A generalized non-local optical response theory for plasmonic nanostructures.

Metal nanoparticles (MNPs) possess optical concentration capabilities that can amplify and localize electromagnetic fields into nanometer length scales. The near-fields of MNPs can be used to tailor optical response of luminescent semiconductor quantum dots (QDs), resulting in fascinating optical phenomena. Plasmonic metaresonances (PMRs) form a class of such optical events gaining increasing popularity due to their promising prospects in sensing and switching applications. Unlike the basic excitonic and plasmonic resonances in MNP-QD nanohybrids, PMRs occur in the space/time domain. A nanohybrid experiences PMR when system parameters such as QD dipole moment, MNP-QD centre separation or submerging medium permittivity reach critical values, resulting in the plasmonically induced time delay of the effective Rabi frequency experienced by the QD asymptotically tending to infinity. Theoretical analyses of PMRs available in the literature utilize the local response approximation (LRA) which does not account for the nonlocal effects of the MNP, and neglect the MNP dependence of the QD decay and dephasing rates which hinder their applicability to QDs in the close vicinity of small MNPs. Here, we address these limitations using an approach based on the generalized nonlocal optical response (GNOR) theory which has proven to yield successful theoretical explanations of experimentally observed plasmonic phenomena. Our results indicate that, omission of the MNP nonlocal response and the associated decay/dephasing rate modifications of the QD tend to raise implications such as significant over-estimation of the QD dipole moment required to achieve PMR, under-estimation of the critical centre separation and prediction of significantly lower near-PMR QD absorption rates, in comparison to the improved GNOR based predictions. In light of our observations, we finally suggest two prospective applications of PMR based nanoswitches, namely, aptamer based in vitro cancer screening and thermoresponsive polymer based temperature sensing. To demonstrate the latter application, we develop and utilize a proof of concept (two dimensional) skin tumor model homogeneously populated by MNP-QD nanohybrids. Our simulations reveal a novel near-PMR physical phenomenon observable under perpendicular illumination, which we like to call the margin pattern reversal, where the spatial absorption pattern reverses when the near-PMR QDs switch from the bright to dark state.

We develop an analytical framework to study the influence of a weakly intercoupled inplane spherical metal nanoparticle (MNP) assembly on a coherently illuminated quantum emitter (QE). We reduce the analytical expressions derived for the aforementioned generic planar setup into simple and concise expressions representing a QE mediated by a symmetric MNP constellation, by exploiting the symmetry. We use the recently introduced generalized nonlocal optical response (GNOR) theory that has successfully explained plasmonic experiments to model the MNPs in our system. Due to the use of GNOR theory, and our analytical approach, the procedure we suggest is extremely computationally efficient. Using the derived model, we analyse the absorption rate, resultant Rabi frequency, effective excitonic energy shift and dephasing rate shift spectra of an exciton bearing QE at the centre of a symmetric MNP setup. We observe that the QE experiences plasmon induced absorption rate spectral linewidth variations that increase in magnitude with decreasing MNP-QE centre separation and increasing number of MNPs. Our results also suggest that, parameter regions where the QE exhibits trends of decreasing linewidth against decreasing MNP-QE centre separation are likely to be associated with plasmon induced excitonic energy redshifts. Similarly, regions where the QE absorption rate linewidth tends to increase against decreasing MNP QE centre separation are likely to be accompanied by plasmon induced excitonic energy blueshifts. In both these cases, the magnitude of the observed red/blueshift was seen to increase with the number of MNPs in the constellation, due to enhancement of the plasmonic influence.

Transition matrix of a nonspherical particle in the non-local optical response theory

Transition matrix of a nonspherical layered particle in the non-local optical response theory

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.

Hybrid nanostructures composed of a semiconductor quantum dot (SQD) and a metal nanoparticle (MNP) are appealing candidates for the investigation of exotic optoelectronic properties and their potential applications due to the coupling between exciton in SQD and surface plasmon in MNP. In most studies on the SQD-MNP hybrid nanostructures, the conventional local response approximation (LRA) is deployed to model the MNP, but the classical LRA fails to interpret experimental results such as the size-dependent frequency shifts and damping of surface plasmon in quantum-sized MNP for decreasing the MNP size. The generalized nonlocal optical response (GNOR) model is a generalization and an extension of the hydrodynamic Drude model, and it can explain surprisingly well the aforementioned experimental results of noble MNP. In this paper, we provide a comparison of the linear and nonlinear optical absorption coefficients (OACs) of the hybridized SQD based on the GNOR model and the LRA model, where silver MNP is adopted. In contrast to the LRA model, the GNOR model not only suggests an enhancement in the peak values of the linear and nonlinear OACs of the hybridized SQD but also causes a blue shift and a smaller spectral linewidth in the linear and nonlinear OACs of the hybridized SQD, the feature for which is more pronounced for small SQD-MNP surface distance. Our work also demonstrates the convergence of the GNOR model to the LRA model for the linear and nonlinear OACs of the hybridized SQD by increasing the SQD-MNP surface distance or increasing the MNP radius. Moreover, the linear and nonlinear OACs of the hybridized SQD as a function of the distance are discussed based on the two models, thereby allowing us to find stronger linear and nonlinear OACs. In addition, the impact of the incident optical intensity on the total OACs of the hybridized SQD under strong and weak exciton-plasmon couplings is discussed based on the two models. Our findings pave the way for optimized designs of linear and nonlinear nanophotonic devices with small footprints by utilizing such hybrid nanostructure made of SQD and quantum-sized noble MNP.

As the dimensions of plasmonic structures or the field confinement length approach the mean free path of electrons, mesoscopic optical response effects, including nonlocality, electron spill‐in or spill‐out, and Landau damping, are expected to become observable. In this work, a quantum‐informed local analogue model (QILAM) that maps these nonclassical optical responses onto a local dielectric film is presented. The primary advantage of this model lies in its compatibility with the highly efficient boundary element method (BEM), which includes retardation effects with relatively large particle sizes. Furthermore, the approach offers a unified framework that connects two important semiclassical theories: the generalized nonlocal optical response (GNOR) theory and the Feibelman d‐parameters formalism. It is envisioned that QILAM can evolve into a multiscale electrodynamic tool for exploring nonclassical optical responses in diverse plasmonic structures in the future. This can be achieved by directly translating mesoscopic effects into observable phenomena, such as plasmon resonance energy shifts and linewidth broadening in the scattering spectrum.

We analytically characterize the influence of a neighboring metal nanoparticle (MNP) on the behavioral trends of a quantum dot (QD) using a generalized nonlocal optical response (GNOR) method based approach, taking the MNP distance dependent modifications to the QD population relaxation and dephasing rates into account. The GNOR model is a recent generalization and an extension of the hydrodynamic Drude model (HDM), which goes beyond HDM by taking into account both the convection current and electron diffusion in the MNPs. It allows unified theoretical explanation of some experimentally observed plasmonic phenomena which otherwise would require ab initio analysis as the conventional local response approximation (LRA) fails to account for them. For example, it has been demonstrated in literature that the GNOR model captures size dependent resonance shifts of small MNPs which are unrevealed by the conventional LRA based methods, and it has proven to yield results displaying better agreement with the experimental observations for plasmonic experiments. Attempts to incorporate MNP nonlocal effects in the analytical characterization of vicinal excitons found in literature utilize the phenomenological hydrodynamic model and assume the absence of MNP interband effects. Moreover, they are only applicable to narrow parameter regions. In this paper we present a complete analytical characterization which overcomes these drawbacks and lends to the perusal of the system over wide continua of various parameters, enabling us to get an elevated view at a much lesser level of complexity compared to the conventional LRA based numerical methods or the conventional ab initio methods of accounting for the nonlocal effects. Our proposed GNOR based model predicts strong modifications to various QD properties such as population difference, absorption, MNP induced shifts to excitonic energy and Förster enhanced broadening, coherent plasmonic field enhanceme

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.

This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.

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.

In this paper, we combine the Mie theory and a novel nonlocal dispersion model named Generalized Non-local Optical Response (GNOR) to study the electromagnetic scattering of metallic nanostructure. We first introduce the GNOR model briefly. Then the Mie theory based on GNOR model is introduced to analyze the scattering of infinitely metallic nanowires. Finally, numerical examples are presented to show the effect of the metallic nanowires based on GNOR model by Mie theory.

After a brief overview of nanoplasmonics experiments that defy explanation with classical electrodynamics, we introduce nonlocal response as a main reason for non-classical effects. This concept is first introduced phenomenologically, and afterwards based on the semi-classical hydrodynamic Drude model (HDM) that indeed exhibits nonlocal response. In particular, we discuss recent generalizations and extensions of the HDM, to include both convection and diffusion dynamics of the induced charges. This generalized nonlocal optical response (GNOR) model allows for the first time unified semi-classical explanations of known experimental phenomena for both monomers and dimers that previously seemed to require microscopic theory. Finally, we turn to Landau damping and discuss the microscopic origin of the size-dependent damping captured by the classical diffusion mechanism in the GNOR model.

Within our recently proposed generalized nonlocal optical response (GNOR) model, where nonlocal response is included by taking into account both convective and diffusive currents of the conduction electrons, we revisit the fundamental problem of an optically excited plasmonic dimer. We consider the transition from separated dimers via touching dimers to finally overlapping dimers. In particular, we focus on the touching case, showing a fundamental limit on the hybridization of the bonding plasmon modes due to nonlocality. Using transformation optics, we determine a simple analytical equation for the resonance energies.

Based on the discrete source method, a rigorous approach has been developed and implemented that allows one to analyze light scattering by models of resonators of plasmonic nanolaser (SPASER). This approach takes into account all features of the boundary value problem for the Maxwell system, including the interaction of the resonators with the prism surface and the nonlocal screening effect, which is treated in the framework of the generalized nonlocal optical response (GNOR) model. It is shown that a resonator model with a dielectric core and a plasmonic shell has significant advantages over a layered model with a plasmonic core. The conditions are established under which the field can be enhanced by several orders of magnitude. It is shown that taking into account the GNOR leads to a decrease in the field intensity by 50%.