Superradiant Modes Research Articles

Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass

Massive bosonic fields of arbitrary spin are predicted by general extensions of the Standard Model. It has been recently shown that there exists a family of bimetric theories of gravity - including massive gravity - which are free of Boulware-Deser ghosts at the nonlinear level. This opens up the possibility to describe consistently the dynamics of massive spin-2 particles in a gravitational field. Within this context, we develop the study of massive spin-2 fluctuations - including massive gravitons - around Schwarzschild and slowly-rotating Kerr black holes. Our work has two important outcomes. First, we show that the Schwarzschild geometry is linearly unstable for small tensor masses, against a spherically symmetric mode. Second, we provide solid evidence that the Kerr geometry is also generically unstable, both against the spherical mode and against long-lived superradiant modes. In the absence of nonlinear effects, the observation of spinning black holes bounds the graviton mass to be smaller than 5x10^{-23} eV.

Tailoring Plasmon Coupling in Self-Assembled One-Dimensional Au Nanoparticle Chains through Simultaneous Control of Size and Gap Separation

We investigated the near- and far-field response of one-dimensional chains of Au nanoparticles (NPs) fabricated with high structural control through template guided self-assembly. We demonstrate that the density of polyethylene glycol (PEG) ligands grafted onto the NP surface, in combination with the buffer conditions, facilitate a systematic variation of the average gap width (g) at short separations of g<1.1nm. The overall size (n) of the cluster was controlled through the template. The ability to independently vary n and g allowed for a rational tuning of the spectral response in individual NP clusters over a broad spectral range. We used this structural control for a systematic investigation of the electromagnetic coupling underlying the superradiant cluster mode. Independent of the chain length, plasmon coupling is dominated by direct neighbor interactions. A decrease in coupling strength at separations ≲0.5nm indicates the presence of non-local and/or quantum mechanical coupling mechanisms.

Coherent Fano resonances in a plasmonic nanocluster enhance optical four-wave mixing

Plasmonic nanoclusters, an ordered assembly of coupled metallic nanoparticles, support unique spectral features known as Fano resonances due to the coupling between their subradiant and superradiant plasmon modes. Within the Fano resonance, absorption is significantly enhanced, giving rise to highly localized, intense near fields with the potential to enhance nonlinear optical processes. Here, we report a structure supporting the coherent oscillation of two distinct Fano resonances within an individual plasmonic nanocluster. We show how this coherence enhances the optical four-wave mixing process in comparison with other double-resonant plasmonic clusters that lack this property. A model that explains the observed four-wave mixing features is proposed, which is generally applicable to any third-order process in plasmonic nanostructures. With a larger effective susceptibility χ(3) relative to existing nonlinear optical materials, this coherent double-resonant nanocluster offers a strategy for designing high-performance third-order nonlinear optical media.

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

Fano resonances in hybridized systems formed from the interaction of bright modes only are reported. Despite precedent works, we demonstrate theoretically and experimentally that Fano resonances can be obtained by destructive interference between two bright dipolar modes out of phase. A simple oscillator model is provided to predict and fit the far-field scattering. The predictions are verified with numerical calculations using a surface integral equation method for a wide range of geometrical parameters. The validity of the model is then further demonstrated with experimental dark-field scattering measurements on actual nanostructures in the visible range. A remarkable set of properties like crossings, avoided crossings, inversion of subradiant and superradiant modes and a plasmonic equivalent of a bound state in the continuum are presented. The nanostructure, that takes advantage of the combination of Fano resonance and nanogap effects, also shows high tunability and strong near-field enhancement. Our study provides a general understanding of Fano resonances as well as a simple tool for engineering their spectral features.

Signatures of Fano Interferences in the Electron Energy Loss Spectroscopy and Cathodoluminescence of Symmetry-Broken Nanorod Dimers

Through numerical simulation, we predict the existence of the Fano interference effect in the electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) of symmetry-broken nanorod dimers that are heterogeneous in material composition and asymmetric in length. The differing selection rules of the electron probe in comparison to the photon of a plane wave allow for the simultaneous excitation of both optically bright and dark plasmons of each monomer unit, suggesting that Fano resonances will not arise in EELS and CL. Yet, interferences are manifested in the dimer's scattered near- and far-fields and are evident in EELS and CL due to the rapid π-phase offset in the polarizations between super-radiant and subradiant hybridized plasmon modes of the dimer as a function of the energy loss suffered by the impinging electron. Depending upon the location of the electron beam, we demonstrate the conditions under which Fano interferences will be present in both optical and electron spectroscopies (EELS and CL) as well as a new class of Fano interferences that are uniquely electron-driven and are absent in the optical response. Among other things, the knowledge gained from this work bears impact upon the design of some of the world's most sensitive sensors, which are currently based upon Fano resonances.

Plasmonic Fano Resonances in Single-Layer Gold Conical Nanoshells

Plasmonic Fano resonances arise in symmetric single-layer conical nanoshells, which can be switched on and off by changing the polarization of the incident electric field. By breaking the symmetry, higher-order dark hybridized modes emerge in the spectrum, which couple to the superradiant bright mode and induce higher-order plasmonic Fano resonances. From a comparison with spherical nanostructures, it comes out that single-layer conical nanoshells are found to be highly capable in the generation of higher-order Fano resonances with larger modulation depths in the optical spectra. Such nanostructures are also found to offer high values of figure of merit and contrast ratio due to which they are highly suitable for biological sensors.

Hawking radiation for a Proca field inDdimensions. II. Charged field in a brane charged black hole

We generalise our first analysis of the wave equation for a massive vector boson in the background of a D-dimensional Schwarzschild black hole, by adding charge both to the field and the black hole, on the 3+1 dimensional Standard Model brane. A detailed numerical study is performed to obtain the transmission factor for the coupled (as well as decoupled) system of equations describing the Proca field modes, varying the angular momentum number, mass, charge and space-time dimensions. A qualitatively new feature arising from the introduction of charge is the appearance of superradiant modes, which we investigate. We then compute the Hawking fluxes, and analyse the effect of the charge. In particular we observe an inverted charge splitting effect for small energies and for two or more extra dimensions. For neutral fields, we compare the emission of massive particles with spins up to one and also compare the Proca bulk-to-brane ratio of energy emission, showing that, as for a scalar field, most of the energy is emitted on the brane.

Analytical study of greybody factor and quasinormal modes for the scalar field in rotating linear dilaton black hole

The rotating linear dilatonic black hole is an asymptotically non-flat solution to Einstein-Maxwell-Dilaton-Axion gravity theory due to the existence of non-trivial matter fields. We have analytically studied the wave equation of scalar field in this background and shown that the radial wave equation can be solved in terms of hypergeometric function. By determining the ingoing and the outgoing fluxes at the asymptotic infinity, we have found the analytical expressions for reflection coefficient and greybody factor for certain scalar modes. In the high frequency regime, we obtain the Hawking temperature by comparing the blackbody spectrum with the radiation spectrum resulting from reflection coefficient. It is shown that the Hawking temperature, which depends only on the linear dilatonic background parameter, does not agree with the temperature calculated from surface gravity. At last, the quasinormal modes of scalar field perturbation are presented, which shows that the rotating linear dilationic black hole is unstable for certain modes apart from the superradiant modes.

Collective effects in emission of localized excitons strongly coupled to a microcavity photon

A theory of nonlinear emission of localized excitons coupled to the optical mode of the microcavity is presented. Numerical results are compared with analytical ones. The effects of exciton–exciton interaction within the quantum dots and with the reservoir formed by non-resonant pumping are considered. It is demonstrated that the nonlinearity due to the interaction strongly affects the shape of the emission spectra. The collective superradiant mode of the excitons is shown to be stable against the nonlinear effects.

PIT-like effect in asymmetric and symmetric C-shaped metamaterials

We present asymmetric and symmetric couplings within a pair of C-shaped resonators (CSRs). The former shows that a typical and prominent plasmon-induced transparency (PIT) spectral response can be observed and it stems from asymmetrically coupled resonance (ACR) between the subradiant and superradiant modes due to exactly identical resonance frequency but different quality factors (Q-factor). The mechanism of such induced transparency is elucidated well by resonant hybridization and the induced currents within the CSRs. Simultaneously, we find that PIT-like effect can also be achieved in symmetric CSRs, symmetrically coupled resonance (SCR) between the subradiant and superradiant modes also give rise to transparency window. Essentially, the phase coupling of near-field, besides symmetry or asymmetry, is the crux of the PIT. Comparing the transparency window in asymmetric coupling, the PIT-like effect in symmetric coupling becomes less strong than the former. We consider that a broken symmetry is not the only prerequisite for PIT-like effect; but it plays an important role of prominent PIT-like transparency window. This not only sharpens our understanding of the existing concept, but also provides a profound insight into the plasmonic coherent interference in the near-field zone.

Analytical study of superradiant instability of the five-dimensional Kerr–Gödel black hole

We present an analytical study of superradiant instability of rotating asymptotically G\"{o}del black hole (Kerr-G\"{o}del black hole) in five-dimensional minimal supergravity theory. By employing the matched asymptotic expansion method to solve Klein-Gordon equation of scalar field perturbation, we show that the complex parts of quasinormal frequencies are positive in the regime of superradiance. This implies the growing instability of superradiant modes. The reason for this kind of instability is the Dirichlet boundary condition at asymptotic infinity, which is similar to that of rotating black holes in anti-de Sitter (AdS) spacetime.

Optical properties of collective excitations for an atomic chain with vacancies

Resonant dipole-dipole interaction modifies the energy and decay rate of electronic excitations for a collection of ultracold atoms. Collective excitations of a finite linear atomic chain can be divided into dark and bright modes. Typically the superradiant mode with maximum effective collective dipole dominates resonant light scattering. The generic case of two chain segments of different length and position exhibits an interaction blockade and spatially structured light emission. Ultimately, an extended system of several interfering segments models a long chain with randomly distributed defects of vacant sites. The corresponding emission pattern provides a sensitive tool to study structural and dynamical properties of the system.

Fano-chain: the Fano resonances in a nanoparticles chain

We show that for a linear chain of nanoparticles the Fano resonances can be excited and tuned through particle number manipulation by adding or removing particles from the chain. Fano modes excited in the chain, the spectrally overlapped bright superradiant and dark subradiant modes, are presented with current flow pictures for the first time, which clearly reveal how each individual particle reacts to light and interacts with other particles in the chain. This work may help design new Fano resonances in plasmonic metamaterials and nanostructures.

Toward Plasmonic Polymers

We establish the concept of a plasmonic polymer, whose collective optical properties depend on the repeat unit. Experimental and theoretical analyses of the super- and sub- radiant plasmon response of plasmonic polymers comprising repeat units of single nanoparticles or dimers of gold nanoparticles show that (1) the redshift of the lowest energy coupled mode becomes minimal as the chain approaches the infinite chain limit at a length of ∼10 particles, (2) the presence and energy of the modes are sensitive to the geometries of the constituents, that is, repeat unit, but (3) spatial disorder and nanoparticle heterogeneity have only small effects on the super-radiant mode.

Fano-Like Resonances in Asymmetric Homodimer of Gold Elliptical Nanowires

The Fano-like resonance properties of the asymmetric dimer for gold nanowires (GNWs) with elliptical section have been investigated based on the 2-D finite element method (2D-FEM). It is found that the reduced symmetry in the GNWs dimer will cause a distinct Fano dip in the absorption spectrum, which arises from the coherent coupling between the superradiant bright mode and the subradiant dark mode. With the increase in the rotation angle of one GNW, the Fano dip in the absorption of the asymmetric dimer enhances first and then reduces. We have further found that the Fano dip in the absorption becomes wider and deeper with the decrease in the separation between two GNWs, whereas the Fano minimum shows a distinct red shift. The tunability in Fano-like resonance of the asymmetric dimer for the GNWs may provide effective applications in sensing and plasmon-induced transparency.

A tunable Fano resonance in silver nanoshell with a spherically anisotropic core

The influences of the anisotropic permittivity and permeability in inner core on the Fano resonance have been investigated in Ag nanoshell by means of Mie scattering theory. The decreased inner core radius can enhance the coupling between superradiant and subradiant dipole modes and hence a distinct Fano profile. With increasing the tangential permittivity or permeability of inner core, the Fano resonance shows a redshift and the magnitude of Fano profile increases. The variation of Fano resonance with anisotropic permeability of the core is much weaker than that induced by anisotropic permittivity. We further find that the combined action of the increased tangential permittivity and permeability of inner core can induce a significant enhancement of Fano resonance in Ag nanoshell.

High Sensitivity Localized Surface Plasmon Resonance Sensing Using a Double Split NanoRing Cavity

Practical implementations of biosensing with metallic nanostructures often suffer from the large line width of the plasmon resonances induced by large radiative damping. A double split nanoring cavity is designed to suppress the radiative damping. The coupling between the superradiant quadrupole mode of a split nanoring with one gap and the subradiant quadrupole mode of a split nanoring with two gaps leads to splitting of the modal energies into bonding and antibonding quadrupole–quadrupole modes. The radiative damping is suppressed effectively, leading to a narrow line width for both bonding and antibonding quadrupole–quadrupole modes. Calculation results show that bulk refractive index sensitivities exceeding 1200 nm/RIU with a figure of merit exceeding 8.5 in the near-infrared are obtained with a Au double split nanoring cavity. The large cavity volumes and uniform electric fields inside the cavity make the double split nanoring cavity a good platform for surface-enhanced molecular sensing.

Superradiance and instability of the charged Myers-Perry black holes in the Gödel universe

We consider scalar field perturbations of the asymptotically G\"odel 5-dimensional charged rotating black holes with two equal angular momenta. It is shown that the spectrum of proper oscillations of the perturbation includes superradiant unstable modes. The reason for the instability is the confining Dirichlet boundary condition at the asymptotically far region of the G\"odel Universe. The confining box makes superradiant modes extract rotational energy from the black hole and, after repeated reflections from the black hole, grow unboundedly. A similar instability takes place for rotating black holes in the asymptotically anti-de Sitter (AdS) space-time.

Subradiant Plasmon Modes in Multilayer Metal–Dielectric Nanoshells

Subradiant plasmon modes play an important role in plasmon coupling, which can couple to the superradiant modes resulting in Fano resonances. In this study, we investigated the behaviors of the subradiant plasmons in multilayer metal–dielectric nanoshells using the generalized Mie theory. We showed that it is possible to get a pronounced Fano resonance in a single concentric nanoshell by controlling the size and geometry. The near-field coupling effects in multilayer nanoshell chains were studied by changing the alignment, particle number, and interparticle spacing. The local electric field and induced surface charge distributions were plotted to gain physical insight into the coupling mechanisms. The interactions between the particles result in a well-developed Fano resonance due to the broadening of bright plasmon modes. The subradiant plasmon modes remain robust and nearly uninfluenced by the near-field coupling and the surrounding medium. At the Fano resonance frequency, the largest field enhancement occurs in the silica layer, which is quite different from solid metal nanoparticle chains.

Excitation and Tuning of Higher-Order Fano Resonances in Plasmonic Oligomer Clusters

Plasmonic oligomer clusters are assemblies of closely packed metallic nanoparticles. They provide a rich set of spectral features such as Fano lineshapes and a simultaneous tunability of the supported resonances in the optical wavelength regime. In this study, we investigate numerically and experimentally clusters of plasmonic nanoparticles that exhibit multiple Fano resonances due to the interference of one broad superradiant mode and multiple narrow subradiant modes. In particular we investigate oligomers with multiple ring modes and elongated chains of nanoparticles surrounded by one ring of nanoparticles. We show that the number of nanoparticles and their respective arrangement in the cluster strongly influence the spectral position and modulation depth of the spectral signature of the supported modes. Our study opens up the pathway to "plasmonic super molecules" that show unprecedented tunability, which renders them highly suitable for applications such as multiwavelength surface-enhanced Raman scattering.