metamaterials, and then at optical frequencies, where they could be important in spectroscopy analysis of a wide class of media with constituents of toroidal symmetry, such as complex organic molecules, fullerenes, bacteriophages, etc. Despite the experimental progress in studying toroidal resonances, no direct link has yet been established between microscopic toroidal excitations and macroscopic scattering characteristics of the medium. To address this essential gap in the electromagnetic theory, we have developed an analytical approach for calculating the transmissivity and reflectivity of thin slabs of materials that exhibit toroidal dipolar excitations.

Optical responses of magnetic-vortex resonance in double-disk metamaterial variations

Optical toroidal resonance in structural variations of the double-disk metamaterial, in viewpoint of an equivalent LC-circuit model, is numerically studied to optimize its geometrically-dependent optical characteristics, such as the enhancement capability of local-field confinement and the extinction coefficient. Responses of high-order magnetic vortex resonances (i.e., the double- and triple-fold vortex modes), in addition to the fundamental toroidal dipole, are excited in accordance with a standing-wave model of oscillating current. The induced strengths for these vortex responses are sensitive, in different manners, to the incident angle of the light, though their frequencies are angularly independent. • Toroidal resonance was studied in accordance with an LC-circuit model. • The fundamental and high-order H -vortex resonances were evaluated. • The toroidal response is promising for trapping and energy harvesting.

Modulation of auroras by Pc5 pulsations in the dawn sector in association with reappearance of energetic particles at geosynchronous orbit

Geomagnetic Pc5 pulsations were observed in the dawn sector of the auroral zone on 17 January 1994 in association with increased energetic ion fluxes at geosynchronous orbit 10min after the Pi2 onset. The characteristic properties of auroras associated with these pulsations were studied using movies taken by an all-sky imager. It was found that a pulsating aurora (PA) can be an optical manifestation of the Pc5 waves by a strong poloidal component observed with ground-based magnetometers. Goes7 observations showed compressional pulsations with the same period which can be attributed to the influence of the finite pressure of plasma and field line curvature on the poloidally polarized Alfvén waves. These poloidal pulsations may be generated by the ion injection observed with the LANL 1989-046 satellite. Two auroral arcs were observed north of the PA with optical features characteristic for the toroidal field line resonances: strong localization across L-shells, 180° phase change across the resonance, poleward phase propagation. Thus the Pc5 oscillations split into the toroidal and poloidal mode and oscillated coherently at latitudes from 62°N to 70°N. This study provides observational evidence of polarization splitting of the Alfven oscillation spectrum. Such a polarization splitting would occur in association with the reappearance of the energetic particles at geosynchronous orbit.

Investigation of the Velocity Profiles in a Ninety-Degree Curved Standing Wave Resonator with Particle Image Velocimetry

Travelling wave thermoacoustic heat engines have been reported to have a higher efficiency than the standing wave ones. The former are generally large systems which consist of toroidal shape resonators. While standing wave heat engines are inherently smaller, a reduction in size could be considered which may involve curvatures as compared to the straight tube conventional systems. However, as with the streaming losses in the travelling wave resonators, losses due to the curvature may be generated. This study involves preliminary experimental measurements using the Particle Image Velocimetry (PIV) method to analyze the velocity profiles in a standing wave resonator before and after a ninety degree curvature. This design can reduce the space generally occupied by the straight standing wave resonator. The overall length of the resonator fits a quarter wavelength wave based on the straight closed-end tube type. The working gas is air at 1 atmospheric pressure. Results have shown that the velocity profiles after the stack but before the curvature exhibit clear straight paths up just as reported elsewhere. Signs of disordered motion could be observed just before the bend and the pattern continues until after the curvature. The results are obtained before one periodic cycle and before the acoustic wave front hit the tube end. The trend is expected to affect the overall thermoacoustic performance of the engine as returning gas particles interact with the oncoming particles that pass by the curvature.

Evanescent straight tapered-fiber coupling of ultra-high Q optomechanical micro-resonators in a low-vibration helium-4 exchange-gas cryostat

We developed an apparatus to couple a 50-μm diameter whispering-gallery silica microtoroidal resonator in a helium-4 cryostat using a straight optical tapered-fiber at 1550 nm wavelength. On a top-loading probe specifically adapted for increased mechanical stability, we use a specifically-developed "cryotaper" to optically probe the cavity, allowing thus to record the calibrated mechanical spectrum of the optomechanical system at low temperatures. We then demonstrate excellent thermalization of a 63-MHz mechanical mode of a toroidal resonator down to the cryostat's base temperature of 1.65 K, thereby proving the viability of the cryogenic refrigeration via heat conduction through static low-pressure exchange gas. In the context of optomechanics, we therefore provide a versatile and powerful tool with state-of-the-art performances in optical coupling efficiency, mechanical stability, and cryogenic cooling.

Low-loss and high-Qplanar metamaterial with toroidal moment

We experimentally observe toroidal dipolar response in a planar metamaterial comprised of asymmetric split-ring resonators (ASRRs) at microwave frequency. It is shown that a toroidal molecule can be constructed through rational arrangement of planar ASRRs as meta-atoms via manipulating structural symmetry and thus coupling of the meta-atoms. We find that the toroidal resonance provides a subwavelength-scale electromagnetic localization style, and that confining the electromagnetic field inside a dielectric medium with toroidal geometry is beneficial for low-loss metamaterials. The planar scheme of manipulating the coupling among the ASRRs may stimulate research in optical regions involving toroidal multipoles. The toroidal geometry together with the Fano resonance of ASRR-induced high-$Q$ response will have enormous potential applications in enhancing light-matter interactions, e.g., for low-threshold lasing, low-power nonlinear processing, and sensitive biosensing.

Toroidal Lasing Spaser

Toroidal shapes are often found in bio-molecules, viruses, proteins and fats, but only recently it was proved experimentally that toroidal structures can support exotic high-frequency electromagnetic excitations that are neither electric or magnetic multipoles. Such excitations, known as toroidal moments, could be playing an important role in enhancing inter-molecular interaction and energy transfer due to its higher electromagnetic energy confinement and weaker coupling to free space. Using a model toroidal metamaterial system, we show that coupling optical gain medium with high Q-factor toroidal resonance mode can enhance the single pass amplification to up to 65 dB. This offers an opportunity of creating the “toroidal” lasing spaser, a source of coherent optical radiation that is fueled by toroidal plasmonic oscillations in the nanostructure.

Folytonos anyagtovábbítású mikrohullámú kezelőegység fejlesztése

Most branches in the food industry have a considerable wastewater output. The problem is not only the total amount of wastewater production, but also the high content of organic matter. Anaerobic digestion is an effective way of treating wastewater for yielding profitable biogas and alleviating environmental concerns. Pre-treatment of sludge to break down its complex structure can be used for enhancing anaerobic digestibility. Research group of the Department of Process Engineering at the University of Szeged has investigated the applicability and the efficiency of microwave pre-treatment for food industry sludge. The results showed that the microwave treatment of sludge solution resulted in higher biodegradability and enhanced biogas production as well. According to these results a continuous-flow microwave toroidal cavity resonator treating-system was developed.

Pc2 EMIC waves generated high off the equator in the dayside outer magnetosphere

It is generally accepted that electromagnetic ion cyclotron (EMIC) waves are generated around the equatorial regions and propagate toward the high latitude ionospheres in both hemispheres. Here we describe a prolonged EMIC wave event in the Pc2 (0.1–0.2 Hz) frequency band above the He+ cyclotron frequency detected by the four Cluster satellites as they traversed sunward from L∼ 13 in the outer magnetosphere to the magnetopause, over 13°–20° magnetic latitude north of the equator and across the high latitude cusp region near local magnetic noon. Wave packet energy propagated dominantly along the geomagnetic field direction, confirming this was a traveling EMIC wave rather than a toroidal field line resonance. The energy packets propagated in alternating directions rather than uni‐directionally from the equator, implying the wave source was located in a high latitude region away from the equator, where a minimum in the B field is located. The CIS‐CODIF H+ion data provided evidence that the waves were generated locally via the ion cyclotron instability. We believe the off‐equatorial minimum magnetic field regions may be important source regions for these waves in the outer magnetosphere.

Plasmonic toroidal resonance at optical frequencies

Simulations of differentially oriented split-ring resonator arrays irradiated by visible light indicate induction of magnetic multipoles, opening up new avenues for high-capacity data storage.

Toroidal dipole response in a multifold double-ring metamaterial

The toroidal response is numerically investigated in a multifold double-ring metamaterials at the antibonding magnetic-dipole mode (i.e., antiparallel magnetic dipoles in one double-ring fold). This intriguing toroidal resonance in metamaterials is considered as a result of the magnetoelectric effect due to the broken balance of the electric near-field environment. We demonstrate that the toroidal dipole response in metamaterials can improve the quality factor of the resonance spectrum. In viewing of the design flexibility on the double-ring geometry, such toroidal metamaterials will offer advantages in application potentials of toroidal dipolar moment.

Current circulation and equilibrium in toroidal electron cyclotron resonance (ECR) plasmas in the LATE device

In toroidal plasmas immersed in a toroidal field of Bϕ, the electrons drift downward, while the ions drift upward due to the field gradient and curvature. The electrons that have reached the bottom wall return through the conducting vessel to the top, on which they recombine with the ions, completing the current circulation. Helical field lines by the superposition of a vertical field BZ provide another return path of internal current circulation, along which the electrons flow toroidally, generating a toroidal current. These conjectures have been examined on electron cyclotron resonance (ECR) plasmas in the Low Aspect ratio Torus Experiment (LATE) device with current-collecting electrodes at the top and bottom of the vacuum chamber. Upon the blocking of the external return path, the discharges terminate when BZ = 0, while they survive with a toroidal current when BZ is applied, showing that current circulation is vital to maintain the discharge. Detailed studies reveal the characteristics of current circulation and equilibrium. When BZ = 0, the electron pressure profile is a uniform vertical ridge along the ECR layer in accordance with the electron vertical drift current circulating via the external circuit, while an upwardly shifted potential hill arises, providing the ions E × B drift paths around the potential peak to the vicinity of the top electrode. When BZ is applied, the central electron pressure rises with an upwardly shifted peak, being relaxed from the vertical uniformity by addition of the internal return circuit. The space potential VS decreases and the electron density obeys the Boltzmann law under VS. The vertical and toroidal currents are found to be equilibrium currents driven by the base and excess portions of electron pressure, respectively, to ensure the radial force balance of the plasma torus.

Solar wind driving of magnetospheric ULF waves: Field line resonances driven by dynamic pressure fluctuations

Several observational studies suggest that solar wind dynamic pressure fluctuations can drive magnetospheric ultralow‐frequency (ULF) waves on the dayside. To investigate this causal relationship, we present results from Lyon‐Fedder‐Mobarry (LFM) global, three‐dimensional magnetohydrodynamic (MHD) simulations of the solar wind–magnetosphere interaction. These simulations are driven with synthetic solar wind input conditions where idealized ULF dynamic pressure fluctuations are embedded in the upstream solar wind. In three of the simulations, a monochromatic, sinusoidal ULF oscillation is introduced into the solar wind dynamic pressure time series. In the fourth simulation, a continuum of ULF fluctuations over the 0–50 mHz frequency band is introduced into the solar wind dynamic pressure time series. In this numerical experiment, the idealized solar wind input conditions allow us to study only the effect of a fluctuating solar wind dynamic pressure, while holding all of the other solar wind driving parameters constant. We show that the monochromatic solar wind dynamic pressure fluctuations drive toroidal mode field line resonances (FLRs) on the dayside at locations where the upstream driving frequency matches a local field line eigenfrequency. In addition, we show that the continuum of upstream solar wind dynamic pressure fluctuations drives a continuous spectrum of toroidal mode FLRs on the dayside. The characteristics of the simulated FLRs agree well with FLR observations, including a phase reversal radially across a peak in wave power, a change in the sense of polarization across the noon meridian, and a net flux of energy into the ionosphere.

Advanced simulation of electron heat transport in fusion plasmas

Electron transport in burning plasmas is more important since fusion products first heat electrons. First-principles simulations of electron turbulence are much more challenging due to the multi-scale dynamics of the electron turbulence, and have been made possible by close collaborations between plasma physicists and computational scientists. The GTC simulations of collisionless trapped electron mode (CTEM) turbulence show that the electron heat transport exhibits a gradual transition from Bohm to gyroBohm scaling when the device size is increased. The deviation from the gyroBohm scaling can be induced by large turbulence eddies, turbulence spreading, and non-diffusive transport processes. Analysis of radial correlation function shows that CTEM turbulence eddies are predominantly microscopic but with a significant tail in the mesoscale. A comprehensive analysis of kinetic and fluid time scales shows that zonal flow shearing is the dominant decorrelation mechanism. The mesoscale eddies result from a dynamical process of linear streamers breaking by zonal flows and merging of microscopic eddies. The radial profile of the electron heat conductivity only follows the profile of fluctuation intensity on a global scale, whereas the ion transport tracks more sensitively the local fluctuation intensity. This suggests the existence of a nondiffusive component in the electron heat flux, which arises from the ballistic radial E X B drift of trapped electrons due to a combination of the presence of mesoscale eddies and the weak de-tuning of the toroidal precessional resonance that drives the CTEM instability. On the other hand, the ion radial excursion is not affected by the mesoscale eddies due to a parallel decorrelation, which is not operational for the trapped electrons because of a bounce averaging process associated with the electron fast motion along magnetic field lines. The presence of the nondiffusive component raises question on the applicability of the usual quasilinear theory for the CTEM electron transport. This is in contrast to the good agreement between the quasilinear transport theory and simulation results of the electron heat transport in electron temperature gradient (ETG) turbulence, which is regulated by a wave-particle decorrelation. Therefore, the transport in the CTEM turbulence is a fluid-like eddy mixing process even though the linear CTEM instability is driven by a kinetic resonance. In contrast, a kinetic process dominates the transport in the ETG turbulence, which is characterized by macroscopic streamers.

Whispering-gallery mode micro-kylix resonators

Owing to their ability to confine electromagnetic energy in ultrasmall dielectric volumes, micro-disk, ring and toroid resonators hold interest for both specific applications and fundamental investigations. Generally, contributions from various loss channels within these devices lead to limited spectral windows (Q-bands) where highest mode Q-factors manifest. Here we describe a strategy for tuning Q-bands using a new class of micro-resonators, named micro-kylix resonators, in which engineered stress within an initially flat disk results in either concave or convex devices. To shift the Q-band by 60 nm towards short wavelengths in flat micro-disks a 50% diameter reduction is required, which causes severe radiative losses suppressing Q's. With a micro-kylix, we achieve similar tuning and even higher Q's by two orders of magnitude smaller diameter modification (0.4%). The phenomenon relies on geometry-induced smart interplay between modified dispersions of material absorption and radiative loss-related Q-factors. Micro-kylix devices can provide new functionalities and novel technological solutions for photonics and micro-resonator physics.

Energy dissipation via electron energization in standing shear Alfvén waves

A two-dimensional hybrid magnetohydrodynamic-kinetic electron model in dipolar coordinates is used to study the case of a fundamental mode toroidal field line resonance (FLR) centered on an L=10 closed dipolar magnetic field line. The model is initialized via a perturbation of the azimuthal shear Alfvén velocity so that only upward field aligned currents (corresponding to downwelling electrons) are present at the ionospheric boundaries during the first half wave period. It is found that the acceleration of the electrons to carry the field aligned currents can be a significant sink of Alfvén wave energy depending on the width of the flux tube. For a FLR with an equatorial perpendicular wavelength of 0.25 RE about 20% of the wave energy is dissipated over a half cycle. This varies inversely with the width of the flux tube increasing to 40% by a width of 0.15 RE, which, unless the system is driven, can completely damp the resonance in about 2–3cycles.

Computing the B1 field of the toroidal MRI coil

We present an analytic solution for the B 1 field produced in a gapped toroidal cavity resonator designed as a probe for high field MRI. This resonator supports standing TEM waves, so its electric and magnetic fields are identical to those produced by a stationary planar current source with the same (constant) cross-section multiplied by a complex exponential propagation factor. An explicit expression for the field may therefore be found by solving Laplace’s equation for the static potential, which is accomplished with a two-dimensional logarithmic conformal transformation algorithm. The equipotential curves are also the contours of the field strength B, and the B (vector) field at any point is directed along the contour passing through that point. With this information, we construct the solution by computing the angle made by the equipotential curve with the horizontal axis at each point, using this angle to analyze the B field into its x and y components, and adding the contributions from the current sources to obtain the magnitude and direction of B at each point in the region of interest. Some proposed extensions of this algorithm are also discussed.

Short wavelength electron temperature gradient instability in toroidal plasmas

The electron temperature gradient (ETG) driven mode in the very short wavelength region k⊥ρe>1 is identified with a gyrokinetic integral equation code in toroidal plasmas. This “double-humped” growth rate of the conventional ETG and short wavelength ETG modes is attributed to the toroidal drift resonance mechanism and the nonmonotonic behavior of normalized real frequency as the poloidal wavelength varies. This instability provides a possibility existence of a kind of turbulence source with very small size of cells. However, the wavelength of the short wavelength ETG mode is too short and induced transport may be small unless there are inverse cascade effects. In addition, the critical threshold of electron temperature gradient (R∕LTe)c for the short wavelength ETG mode is higher than that for the conventional ETG mode.

Designing coupled-resonator optical waveguide delay lines

We address the trade-offs among delay, loss, and bandwidth in the design of coupled-resonator optical waveguide (CROW) delay lines. We begin by showing the convergence of the transfer matrix, tight-binding, and time domain formalisms in the theoretical analysis of CROWs. From the analytical formalisms we obtain simple, analytical expressions for the achievable delay, loss, bandwidth, and a figure of merit to be used to compare delay line performance. We compare CROW delay lines composed of ring resonators, toroid resonators, Fabry-Perot resonators, and photonic crystal defect cavities based on recent experimental results reported in the literature.