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The creation of single photon sources on a chip is a mid-term milestone on the road to chip-scale quantum computing. An in-depth understanding of the extended multipole decomposition of non-isolated sources of electromagnetic radiation is not only relevant for a microscopic description of fundamental phenomena, such as light propagation in a medium, but also for emerging applications such as single-photon sources. To design single photon emitters on a chip, we consider a ridge dielectric waveguide perturbed with a cylindrical inclusion. For this, we expanded classical multipole decomposition that allows simplifying and interpreting complex optical interactions in an intuitive manner to make it suitable for analyzing light-matter interactions with non-isolated objects that are parts of a larger network, e.g. individual components such as a single photon source of an optical chip. It is shown that our formalism can be used to design single photon sources on a chip.

A coordinate system is proposed for the purposes of analysis of far-field radiation from a localized source at the origin. The proposed coordinates exhibit no singularities over the far-field hemi-sphere, making them a good choice for automated radiation pattern analysis. Finally, it is shown that Ludwig polarization basis, commonly used to represent polarization of the far-field radiation, arises naturally, as a coordinate basis, when one uses stereographic coordinates.

Optical nonlinearities of matter are often associated with the response of individual atoms. Here, using a toy oscillator model, we show that in the confined geometry of a two-dimensional dielectric nanoparticle a collective nonlinear response of the atomic array can arise from the Coulomb interactions of the bound optical electrons, even if the individual atoms exhibit no nonlinearity. We determine the multipole contributions to the nonlinear response of nanoparticles and demonstrate that the odd order and even order nonlinear electric dipole moments scale with the area and perimeter of the nanoparticle, respectively.

Flying doughnuts (FDs) are exact propagating solutions of Maxwell equations in the form of single-cycle, space-time non-separable toroidal pulses. Here we review their properties and reveal the existence of a complex and robust fine topological structure. In particular, the electric and magnetic fields of the FD pulse vanish across a number of planes, spherical shells and rings, and display a number of point singularities including saddle points and vortices. Moreover, the instantaneous Poynting vector of the field exhibits a large number of singularities, which are often accompanied by extended areas energy backflow.

We introduce a non-intrusive far-field optical microscopy, which reveals the fine structure of an object through its far-field scattering pattern under illumination with topologically structured light containing deeply subwavelength singularity features. The object is reconstructed by a neural network trained on a large number of scattering events. We demonstrate resolving powers two orders of magnitude beyond the conventional “diffraction limit” of λ/2.

High-index dielectric materials are in great demand for nanophotonic devices and applications, from ultrathin optical elements to metal-free sub-diffraction light confinement and waveguiding. Here we show that chalcogenide topological insulators are particularly apt candidates for dielectric nanophotonic architectures in the infrared spectral range by reporting metamaterial resonances in chalcogenide crystals sustained well inside the mid-infrared, choosing Bi$_2$Te$_3$ as case study within this family of materials. Strong resonant modulation of the incident electromagnetic field is achieved thanks to the exceptionally high refractive index ranging between 7 and 8 throughout the 2-10 $\mu$m region. Analysis of the complex mode structure in the metamaterial allude to the excitation of poloidal surface currents which could open pathways for enhanced light-matter interaction and low-loss plasmonic configurations by coupling to the spin-polarized topological surface carriers, thereby providing new opportunities to combine dielectric, plasmonic and magnetic metamaterials in a single platform., Comment: 21 pages, 6 figures

We report the generation of space-time non-separable toroidal pulses of complex topological structure. Such pulses, a formation of singularities propagating in free space, are ideal probes for toroidal and anapole modes in matter.

We introduce a new far-field and label-free imaging paradigm based on combining singularity illumination with artificial-intelligence enabling reconstruction of an object from the scattered light. We demonstrate imaging resolution beyond X/100.

Maxwell's equations can be satisfied not only by plane electromagnetic waves, but also by more exotic space-time nonseparable electromagnetic pulses which cannot be represented as a product of time- and space-dependent functions. A family of such pulses with finite energy was identified by Ziolkowski [Phys. Rev. A 39, 2005 (1989)]. Later, Hellwarth and Nouchi [Phys. Rev. E 54, 889 (1996)] highlighted a subset of Ziolkowski's pulses, now known as flying donuts, a formation of polarization singularities of toroidal topology traveling at the speed of light. Spurred by recent advances in ultrafast and topological optics, space-time nonseparable electromagnetic excitations are now becoming the focus of growing experimental efforts as they hold promise for topological information transfer, probing and inducing transient excitations in matter such as anapole and toroidal modes. Here we demonstrate that the flying donut can be constructed from an ensemble of monochromatic plane waves with continuous spatial and frequency spectrum and hence can be generated by converting broadband conventional transverse electromagnetic pulses. Ministry of Education (MOE) Published version The authors acknowledge the support of the MOE Singapore (Grant No. MOE2016-T3-1-006), the UK Engineering and Physical Sciences Research Council (Grant No. EP/M009122/1), the European Research Council (Advanced Grant No. FLEET-786851), and the Defense Advanced Research Projects Agency (DARPA) under the Nascent Light Matter Interactions program.

A nonintrusive far‐field optical microscopy resolving structures at the nanometer scale would revolutionize biomedicine and nanotechnology but is not yet available. Here, a new type of microscopy is introduced, which reveals the fine structure of an object through its far‐field scattering pattern under illumination with light containing deeply subwavelength singularity features. The object is reconstructed by a neural network trained on a large number of scattering events. In numerical experiments on imaging of a dimer, resolving powers better than λ/200, i.e., two orders of magnitude beyond the conventional “diffraction limit” of λ/2, are demonstrated. It is shown that imaging is tolerant to noise and is achievable with low dynamic range light intensity detectors. Proof‐of‐principle experimental confirmation of DSTM is provided with a training set of small size, yet sufficient to achieve resolution five‐fold better than the diffraction limit. In principle, deep learning reconstruction can be extended to objects of random shape and shall be particularly efficient in microscopy of a priori known shapes, such as those found in routine tasks of machine vision, smart manufacturing, and particle counting for life sciences applications., Nonintrusive, label‐free, far‐field optical microscopy is introduced based on illumination of an object with topologically structured light that contains multiple deeply subwavelength singularity features. This new type of optical microscopy allows to resolve the fine structure of an object with resolution that can exceed the conventional diffraction limit by two orders of magnitude.

Flying Doughnuts are exact propagating solutions of Maxwell equations in the form of single-cycle, space-time non-separable pulses with complex topology of spectrally broadband vortices. We present the experimental generation of Flying Doughnut pulses and discuss their topological and spatiotemporal structure.

We show that Flying Doughnuts, the exact propagating solutions of Maxwell equations in the form of single-cycle toroidal pulses have complex and robust fine topological structure of spectrally broadband vortices and extended areas of energy backflow.

We demonstrate second harmonic generation by using an amorphous silicon metamaterial fabricated on the tip of an optical fiber that collects the generated light. The metamaterial is a double-chevron array that supports a closed-mode resonance for the fundamental wavelength at 1510 nm with a quality factor of 30. The normalized resonant second harmonic conversion efficiency calculated per intensity and square of interaction length is ∼10 −11 W −1, which exceeds the previously achieved value for a silicon metamaterial by two orders of magnitude.

We show how structuring of matter can lead to second order optical nonlinearity. Coulomb interactions involving bound electrons cause a nonlinear optical response at boundaries. We demonstrate that second order nonlinearity is proportional to the perimeter of a planar structure cut from a centrosymmetric lattice of harmonic oscillators. This proportionality and our model can instruct the design of dielectric nonlinear particles, surfaces and metamaterials for optical second harmonic generation.

The interaction between microscopic particles has always been a fascinating and intriguing area of science. Direct interrogation of such interactions is often difficult. Structured electromagnetic systems offer a rich toolkit for mimicking and reproducing the key dynamics that governs the microscopic interactions, and thus provide an avenue to explore and interpret the microscopic phenomena. In particular, metamaterials offer the freedom to artificially tailor light-matter coupling and to control the interaction between unit cells in the metamaterial array. Here we demonstrate a terahertz metamaterial that mimics spin-related interactions of microscopic particles in a 2D lattice via complex electromagnetic multipoles scattered within the metamaterial array. Fano resonances featured by distinct mode properties due to strong nearest-neighbor interactions are discussed that draw parallels with the 2D Ising model. Interestingly, a phase transition from single Fano resonance to hyperfine splitting of Fano spectrum is observed by manipulating the 2D interactions without applying external magnetic or electric fields, which provides a potential multispectral platform for applications in super-resolution imaging, biosensing, and selective thermal emission. The dynamic approach to reproduce static interaction between microscopic particles would enable more profound significance in exploring the unknown physical world by the macroscopic analogues.

The toroidal dipole is a localized electromagnetic excitation independent from the familiar magnetic and electric dipoles. It corresponds to currents flowing along minor loops of a torus. Interference of radiating induced toroidal and electric dipoles leads to anapole, a nonradiating charge-current configuration. Interactions of induced toroidal dipoles with electromagnetic waves have recently been observed in artificial media at microwave, terahertz, and optical frequencies. Here, we demonstrate a quasi-planar plasmonic metamaterial, a combination of dumbbell aperture and vertical split-ring resonator, that exhibits transverse toroidal moment and resonant anapole behavior in the optical part of the spectrum upon excitation with a normally incident electromagnetic wave. Our results prove experimentally that toroidal modes and anapole modes can provide distinct and physically significant contributions to the absorption and dispersion of slabs of matter in the optical part of the spectrum in conventional transmission and reflection experiments. MOE (Min. of Education, S’pore)

The mechanism of Cooper pair formation and its underlying physics has long occupied the investigation into high temperature (high-Tc ) cuprate superconductors. One of the ways to unravel this is to observe the ultrafast response present in the charge carrier dynamics of a photoexcited specimen. This results in an interesting approach to exploit the dissipation-less dynamic features of superconductors to be utilized for designing high-performance active subwavelength photonic devices with extremely low-loss operation. Here, dual-channel, ultrafast, all-optical switching and modulation between the resistive and the superconducting quantum mechanical phase is experimentally demonstrated. The ultrafast phase switching is demonstrated via modulation of sharp Fano resonance of a high-Tc yttrium barium copper oxide (YBCO) superconducting metamaterial device. Upon photoexcitation by femtosecond light pulses, the ultrasensitive cuprate superconductor undergoes dual dissociation-relaxation dynamics, with restoration of superconductivity within a cycle, and thereby establishes the existence of dual switching windows within a timescale of 80 ps. Pathways are explored to engineer the secondary dissociation channel which provides unprecedented control over the switching speed. Most importantly, the results envision new ways to accomplish low-loss, ultrafast, and ultrasensitive dual-channel switching applications that are inaccessible through conventional metallic and dielectric based metamaterials. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Accepted version

Increasing interest in electrodynamics and spectroscopy of toroidal excitations in matter has initiated a discussion on independent physical significance of toroidal and electric dipole excitations. Here we introduce three Gedanken-Experiments that reveal their fundamental differences.

Plasmonics is a rapidly developing field at the boundary of physical optics and condensed matter physics. It studies phenomena induced by and associated with surface plasmons - elementary polar excitations bound to surfaces and interfaces of good nanostructured metals. This Roadmap is written collectively by prominent researchers in the field of plasmonics. It encompasses selected aspects of nanoplasmonics. Among them are fundamental aspects, such as quantum plasmonics based on the quantum-mechanical properties of both the underlying materials and the plasmons themselves (such as their quantum generator, spaser), plasmonics in novel materials, ultrafast (attosecond) nanoplasmonics, etc. Selected applications of nanoplasmonics are also reflected in this Roadmap, in particular, plasmonic waveguiding, practical applications of plasmonics enabled by novel materials, thermo-plasmonics, plasmonic-induced photochemistry and photo-catalysis. This Roadmap is a concise but authoritative overview of modern plasmonics. It will be of interest to a wide audience of both fundamental physicists and chemists, as well as applied scientists and engineers., J Schötz for financial support by the European Union via the ERC grant ATTOCO, by the DFG via SPP1840.

Multi-photon absorption processes have a nonlinear dependence on the amplitude of the incident optical field i.e. the number of photons. However, multi-photon absorption is generally weak and multi-photon events occur with extremely low probability. Consequently, it is extremely challenging to engineer quantum nonlinear devices that operate at the single photon level and the majority of quantum technologies have to rely on single photon interactions. Here, we demonstrate experimentally and theoretically that exploiting coherent absorption of N = 2 N00N states makes it possible to enhance the number of two-photon states that are absorbed. An absorbing metasurface placed inside a Sagnac-style interferometer into which we inject an N = 2 N00N state, exhibits two-photon absorption with 40.5% efficiency, close to the theoretical maximum. This high probability of simultaneous absorption of two photons holds the promise for applications in fields that require multi-photon upconversion but are hindered by high peak intensities., 13 page, 5 figures

Natural toroidal molecules, such as biomolecules and proteins, possess toroidal dipole moments that are hard to be detected, which leads to extensive studies of artificial toroidal materials. Recently, toroidal metamaterials have been widely investigated to enhance toroidal dipole moments while the other multipoles are eliminated due to the spacial symmetry. In this talk, we will show several cases on the plasmonic toroidal excitation by engineering the near-field coupling between metamaterials, including their promising applications. In addition, a novel design for a toroidal metamaterial with engineering anapole mode will also be discussed. Published version

We show for the first time that, contrary to common expectations, transition to superconductivity affects plasmonic behaviour of niobium at optical frequencies. This result is unexpected as photon energy is orders of magnitude higher than the binding energy of the Cooper pairs, the superconducting charge carriers.

Emission of electromagnetic radiation by accelerated particles with electric, toroidal and anapole dipole moments is analyzed. It is shown that ellipticity of the emitted light can be used to differentiate between electric and toroidal dipole sources, and that anapoles, elementary neutral non-radiating configurations, which consist of electric and toroidal dipoles, can emit light under uniform acceleration. The existence of non-radiating configurations in electrodynamics implies that it is impossible to fully determine the internal makeup of the emitter given only the distribution of the emitted light. Here we demonstrate that there is a loop-hole in this `inverse source problem'. Our results imply that there may be a whole range of new phenomena to be discovered by studying the electromagnetic response of matter under acceleration., Comment: Change from previous version. Further corrections to figure 1. Much more calculations in the main paper. Added a section on ellipticity

We report on approaches to the integration of metasurfaces and active metadevices with optical fiber platforms, including all-optical and electro-optic nano-mechanical switching devices, dispersion control solutions and coherent absorption modulators.

The toroidal dipole moments of natural molecules are hard to be detected so the artificial toroidal materials made by metamaterial attract more attentions. Metamaterial, the sub-wavelength artificial structures, can modulate reflection or transmission of light. The toroidal metamaterial can not only amplify the toroidal moment but also repress the electric and magnetic dipole so it can be used to study the properties of toroidal dipole moment. However, there are many limitations for the experiments, such as the lateral light is necessary to excite the toroidal response. Most of the toroidal dipole moments oscillate perpendicularly to the substrate, therefore it is difficult to couple it with other dipole moments and could be only excited in the microwave region. In this paper, we design a toroidal metamaterial consisting of dumbbell-shaped aperture and vertical split ring resonator (VSRR) vertically. The toroidal dipole moment of our metamaterial is excited in the optical region. The arrangement of our nanostructures is vertical instead of planar annular arrangement to reduce the size of the unit cell and increase the density of the toroidal dipole moment. Moreover, the direction of toroidal dipole moment is parallel to the substrate which can be used for the study of the coupling effect with other kinds of dipolar moments.

Toroidal multipoles, which along with the familiar electric and magnetic multipoles is necessary for the complete multipole representation of an arbitrary radiating source. We have designed a planar metasurface with resonant response in the terahertz range, which is easy to fabricate and exhibits the signature of a toroidal excitation.

A toroidal dipole in metasurfaces provides an alternate approach for the excitation of high-Q resonances. In contrast to conventional multipoles, the toroidal dipole interaction strength depends on the time derivative of the surrounding electric field. A characteristic feature of toroidal dipoles is tightly confined loops of oscillating magnetic field that curl around the fictitious arrow of the toroidal dipole vector.

The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information.

Toroidal dipole moments, the third kind of fundamental dipole moment, have unusual electromagnetic properties different from the electric and magnetic multipoles. We fabricate a new type of 3D plasmonic toroidal metamaterial by using mutual coupling between dumbbell-shaped gold apertures with vertical split-ring resonators (VSRRs) at optical frequency. The radiated power of multipole moments are calculated and analyzed to improve the meta-system is dominated by the toroidal dipole moment. This result paves a way for practical application on metamaterial based devices, such as biosensor and lasing spaser.

Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here, we propose and theoretically study all-dielectric metamaterials of a special class that represent a simple electromagnetic system supporting toroidal dipolar excitations in the THz part of the spectrum. We show that resonant transmission and reflection of such metamaterials is dominated by toroidal dipole scattering, the neglect of which would result in a misunderstanding interpretation of the metamaterials’ macroscopic response. Because of the unique field configuration of the toroidal mode, the proposed metamaterials could serve as a platform for sensing or enhancement of light absorption and optical nonlinearities. Published version

We introduce a new quantum interference effect that can be observed in a plasmonic interferometer and is controlled by an applied magnetic field. We show that the introduced phenomenon will result in nonlinear magnetically-tuneable transmission of the interferometer even at low light intensity (few µW) and low applied magnetic field (tens of mT).

Bragg gratings fabricated along the mode propagation direction in optical fibers are a powerful technology for controlling dispersion. Here, we show that a dielectric metamaterial grating with sub-wavelength period fabricated in the thin layer of silicon on the fiber facet exhibits transmission resonance with the quality factor exceeding 300. We demonstrate how focused ion beam patterning, commonly expected to degrade the optical performance of materials, can be exploited to create low-loss photonic nanostructures on the fiber facet. Only a few tens of nanometers in thickness, such facet gratings can be used in compact interconnects, dispersion compensation, and sensing applications. MOE (Min. of Education, S’pore) Published version

Split ring resonator (SRR) has attracted wide attentions since the discovery of negative refraction in 2002. Here, we designed and fabricated vertical SRR (VSRR) arrays and toroidal metamolecule by using double exposure e-beam lithography with precise alignment technique, and their resonance behaviors are subsequently studied in optical region. The fundamental resonance properties of VSRR are studied as well as the plasmon coupling in a VSRR dimer structure by changing the gap distance between SRRs. In addition, we proposed a three-dimensional toroidal structure composed a VSRR with a dumbbell structure that supported a toroidal resonance under normal incidence with broadband working frequency. Such toroidal metamaterial confines effectively the electric as well as magnetic energy paving a way for promising applications in the field of plasmonics, such as integrated 3D plasmonic metamaterials, plasmonic biosensor and lasing spaser.

We present a superconducting metamaterial with ultra-strong nonlinear response in the sub-terahertz range. A change in transmission of more than 10% has been achieved by ramping up the radiation intensity from 100µW/cm2 to just 800µW/cm2.

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. Published version

We present a superconducting metamaterial with ultra-strong nonlinear response in the sub-terahertz range. A change in transmission of more than 10% has been achieved by ramping up the radiation intensity from 100μW/cm2 to just 800μW/cm2.

Engaging strongly resonant interactions allows dramatic enhancement of functionalities of many electromagnetic devices. However, resonances can be dampened by Joule and radiation losses. While in many cases Joule losses may be minimized by the choice of constituting materials, controlling radiation losses is often a bigger problem. Recent solutions include the use of coupled radiant and sub-radiant modes yielding narrow asymmetric Fano resonances in a wide range of systems, from defect states in photonic crystals and optical waveguides with mesoscopic ring resonators to nanoscale plasmonic and metamaterial systems exhibiting interference effects akin to electromagnetically-induced transparency. Here we demonstrate theoretically and confirm experimentally a new mechanism of resonant electromagnetic transparency, which yields very narrow isolated symmetric Lorentzian transmission lines in toroidal metamaterials. It exploits the long sought non-trivial non-radiating charge-current excitation based on interfering electric and toroidal dipoles that was first proposed by Afanasiev and Stepanovsky in [J. Phys. A Math. Gen. 28, 4565 (1995)].

Summary form only given. The ability of metamaterials to concentrate energy of the incident radiation on the sub-wavelength scale has long been predicted to lead to new device applications with a significantly improved and even superior functionality; the concrete implementations are, however, only beginning to emerge. Here we show how combining the concept of a superconducting bolometer with the coherent metamaterial paradigm allows to create a very sensitive sub-THz radiation detector with high spectral selectivity of ν0/Δν ~ 90.Figure 1a illustrates the solution. Our bolometer is based on asymmetrically-split-ring (ASR) metamaterial with a characteristic narrow BIT-like resonance which is extremely sensitive to Joule losses. It also belongs to a novel, special class of coherent metamaterials, where the resonant response results from the collective excitation of the entire metamaterial array underpinned by strong interactions between its metamolecules. The metamaterial design features an additional `signal line' that electrically connects all metamolecules into a single network. We manufacture the metamaterial by patterning the thin niobium film on the sapphire substrate with standard UVphotolithography. The measurements are conducted by placing the metamaterial into the optical cryostat and cooling it down to temperature 5K. At such temperatures the niobium becomes superconducting which results in a sharp, low-loss metamaterial response in the sub-THz range (see Fig. 1b). We apply the bias of Vb = 4V (see Fig. 1a) to create a small hotspot within the metamaterial array (- 5% of the total area) where niobium is just below the superconducting transition point and is therefore very sensitive to Joule heating caused by the incident radiation. Strong interactions between the metamolecules that are typical to ASR metamaterial at its coherent resonance lead to channelling of radiation energy from the outer regions of the metamaterial into the hotspot, thus allowing to combine the narrow spectral response with the extreme sensitivity, resulting in the overall very efficient radiation-detecting device.

A long chase for the elusive dynamic toroidal moments has been recently concluded by detecting a spectral signature of the toroidal dipolar resonance in the response of a specially designed electromagnetic metamaterial [1]. This observation brings up a new interest to the prediction made by Afanasiev and Stepanovsky in 1994 that a combination of oscillating toroidal and conventional electric dipoles forms a non-trivial non-radiating electromagnetic system producing gauge-irreducible waves of vector potential in absence of electric and magnetic fields [2]. Here we report the observation of extremely narrow transmission resonances in toroidal void metamaterials that result from the interference of its electric and toroidal dipolar response thus indicating the existence of such non-radiating system. Our results provide new evidence for the discussion on independent physical significance of vector-potential and its role as an independent information carrier.

We show that subterahertz transmission of the superconducting metamaterial, an interlinked two-dimensional network of subwavelength resonators connected by a continuous superconducting wire loop, can be dynamically modulated by passing electrical current through it. We have identified the main mechanisms of modulation that correspond to the suppression of the superconductivity in the network by magnetic field and heat dissipation. Using the metamaterial fabricated from thin niobium film, we were able to demonstrate a transmission modulation depth of up to 45% and a bandwidth of at least 100 kHz. The demonstrated approach may be implemented with other superconducting materials at frequencies below the superconducting gap in the THz and subterahertz bands. Published version

Nonlinear and switchable metamaterials achieved by artificial structuring on the subwavelength scale have become a central topic in photonics research. Switching with only a few quanta of excitation per metamolecule, metamaterial's elementary building block, is the ultimate goal, achieving which will open new opportunities for energy efficient signal handling and quantum information processing. Recently, arrays of Josephson junction devices have been proposed as a possible solution. However, they require extremely high levels of nanofabrication. Here we introduce a new quantum superconducting metamaterial which exploits the magnetic flux quantization for switching. It does not contain Josephson junctions, making it simple to fabricate and scale into large arrays. The metamaterial was manufactured from a high-temperature superconductor and characterized in the low intensity regime, providing the first observation of the quantum phenomenon of flux exclusion affecting the far-field electromagnetic properties of the metamaterial.

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 moments are fundamental electromagnetic excitations that cannot be represented in terms of the standard multipole expansion [1]. They were first considered by Zel’dovich back in 1957 [2], but only recently have become the subject of growing interest owing to their peculiar electromagnetic properties. Electromagnetic interactions with toroidal currents were predicted to disobey such widely accepted principle as the action-reaction equality. Toroidal currents can also form charge-current configurations generating vector potential fields in the absence of radiated electromagnetic waves. Although toroidal moments are held responsible for parity violation in nuclear and particle physics, no direct evidence of their importance for classical electrodynamics has been reported so far. This is because effects associated with toroidal moments in naturally available materials are extremely weak and usually masked by much stronger effects due to conventional electric and magnetic dipole and quadrupole moments.

The toroidal spectral responses of toroidal metamolecule integrated by four gold U-shaped SRRs at optical frequencies are numerically studied. Downsizing the structure achieve observation of a plasmonic toroidal mode at optical frequencies.

We demonstrate the first superconducting metamaterial that can exhibit a profound toroidal dipolar resonance. Quantum behaviour of the superconductor and toroidal excitation of the metamaterial are both necessary prerequisites for observing the time-dependent Aharonov-Bohm effect. Published version