Nonlocal Optical Response Research Articles

Nonlocal optical response in topological phase transitions in the graphene family

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. We also consider the plasmon excitations in the graphene family and find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. The expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.

Optoelectronic figure of merit of a metal nanoparticle—quantum dot (MNP-QD) hybrid molecule for assessing its suitability for sensing applications

Recently, many have studied various configurations of metal nanoparticle-quantum dot (MNP-QD) hybrid molecules based on different metals and tunable parameters. In this paper, we aim to incite the interest in using MNP-QD nanohybrids, which possess sensing capabilities superior to those of the individual constituents, for sensing applications that rely on scattered light. When assessing whether a given MNP-QD configuration is suited for an application, sometimes it is hard to assess the pros and cons of a given configuration against other candidates. Here we propose a simple, elegant relative figure of merit (RFoM), which focuses on maximizing the scattered intensity and the refractive index sensitivity of the nanohybrid, to rank the suitability of viable MNP-QD configurations for a particular sensing application. We use the proposed RFoM to analyse the optical spectra of noble, transition, post transition and alkali metal based MNP-QD nanohybrids using the representative metals Au, Ag, Cu, Al and Na, adopting a generalized nonlocal optical response (GNOR) method based cavity QED approach. Based on our observations, we suggest how the usage of MNP-QD nanohybrids could improve the conventionally studied tumour targeting applications. Moreover, we propose potential substitutes for noble metals conventionally considered for MNP-QD nanohybrids.

Nonlocal quasinormal modes for arbitrarily shaped three-dimensional plasmonic resonators

Nonlocal effects have been shown to be responsible for a variety of non-trivial optical effects in small-size plasmonic nanoparticles, beyond classical electrodynamics. However, it is not clear whether optical mode descriptions can be applied to such extreme confinement regimes. Here, we present a powerful and intuitive quasinormal mode description of the nonlocal optical response for three-dimensional plasmonic nanoresonators. The nonlocal hydrodynamical model and a generalized nonlocal optical response model for plasmonic nanoresonators are used to construct an intuitive modal theory and to compare to the local Drude model response theory. Using the example of a gold nanorod, we show how an efficient quasinormal mode picture is able to accurately capture the blueshift of the resonances, the higher damping rates in plasmonic nanoresonators, and the modified spatial profile of the plasmon quasinormal modes, even at the single mode level. We exemplify the use of this theory by calculating the Purcell factors of single quantum emitters, the electron energy-loss spectroscopy spatial maps, as well as the Mollow triplet spectra of field-driven quantum dots with and without nonlocal effects for different size nanoresonators. Our nonlocal quasinormal mode theory offers a reliable and efficient technique to study both classical and quantum optical problems in nanoplasmonics.

Third order nonlinear optics in Ag nanocubes: local and nonlocal optical responses as a function of excitation wavelength and particle size.

Colloidal silver nanocubes in solution were analyzed by the Z-scan technique in the resonant and non-resonant regimes. Three different systems with particle sizes of 56, 99 and 215 nm, and concentrations of 0.378, 0.831 and 0.715 mg/mL, respectively, were obtained by the polyol method. Nonlinear excitation of the samples was performed with laser pulses of 26 ps, at a repetition rate of 10 Hz, and using three different wavelenghts (355, 532 and 1064 nm), exciting only the electronic part of the optical nonlinearity, and avoiding induced thermal loading of the samples. Whenever observable, samples showed saturable absorption for all wavelengths, which was dependent, in general, on concentration and incident intensity. For samples featuring sizes of 55 and 99 nm, saturable absorption could be observed for wavelengths close to their dipolar surface plasmon resonances; while, for samples with sizes of 99 and 215 nm, saturable absorption and positive nonlinear optical refraction (only for size of 215 nm) could be observed at 1064 nm. Besides, for some samples, nonlinear optical response followed the incident intensity profile at wavelengths close to resonance. On the contrary, for wavelengths out of resonance, the nonlinear optical behavior showed to be nonlocal, ie, its profile was narrower than the incident one.

Investigation on plasmonic responses in multilayered nanospheres including asymmetry and spatial nonlocal effects

In this work, we present a rigorous approach for analyzing the optical response of multilayered spherical nano-particles comprised of either plasmonic metal or dielectric, when there is no longer radial symmetry and when nonlocality is included. The Lorenz–Mie theory is applied, and a linearized hydrodynamic Drude model as well as the general nonlocal optical response model for the metals are employed. Additional boundary conditions, viz., the continuity of normal components of polarization current density and the continuity of first-order pressure of free electron density, respectively, are incorporated when handling interfaces involving metals. The application of spherical addition theorems, enables us to express a spherical harmonic about one origin to spherical harmonics about a different origin, and leads to a linear system of equations for the inward- and outward-field modal coefficients for all the layers in the nanoparticle. Scattering matrices at interfaces are obtained and cascaded to obtain the expansion coefficients, to yield the final solution. Through extensive modelling of stratified concentric and eccentric metal-involved spherical nanoshells illuminating by a plane wave, we show that, within a nonlocal description, significant modifications of plasmonic response appear, e.g. a blue-shift in the extinction / scattering spectrum and a broadening spectrum of the resonance. In addition, it has been demonstrated that core–shell nanostructures provide an option for tunable Fano-resonance generators. The proposed method shows its capability and flexibility to analyze the nonlocal response of eccentric hybrid metal–dielectric multilayer structures as well as adjoined metal-involved nanoparticles, even when the number of layers is large.

On the origin of nonlocal damping in plasmonic monomers and dimers

The origin and importance of nonlocal damping is discussed through simulations with the generalized nonlocal optical response (GNOR) theory, in conjunction with time-dependent density functional theory (TDDFT) calculations and equivalent circuit modeling, for some of the most typical plasmonic architectures: metal–dielectric interfaces, metal–dielectric–metal gaps, spherical nanoparticles and nanoparticle dimers. It is shown that diffusive damping, as introduced by the convective–diffusive GNOR theory, describes well the enhanced losses and plasmon broadening predicted by ab initio calculations in few-nm particles or few-to-sub-nm gaps. Through the evaluation of a local effective dielectric function, it is shown that absorptive losses appear dominantly close to the metal surface, in agreement with TDDFT and the mechanism of Landau damping due to generation of electron–hole pairs near the interface. Diffusive nonlocal theories provide therefore an efficient means to tackle plasmon damping when electron tunneling can be safely disregarded, without the need to resort to more accurate, but time-consuming fully quantum-mechanical studies.

Robustness of the Rabi Splitting under Nonlocal Corrections in Plexcitonics

We explore theoretically how nonlocal corrections in the description of the metal affect the strong coupling between excitons and plasmons in typical examples where nonlocal effects are anticipated to be strong, namely small metallic nanoparticles, thin metallic nanoshells or dimers with narrow separations, either coated with or encapsulating an excitonic layer. Through detailed simulations based on the generalised nonlocal optical response theory, which simultaneously accounts both for modal shifts due to screening and for surface-enhanced Landau damping, we show that, contrary to expectations, the influence of nonlocality is rather limited, as in most occasions the width of the Rabi splitting remains largely unaffected and the two hybrid modes are well distinguishable. We discuss how this behaviour can be understood in view of the popular coupled-harmonic-oscillator model, while we also provide analytic solutions based on Mie theory to describe the hybrid modes in the case of matryoshka-like single nanoparticles. Our analysis provides an answer to a so far open question, that of the influence of nonlocality on strong coupling, and is expected to facilitate the design and study of plexcitonic architectures with ultrafine geometrical details.

How nonlocal damping reduces plasmon-enhanced fluorescence in ultranarrow gaps

The nonclassical modification of plasmon-assisted fluorescence enhancement is theoretically explored by placing two-level dipole emitters at the narrow gaps encountered in canonical plasmonic architectures, namely dimers and trimers of different metallic nanoparticles. Through detailed simulations, in comparison with appropriate analytical modelling, it is shown that within classical electrodynamics, and for the reduced separations explored here, fluorescence enhancement factors of the order of $10^{5}$ can be achieved, with a divergent behaviour as the particle touching regime is approached. This remarkable prediction is mainly governed by the dramatic increase in excitation rate triggered by the corresponding field enhancement inside the gaps. Nevertheless, once nonclassical corrections are included, the amplification factors decrease by up to two orders of magnitude and a saturation regime for narrower gaps is reached. These nonclassical limitations are demonstrated by simulations based on the generalised nonlocal optical response theory, which accounts in an efficient way not only for nonlocal screening, but also for the enhanced Landau damping near the metal surface. A simple strategy to introduce nonlocal corrections to the analytic solutions is also proposed. It is therefore shown that the nonlocal optical response of the metal imposes more realistic, finite upper bounds to the enhancement feasible with ultrasmall plasmonic cavities, thus providing a theoretical description closer to state of the art experiments.

Cavity QED analysis of an exciton-plasmon hybrid molecule via the generalized nonlocal optical response method

A metal nanoparticle coupled to a semiconductor quantum dot forms a tunable hybrid system which exhibits remarkable optical phenomena. Small metal nanoparticles possess nanocavitylike optical concentration capabilities due to the presence of strong dipolar excitation modes in the form of localized surface plasmons. Semiconductor quantum dots have strong luminescent capabilities widely used in many applications such as biosensing. When a quantum dot is kept in the vicinity of a metal nanoparticle, a dipole-dipole coupling occurs between the two nanoparticles giving rise to various optical signatures in the scattered spectra. This coupling makes the two nanoparticles behave like a single hybrid molecule. Hybrid molecules made of metal nanoparticles (MNPs) and quantum dots (QDs) under the influence of an external driving field have been extensively studied in literature, using the local response approximation (LRA). However, such previous work in this area was not adequate to explain some experimental observations such as the size-dependent resonance shift of metal nanoparticles which becomes quite significant with decreasing diameter. The nonlocal response of metallic nanostructures which is hitherto disregarded by such studies is a main reason for such nonclassical effects. The generalized nonlocal optical response (GNOR) model provides a computationally less-demanding path to incorporate such properties into the theoretical models. It allows unified theoretical explanation of observed experimental phenomena which previously seemed to require ab initio microscopic theory. In this paper, we analyze the hybrid molecule in an external driving field as an open quantum system using a cavity-QED approach. In the process, we quantum mechanically model the dipole moment operator and the dipole response field of the metal nanoparticle taking the nonlocal effects into account. We observe that the spectra resulting from the GNOR based model effectively demonstrate the experimentally observed size dependent amplitude scaling, linewidth broadening, and resonance shift phenomena compared to the respective LRA counterparts. Then, we provide a comparison between our suggested GNOR based cavity-QED model and the conventional LRA model, where it becomes evident that our analytical model provides a close match to the experimentally suggested behavior. Furthermore, we show that the Rayleigh scattering spectra of the MNP-QD hybrid molecule possess an asymmetric Fano interference pattern that is tunable to suit various applications.

A hybridizable discontinuous Galerkin method for solving nonlocal optical response models

We propose Hybridizable Discontinuous Galerkin (HDG) methods for solving the frequency-domain Maxwell’s equations coupled to the Nonlocal Hydrodynamic Drude (NHD) and Generalized Nonlocal Optical Response (GNOR) models, which are employed to describe the optical properties of nano-plasmonic scatterers and waveguides. Brief derivations for both the NHD model and the GNOR model are presented. The formulations of the HDG method for the 2D TM mode are given, in which we introduce two hybrid variables living only on the skeleton of the mesh. The local field solutions are expressed in terms of the hybrid variables in each element. Two conservativity conditions are globally enforced to make the problem solvable and to guarantee the continuity of the tangential component of the electric field and the normal component of the current density. Numerical results show that the proposed HDG methods converge at optimal rate. We benchmark our implementation and demonstrate that the HDG method has the potential to solve complex nanophotonic problems.

An extension of the generalized nonlocal theory for the mode analysis of plasmonic waveguides at telecommunication frequency

We present an extension of the generalized nonlocal (GNL) optical response theory for the mode analysis of several plasmonic waveguides. We show that, compared with the local description, the imaginary part of the effective mode index is enlarged using the GNL response model. We ascribe this enlargement to the ‘effective’ surface modification and the induced charge diffusion. This result is quite different from that of the hydrodynamic model, where the imaginary part becomes smaller compared with that of the local model. Further, we investigate the influence of geometry parameters on propagation properties and find that the nonlocal effects are much more remarkable for smaller gap and sharper tip. Although the introduction of diffusion has a negative impact on the propagation length, it reveals the true physical insight and should be taken care when dealing with nanoplasmonic waveguide for photonic integration applications.

Signatures of chiral anomaly multiply.

Physics Chiral anomaly is one of the most striking phenomena predicted to occur in Dirac and Weyl semimetals. One of its consequences, the decrease in electrical resistance with applied magnetic field, has been observed in several of these materials, but disentangling it from other, less exotic effects is tricky. Working with nanoplates of the Dirac semimetal Cd3As2, Zhang et al. observed two additional signatures of the chiral anomaly in nonlocal transport and optical response. The unusual nonlocal transport was caused partly by the diffusion of valley polarization, which in turn was a consequence of the chiral anomaly. These complementary signatures will make it possible to study the phenomenon more closely. Nat. Commun. 10.1038/ncomms13741 (2017).

Highly nonlocal optical response: Benefit or drawback?

A highly nonlocal optical response in space has been shown to heal several shortcomings of beam self-action in nonlinear optics. At the same time, nonlocality is often connected to limits and constraints in both temporal and spatial domains. We provide a brief and rather subjective review of what we consider the main benefits and some drawbacks of a highly nonlocal response in light localization through nonlinear optics, with several examples related to reorientational soft matter, specifically nematic liquid crystals.

Robustness of the far-field response of nonlocal plasmonic ensembles.

Contrary to classical predictions, the optical response of few-nm plasmonic particles depends on particle size due to effects such as nonlocality and electron spill-out. Ensembles of such nanoparticles are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size distribution. For a normal distribution of free-electron nanoparticles, and within the simple nonlocal hydrodynamic Drude model, both the nonlocal blueshift and the plasmon linewidth are shown to be considerably affected by ensemble averaging. Size-variance effects tend however to conceal nonlocality to a lesser extent when the homogeneous size-dependent broadening of individual nanoparticles is taken into account, either through a local size-dependent damping model or through the Generalized Nonlocal Optical Response theory. The role of ensemble averaging is further explored in realistic distributions of isolated or weakly-interacting noble-metal nanoparticles, as encountered in experiments, while an analytical expression to evaluate the importance of inhomogeneous broadening through measurable quantities is developed. Our findings are independent of the specific nonclassical theory used, thus providing important insight into a large range of experiments on nanoscale and quantum plasmonics.

Nonlocal optical effects on the Goos–Hänchen shifts at multilayered hyperbolic metamaterials

The lateral beam shift of light incident on a multilayered hyperbolic metamaterial (HMM) is investigated using a theoretical model which emphasizes the nonlocal optical response of the indefinite material. By applying an effective local response theory formulated recently in the literature, it is found that nonlocal effects only affect p polarized light in this Goos–Hänchen (GH) shift of the incident beam; leading to a blue-shifted peak for positive shifts at high frequencies and red-shifted dip for negative shifts at low frequencies in the GH shift spectrum. An account for the observed phenomenon is given by referring to the ‘Brewster condition’ for the reflected wave from the HMM. This observation thus provides a relatively direct probe for the nonlocal response of the HMM.

Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects.

Molecular spontaneous emission and fluorescence depend strongly on the emitter local environment. Plasmonic nanoparticles provide excellent templates for tailoring fluorophore emission, as they exhibit potential for both fluorescence enhancement and quenching, depending on emitter positioning in the nanoparticle vicinity. Here we explore the influence of hitherto disregarded nonclassical effects on the description of emitter-plasmon hybrids, focusing on the roles of the metal nonlocal response and especially size-dependent plasmon damping. Through extensive modelling of metallic nanospheres and nanoshells coupled to dipole emitters, we show that within a purely classical description a remarkable fluorescence enhancement can be achieved. However, once departing from the local-response approximation, and particularly by implementing the recent generalised nonlocal optical response theory, which provides a more complete physical description combining electron convection and diffusion, we show that not only are fluorescence rates dramatically reduced compared to the predictions of the local description and the common hydrodynamic Drude model, but the optimum emitter-nanoparticle distance is also strongly affected. In this respect, experimental measurements of fluorescence, the theoretical description of which requires a precise concurrent evaluation of far- and near-field properties of the system, constitute a novel, more sensitive probe for assessing the validity of state-of-the-art nonclassical theories.

Classification of scalar and dyadic nonlocal optical response models

Nonlocal optical response is one of the emerging effects on the nanoscale for particles made of metals or doped semiconductors. Here we classify and compare both scalar and tensorial nonlocal response models. In the latter case the nonlocality can stem from either the longitudinal response, the transverse response, or both. In phenomenological scalar models the nonlocal response is described as a smearing out of the commonly assumed infinitely localized response, as characterized by a distribution with a finite width. Here we calculate explicitly whether and how tensorial models, such as the hydrodynamic Drude model and generalized nonlocal optical response theory, follow this phenomenological description. We find considerable differences, for example that nonlocal response functions, in contrast to simple distributions, assume negative and complex values. Moreover, nonlocal response regularizes some but not all diverging optical near fields. We identify the scalar model that comes closest to the hydrodynamic model. Interestingly, for the hydrodynamic Drude model we find that actually only one third (1/3) of the free-electron response is smeared out nonlocally. In that sense, nonlocal response is stronger for transverse and scalar nonlocal response models, where the smeared-out fractions are 2/3 and 3/3, respectively. The latter two models seem to predict novel plasmonic resonances also below the plasma frequency, in contrast to the hydrodynamic model that predicts standing pressure waves only above the plasma frequency.

Nonlocal nonlinear optical response of graphene oxide-Au nanoparticles dispersed in different solvents

In this paper, we report on the preparation of graphene oxide and graphene oxide-Au nanodispersions in various solvents, such as water, DMF (N,N-dimethylformamide) and NMP (N-methyl-2-pyrrolidone). Optical, structural and nonlinear optical properties of all the samples have been studied. The nonlinear optical properties have been measured using the z-scan technique. It is shown that the incorporation of Au nanoparticles can greatly improve the nonlinear optical properties of graphene oxide. More importantly, the fact is recognized that the media that surround the nonlinear sample can influence its nonlinear optical properties by their nonlocal action. The nonlocal z-scan theory has been used to estimate the role of the surrounding medium in changing the samples’ nonlinear responses.

Multipole plasmons and their disappearance in few-nanometre silver nanoparticles.

Electron energy-loss spectroscopy can be used for detailed spatial and spectral characterization of optical excitations in metal nanoparticles. In previous electron energy-loss experiments on silver nanoparticles with radii smaller than 20 nm, only the dipolar surface plasmon resonance was assumed to play a role. Here, applying electron energy-loss spectroscopy to individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an additional surface plasmon resonance corresponding to higher angular momenta for nanoparticle radii as small as 4 nm. We study the radius and electron beam impact position dependence of both resonances separately. For particles smaller than 4 nm in radius the higher-order surface plasmon mode disappears, in agreement with generalized non-local optical response theory, while the dipole resonance blueshift exceeds our theoretical predictions. Unlike in optical spectra, multipole surface plasmons are important in electron energy-loss spectra even of ultrasmall metallic nanoparticles.

Nonlocal effects on intersubband optical absorption in square quantum wells

Based on the microscopic nonlocal optical response theory, the influence from the width and depth of the potential well on the nonlocal effects and optical absorption spectra of the square quantum well is investigated in detail. The numerical results show that the radiative shift of the spectrum line, which stems from the nonlocality of optical responses, is dependent closely on the width and depth of the potential well. It is also demonstrated that the width and depth of the quantum well have important influence on the optical absorbance from the intersubband transitions. The theoretical work may be important for the growth of the nonlocal nano-materials and the potential application in optoelectronics.