Surface Response Function Research Articles

Nonlocal effects in plasmon-emitter interactions

Abstract Nonlocal and quantum mechanical phenomena in noble metal nanostructures become increasingly crucial when the relevant length scales in hybrid nanostructures reach the few-nanometer regime. In practice, such mesoscopic effects at metal–dielectric interfaces can be described using exemplary surface-response functions (SRFs) embodied by the Feibelman d-parameters. Here we show that SRFs dramatically influence quantum electrodynamic phenomena – such as the Purcell enhancement and Lamb shift – for quantum light emitters close to a diverse range of noble metal nanostructures interfacing different homogeneous media. Dielectric environments with higher permittivities are shown to increase the magnitude of SRFs calculated within the specular-reflection model. In parallel, the role of SRFs is enhanced in noble metal nanostructures characterized by large surface-to-volume ratios, such as thin planar metallic films or shells of core–shell nanoparticles, for which the spill-in of electron wave functions enhances plasmon hybridization. By investigating emitter quantum dynamics close to such plasmonic architectures, we show that decreasing the width of the metal region, or increasing the permittivity of the interfacing dielectric, leads to a significant change in the Purcell enhancement, Lamb shift, and visible far-field spontaneous emission spectrum, as an immediate consequence of SRFs. We anticipate that fitting the theoretically modelled spectra to experiments could allow for experimental determination of the d-parameters.

Static Robust Design Optimization Using the Stochastic Frontier Method: A Case Study of Pulsed EPD Process on TiO2 Films

This paper aims to optimize a pulsed electrophoretic deposition (EPD) process for TiO2 films. This is accomplished by determining the optimal configuration of the coating parameters from a robust optimization perspective. The experimental study uses a composite central design (CCD) with four control factors, i.e., the initial concentration (x1 in g/L), the deposition time (x2 in s), the duty cycle (x3 in %), and the voltage (x4 in V). The process responses that should all be maximized are the photocatalytic efficiency of the thin film (De) and three critical charges, which characterize the adhesion failure, i.e., LC1: the load at which the first cracks occurred; LC2: the load at which the film starts to delaminate at the edge level of the scratch track; and LC3: the load when the damage of the film exceeds 50%. This paper compares the robust optimization design of the EPD process using two methods: the robust design of processes and products using the stochastic frontier (RDPP-SF) and the surface response and desirability function methods. The findings show that the RDPP-SF method is superior to the response surface–desirability method for the process responses De and LC2 because of non-natural sources of variation; however, both methods perform comparably well while analyzing the LC1 and LC3 responses, which are subjected to pure random variability. The parameters setting for the process robust optimization are met in run 25 (x1 = 14 g/L, x2 = 150 s, x3 = 50%, and x4 40 V).

Collective modes and quantum effects in two-dimensional nanofluidic channels.

Nanoscale fluid transport is typically pictured in terms of atomic-scale dynamics, as is natural in the real-space framework of molecular simulations. An alternative Fourier-space picture, that involves the collective charge fluctuation modes of both the liquid and the confining wall, has recently been successful at predicting new nanofluidic phenomena such as quantum friction and near-field heat transfer, that rely on the coupling of those fluctuations. Here, we study the charge fluctuation modes of a two-dimensional (planar) nanofluidic channel. Introducing confined response functions that generalize the notion of surface response function, we show that the channel walls exhibit coupled plasmon modes as soon as the confinement is comparable to the plasmon wavelength. Conversely, the water fluctuations remain remarkably bulk-like, with significant confinement effects arising only when the wall spacing is reduced to 7 Å. We apply the confined response formalism to predict the dependence of the solid-water quantum friction and thermal boundary conductance on channel width for model channel wall materials. Our results provide a general framework for Coulomb interactions of fluctuating matter under nanoscale confinement.

ARAMIS: a Martian radiative environment model built from GEANT4 simulations

A new model of the Martian surface radiative environment has been built: Atmospheric RAdiation Model for Ionizing spectra on martian Surface (ARAMIS). Based on Monte Carlo calculations, it offers high computational flexibility for surface flux spectra with several GEANT4 physics lists tested for different exposures and mission scenarios. ARAMIS performs Monte Carlo simulations independently of any exposure scenario to determine a surface response function that can then be convolved to any input spectrum, avoiding simulation repetition while maintaining results accuracy, using a parametric atmosphere geometry. In particular, the adopted approach enables secondary spectra to be discriminated by type and origin, in order to observe the impact of different primary flux components on the surface dose calculation. The ARAMIS model has been validated with experimental measurements from the RAD (Radiation Assessment Detector) instrument on board the Mars Science Laboratory (MSL) Curiosity rover, and benchmarked against other models in the literature. Built using version 11.1.0 of the GEometry ANd Tracking (GEANT4) toolbox and established models of Galactic Cosmic Ray (GCR) or Solar Particle Event (SEP) spectra, the surface neutron and photon spectra provided by ARAMIS show a better agreement than other models with high-energy experimental data, reducing model uncertainty for radiation protection calculations.

Robust surface light scattering spectroscopy for fluid interfaces

Surface Light Scattering Spectroscopy (SLSS) can characterize the dynamics of an interface between two immiscible fluids by measuring the frequency spectrum of coherent light scattered from thermophysical fluctuations—‘ripplons’. In principle, and for many interfaces, SLSS can simultaneously measure surface tension and viscosity, with the potential for higher-order properties, such as surface elasticity and bending moments. Previously, this has been challenging. We describe and present some measurements from an instrument with improvements in optical design, specimen access, vibrational stability, signal-to-noise ratio, electronics, and data processing. Quantitative improvements include total internal reflection at the interface to enhance the typically available signal by a factor of order 40 and optical improvements that minimize adverse effects of sloshing induced by external vibrations. Information retrieval is based on a comprehensive surface response function, an instrument function, which compensates for real geometrical and optical limitations, and processing of almost real-time data to report results and their likely accuracy. Detailed models may be fit to the power spectrum in real time. The raw one-dimensional digitized data stream is archived to allow post-experiment processing. This paper reports a system design and implementation that offers substantial improvements in accuracy, simplicity, ease of use, and cost. The presented data are for systems in regions of low viscosity where the ripplons are underdamped, but the hardware described is more widely applicable.

Study of Field Enhancement in the Subnanometer Gap of Plasmonic Dimers Accounting for the Surface Quantum Effect

We investigate the influence of the surface quantum effect on the optical characteristics of a plasmonic dimer consisting of two identical gold nanoparticles with a tiny gap. To account for the corresponding surface quantum effect, an electromagnetic theory based on mesoscopic boundary conditions and surface response functions is used. It is shown that the quantum surface effect leads to a blue shift and damping of the corresponding plasmon resonance. This effect becomes more substantial when the constituent particles are elongated, and the gap size shrinks to subnanometer values. In this case, the difference in the results obtained using the surface response functions and the local response approximation can be up to four times and is accompanied by a spectral blue shift of 10 nm.

Plasmon Damping Rates in Coulomb-Coupled 2D Layers in a Heterostructure.

The Coulomb excitations of charge density oscillation are calculated for a double-layer heterostructure. Specifically, we consider two-dimensional (2D) layers of silicene and graphene on a substrate. From the obtained surface response function, we calculated the plasmon dispersion relations, which demonstrate how the Coulomb interaction renormalizes the plasmon frequencies. Most importantly, we have conducted a thorough investigation of how the decay rates of the plasmons in these heterostructures are affected by the Coulomb coupling between different types of two-dimensional materials whose separations could be varied. A novel effect of nullification of the silicene band gap is noticed when graphene is introduced into the system. To utilize these effects for experimental and industrial purposes, graphical results for the different parameters are presented.

Scattering solution to the problem of additional boundary conditions

Maxwell's boundary conditions (MBCs) were long known insufficient to determine the optical responses of spatially dispersive medium. Supplementing MBCs with additional boundary conditions (ABCs) has become a normal yet controversial practice. Here the problem of ABCs is solved by analyzing some subtle aspects of a physical surface. A generic theory is presented for handling the interaction of light with the surfaces of an arbitrary medium and applied to study the traditional problem of exciton polaritons. We show that ABCs can always be adjusted to fit the theory but they can by no means be construed as intrinsic surface characteristics, which are instead captured by a \textit{surface response function} (SRF). Unlike any ABCs, a SRF describes essentially non-local boundary effects. Methods for experimentally extracting the spatial profile of this function are proposed.

Interaction confinement and electronic screening in two-dimensional nanofluidic channels.

The transport of fluids at the nanoscale is fundamental to manifold biological and industrial processes, ranging from neurotransmission to ultrafiltration. Yet, it is only recently that well-controlled channels with cross sections as small as a few molecular diameters became an experimental reality. When aqueous electrolytes are confined within such channels, the Coulomb interactions between the dissolved ions are reinforced due to dielectric contrast at the channel walls: We dub this effect "interaction confinement." Yet, no systematic way of computing these confined interactions has been proposed beyond the limiting cases of perfectly metallic or perfectly insulating channel walls. Here, we introduce a new formalism, based on the so-called surface response functions, that expresses the effective Coulomb interactions within a two-dimensional channel in terms of the wall's electronic structure, described to any desired level of precision. We use it to demonstrate that in few-nanometer-wide channels, the ionic interactions can be tuned by the wall material's screening length. We illustrate this approach by implementing these interactions in Brownian dynamics simulations of a strongly confined electrolyte and show that the resulting ionic conduction can be adjusted between Ohm's law and a Wien effect behavior. Our results provide a quantitative approach to tuning nanoscale ion transport through the electronic properties of the channel wall material.

Analytical solution of unsteady heat conduction in multilayer internal combustion engine walls

An analytical solution of the unsteady heat conduction problem in multilayer walls was developed and applied to study thermal barrier coatings for reciprocating internal combustion engines. The mathematical solution was derived using the matrix method and complex analysis/residue-calculus Laplace transform inversion techniques. The one-dimensional domain includes a time-varying heat flux on the combustion chamber surface, and a time-varying temperature on the backside coolant surface. These boundary conditions are simulated as the superposition of two adjacent triangular, unit-magnitude pulses, which gives a piece-wise linear representation of the applied flux or temperature history. The temperature at any location of interest is found as the convolution of the transfer function, which results from the inversion, with the discrete-time heat flux or backside temperature history. The transfer functions describe the exact response and only depend on multilayer architecture, therefore, they can be computed a priori. The triangular pulse method provides a more than two order of magnitude reduction in computation time compared to a finite difference solution at the same level of accuracy. A 104-fold speed increase relative to a finite difference solution was realized when using the Overlap-add convolution technique for a full drive cycle simulation, i.e., a long time record. The surface response or transfer function acts like a finite impulse response and can be viewed in the frequency domain to reveal complementary information about coating performance.

Quantum surface-response of metals revealed by acoustic graphene plasmons

A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light–matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultraconfined acoustic graphene plasmons in graphene–dielectric–metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman d-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the acoustic graphene plasmons dispersion, and demonstrate that the high field confinement of acoustic graphene plasmons can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of acoustic graphene plasmons as plasmon rulers with ångström-scale accuracy.

Optical response of noble metal nanostructures: quantum surface effects in crystallographic facets

Noble metal nanostructures are ubiquitous elements in nano-optics, supporting plasmon modes that can focus light down to length scales commensurate with nonlocal effects arising from quantum confinement and spatial dispersion in the underlying electron gas. Quantum and nonlocal effects can be more prominent in crystalline noble metals, due to their lower intrinsic loss (when compared with their polycrystalline counterparts), and because particular crystal facets give rise to distinct electronic surface states whose signatures can be imprinted in the optical response of a structure. Here, we employ an atomistic method to describe nonclassical effects impacting the optical response of crystalline noble metal surfaces and demonstrate that these effects can be well captured using a set of surface-response functions known as Feibelman d -parameters determined from such quantum-mechanical models. In particular, we characterize the d -parameters associated with the (111) and (100) crystal facets of gold, silver, and copper, emphasizing the importance of quantum surface effects associated with electron wave function spill-out/spill-in and with the surface-projected band gap emerging from the atomic-layer corrugation. Furthermore, we show that the extracted d -parameters can be straightforwardly applied to describe the optical response of various nanoscale metal morphologies of interest, including metallic ultrathin films, graphene–metal heterostructures hosting ultraconfined acoustic graphene plasmons, and crystallographic faceted metallic nanoparticles supporting localized surface plasmons. We envision that the d -parameters presented here, along with the prescription to extract and apply them, could help circumvent computationally expensive first-principles atomistic calculations to describe quantum nonlocal effects in the optical response of mesoscopic crystalline metal surfaces, which are becoming widely available with increasing control over morphology down to atomic length scales for state-of-the-art experiments in nano-optics.

Surface-response functions obtained from equilibrium electron-density profiles

Abstract Surface-response functions are one of the most promising routes for bridging the gap between fully quantum-mechanical calculations and phenomenological models in quantum nanoplasmonics. Among all currently available recipes for obtaining such response functions, the use of ab initio methods remains one of the most conspicuous trends, wherein the surface-response functions are retrieved via the metal’s non-equilibrium response to an external time-dependent perturbation. Here, we present a complementary approach to approximate one of the most appealing surface-response functions, namely the Feibelman d-parameters, yield a finite contribution even when they are calculated solely with the equilibrium properties of the metal, described under the local-response approximation (LRA) but with a spatially varying equilibrium electron density, as input. Using model calculations that mimic both spill-in and spill-out of the equilibrium electron density, we show that the obtained d-parameters are in qualitative agreement with more elaborate, but also more computationally demanding, ab initio methods. The analytical work presented here illustrates how microscopic surface-response functions can emerge out of entirely local electrodynamic considerations.

Evidence for a spin acoustic surface plasmon from inelastic atom scattering

Closed-shell atoms scattered from a metal surface exchange energy and momentum with surface phonons mostly via the interposed surface valence electrons, i.e., via the creation of virtual electron-hole pairs. The latter can then decay into surface phonons via electron-phonon interaction, as well as into acoustic surface plasmons (ASPs). While the first channel is the basis of the current inelastic atom scattering (IAS) surface-phonon spectroscopy, no attempt to observe ASPs with IAS has been made so far. In this study we provide evidence of ASP in Ni(111) with both Ne atom scattering and He atom scattering. While the former measurements confirm and extend so far unexplained data, the latter illustrate the coupling of ASP with phonons inside the surface-projected phonon continuum, leading to a substantial reduction of the ASP velocity and possibly to avoided crossing with the optical surface phonon branches. The analysis is substantiated by a self-consistent calculation of the surface response function to atom collisions and of the first-principle surface-phonon dynamics of Ni(111). It is shown that in Ni(111) ASP originate from the majority-spin Shockley surface state and are therefore collective oscillation of surface electrons with the same spin, i.e. it represents a new kind of collective quasiparticle: a Spin Acoustic Surface Plasmon (SASP).

Role of diffusive surface scattering in nonlocal plasmonics

The recent generalised nonlocal optical response (GNOR) theory for plasmonics is analysed, and its main input parameter, namely the complex hydrodynamic convection–diffusion constant, is quantified in terms of enhanced Landau damping due to diffusive surface scattering of electrons at the surface of the metal. GNOR has been successful in describing plasmon damping effects, in addition to the frequency shifts originating from induced-charge screening, through a phenomenological electron diffusion term implemented into the traditional hydrodynamic Drude model of nonlocal plasmonics. Nevertheless, its microscopic derivation and justification is still missing. Here we discuss how the inclusion of a diffusion-like term in standard hydrodynamics can serve as an efficient vehicle to describe Landau damping without resorting to computationally demanding quantum-mechanical calculations, and establish a direct link between this term and the Feibelman d parameter for the centroid of charge. Our approach provides a recipe to connect the phenomenological fundamental GNOR parameter to a frequency-dependent microscopic surface-response function. We therefore tackle one of the principal limitations of the model, and further elucidate its range of validity and limitations, thus facilitating its proper application in the framework of nonclassical plasmonics.

A general theoretical and experimental framework for nanoscale electromagnetism.

The macroscopic electromagnetic boundary conditions, which have been established for over a century1, are essential for the understanding of photonics at macroscopic length scales. Even state-of-the-art nanoplasmonic studies2-4, exemplars of extremely interface-localized fields, rely on their validity. This classical description, however, neglects the intrinsic electronic length scales (of the order of ångström) associated with interfaces, leading to considerable discrepancies between classical predictions and experimental observations in systems with deeply nanoscale feature sizes, which are typically evident below about 10 to 20 nanometres5-10. The onset of these discrepancies has a mesoscopic character: it lies between the granular microscopic (electronic-scale) and continuous macroscopic (wavelength-scale) domains. Existing top-down phenomenological approaches deal only with individual aspects of these omissions, such as nonlocality11-13 and local-response spill-out14,15. Alternatively, bottom-up first-principles approaches-for example, time-dependent density functional theory16,17-are severely constrained by computational demands and thus become impractical for multiscale problems. Consequently, a general and unified framework for nanoscale electromagnetism remains absent. Here we introduce and experimentally demonstrate such a framework-amenable to both analytics and numerics, and applicable to multiscale problems-that reintroduces the electronic length scale via surface-response functions known as Feibelman d parameters18,19. We establish an experimental procedure to measure these complex dispersive surface-response functions, using quasi-normal-mode perturbation theory and observations of pronounced nonclassical effects. We observe nonclassical spectral shifts in excess of 30 per cent and the breakdown of Kreibig-like broadening in a quintessential multiscale architecture: film-coupled nanoresonators, with feature sizes comparable to both the wavelength and the electronic length scale. Our results provide a general framework for modelling and understanding nanoscale (that is, all relevant length scales above about 1 nanometre) electromagnetic phenomena.

Probabilistic assessment of rock slopes stability using the response surface approach – A case study

This paper examines the stability condition of a jointed rock slope in the south western region of Saudi Arabia using deterministic and probabilistic approaches, under both dry and wet conditions. The study area is characterized by complex geology in rugged terrains. The stability analysis is carried out using the code FLAC3D to generate a 3-dimensional, ubiquitous joint model, to determine the influence of the dominant, unfavourable discontinuity orientation with respect to the slope face. The deterministic analysis is first implemented using the mean values of the selected random variables, namely the dip, dip direction and friction angle of the dominant discontinuity set, and the stability condition is assessed with a factor of safety based on the classical frictional joint constitutive model. A Box-Behnken design (BBD) approach is then adopted to create the surface response function as a second order polynomial for the factor of safety. To do so, fifteen FLAC3D models are generated in accordance with the BBD. Based on this, 10,000 simulations of different slope realizations are carried out using Monte-Carlo simulation technique, and the probability of unsatisfactory of performance of the rock slope is assessed. It is shown that the probabilistic approach provides more insight and confidence in the stability condition of the rock slope, both under dry and steady state heavy rainfall conditions. A discussion is presented on the significance of accepting lower safety factors when heavy rainfall conditions are encountered.

Effect of strain on plasmons, screening, and energy loss in graphene/substrate contacts

The combined effect due to mechanical strain, coupling to the plasmons in a doped conducting substrate, the plasmon-phonon scattering in conjunction with the role played by encapsulation of a secondary two-dimensional (2D) layer is investigated both theoretically and numerically. The calculations are based on the random-phase approximation (RPA) for the surface response function which yields the plasmon dispersion equation that is applicable in the presence or absence of an applied uniaxial strain. We present results showing the dependence of the frequency of the charge density oscillations on the strain modulus and direction of the wave vector in the Brillouin zone. The shielding of a dilute distribution of charges as well as the rate of loss of energy for impinging charges is investigated for this hybrid layered structure.

An Evaluation of Surface Response Function Re {d_┴ (ω)} and y (ω) for rs = 4 with Surface Damping rs = 0.3 ω p and 0.15 ω p

An Evaluation of Surface Response Function Re {d_┴ (ω)} and y (ω) for rs = 4 with Surface Damping rs = 0.3 ω p and 0.15 ω p

An Evaluation of Surface Response Function Re {d_┴ (ω)} and y (ω) for rs = 4 with Surface Damping rs = 0.3 ω p and 0.15 ω p

An Evaluation of Surface Response Function Re {d_┴ (ω)} and y (ω) for rs = 4 with Surface Damping rs = 0.3 ω p and 0.15 ω p