Comparison of Hydrodynamic Models for the Electromagnetic Nonlocal Response of Nanoparticles

Madelung Formalism for Electron Spill-Out in Nonlocal Nanoplasmonics

Current multiscale plasmonic systems pose a modeling challenge. Classical macroscopic theories fail to capture quantum effects in such systems, whereas quantum electrodynamics is impractical given the total size of the experimentally relevant systems, as the number of interactions is too large to be addressed one by one. To tackle the challenge, in this paper we propose to use the Madelung form of the hydrodynamic Drude model, in which the quantum effect electron spill-out is incorporated by describing the metal-dielectric interface using a super-Gaussian function. The results for a two-dimensional nanoplasmonic wedge are correlated to those from nonlocal full-wave numerical calculations based on a linearized hydrodynamic Drude model commonly employed in the literature, showing good qualitative agreement. Additionally, a conformal transformation perspective is provided to explain qualitatively the findings. The methodology described here may be applied to understand, both numerically and theoretically, the modular inclusions of additional quantum effects, such as electron spill-out and nonlocality, that cannot be incorporated seamlessly by using other approaches.

Orbital-Free Methods for Plasmonics: Linear Response

Plasmonic systems, such as metal nanoparticles, are widely used in different application areas, going from biology to photovoltaics.The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties.When the characteristic sizes/distances reach a few nanometers, non-local and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density-Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications.On the other hand, methods based on the Orbital-Free (OF) formulation of TD-DFT, can scale linearly with the system size.In this Review, OF methods ranging from semiclassical models to the quantum hydrodynamic theory, will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will be then validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy andwithout system-tuned parameters. The accuracy on these methods depends only on the accuracy on the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will be indicated.

Quantum surface effects in the electromagnetic coupling between a quantum emitter and a plasmonic nanoantenna: time-dependent density functional theory vs. semiclassical Feibelman approach

We use time-dependent density functional theory (TDDFT) within the jellium model to study the impact of quantum-mechanical effects on the self-interaction Green's function that governs the electromagnetic interaction between quantum emitters and plasmonic metallic nanoantennas. A semiclassical model based on the Feibelman parameters, which incorporates quantum surface-response corrections into an otherwise classical description, confirms surface-enabled Landau damping and the spill out of the induced charges as the dominant quantum mechanisms strongly affecting the nanoantenna-emitter interaction. These quantum effects produce a redshift and broadening of plasmonic resonances not present in classical theories that consider a local dielectric response of the metals. We show that the Feibelman approach correctly reproduces the nonlocal surface response obtained by full quantum TDDFT calculations for most nanoantenna-emitter configurations. However, when the emitter is located in very close proximity to the nanoantenna surface, we show that the standard Feibelman approach fails, requiring an implementation that explicitly accounts for the nonlocality of the surface response in the direction parallel to the surface. Our study thus provides a fundamental description of the electromagnetic coupling between plasmonic nanoantennas and quantum emitters at the nanoscale.

Nonlocal response of plasmonic core-shell nanotopologies excited by dipole emitters

In light of the emergence of nonclassical effects, a paradigm shift in the conventional macroscopic treatment is required to accurately describe the interaction between light and plasmonic structures with deep-nanometer features. Towards this end, several nonlocal response models, supplemented by additional boundary conditions, have been introduced, investigating the collective motion of the free electron gas in metals. The study of the dipole-excited core-shell nanoparticle has been performed, by employing the following models: the hard-wall hydrodynamic model; the quantum hydrodynamic model; and the generalized nonlocal optical response. The analysis is conducted by investigating the near and far field characteristics of the emitter-nanoparticle system, while considering the emitter outside and inside the studied topology. It is shown that the above models predict striking spectral features, strongly deviating from the results obtained via the classical approach, for both simple and noble constitutive metals.

Bright Optical Eigenmode of 1 nm^{3} Mode Volume

We report on the discovery and rationale to devise bright single optical eigenmodes that feature quantum-optical mode volumes of about 1  nm^{3}. Our findings rely on the development and application of a quasinormal mode theory that self-consistently treats fields and electron nonlocality, spill-out, and Landau damping around atomistic protrusions on a metallic nanoantenna. By outpacing Landau damping with radiation via properly designed antenna modes, the extremely localized modes become bright with radiation efficiencies reaching 30% and could provide up to 4×10^{7} times intensity enhancement.