Modeling Surface-Enhanced Spectroscopy With Perturbation Theory

Theoretical modeling of surface-enhanced Raman scattering (SERS) is of central importance for unraveling the interplay of underlying processes and a predictive design of SERS substrates. In this work we model the plasmonic enhancement mechanism of SERS with perturbation theory. We consider the excitation of plasmonic modes as an integral part of the Raman process and model SERS as higher-order Raman scattering. Additional resonances appear in the Raman cross section which correspond to the excitation of plasmons at the wavelengths of the incident and the Raman-scattered light. The analytic expression for the Raman cross section can be used to explain the outcome of resonance Raman measurements on SERS analytes as we demonstrate by comparison to experimental data. We also implement the theory to calculate the optical absorption cross section of plasmonic nanoparticles. From a comparison to experimental cross sections, we show that the coupling matrix elements need to be renormalized by a factor that accounts for the depolarization by the bound electrons and interband transitions in order to obtain the correct magnitude. With model calculations we demonstrate that interference of different scattering channels is key to understand the excitation energy dependence of the SERS enhancement for enhancement factors below 103

Microscopic theory of optical absorption in graphene enhanced by lattices of plasmonic nanoparticles

We present a microscopic description of plasmon-enhanced optical absorption in graphene, which is based on perturbation theory. We consider the interaction of graphene with a lattice of plasmonic nanoparticles, as was previously realized experimentally. By using tight-binding wave functions for the electronic states of graphene and the dipole approximation for the plasmon, we obtain analytic expressions for the coupling matrix element and enhanced optical absorption. The plasmonic nanostructure induces nonvertical optical transitions in the band structure of graphene with selection rules for the momentum transfer that depend on the periodicity of the plasmonic lattice. The plasmon-mediated optical absorption leads to an anisotropic carrier population around the K point in phase space, which depends on the polarization pattern of the plasmonic near field in the graphene plane. Using Fourier optics, we draw a connection to a macroscopic approach, which is independent from graphene-specific parameters. Each Fourier component of the plasmonic near field corresponds to the momentum transfer of an optical transition. Both approaches lead to the same expression for the integrated optical absorption enhancement, which is relevant for the photocurrent enhancement in graphene-based optoelectronic devices

Selection rules for structured light in nanooligomers and other nanosystems

Structured light is a custom light field where the phase, polarization, and intensity vary with position. It has been used for nanotweezers, nanoscale imaging, and quantum information technology, but its role in exciting optical transitions in materials has been little examined so far. Here we use group theory to derive the optical selection rules for nanosystems that get excited by structured light. If the size of the nanostructure is comparable to the light wavelength, it will sample the full beam profile during excitation with profound consequences on optical excitations. Using nano-oligomers as model nanosystems, we show that structured light excites optical transitions that are forbidden for linearly polarized or unpolarized light. Such dipole forbidden modes have longer lifetimes and narrower resonances than dipole-allowed transitions. We derive symmetry-adapted eigenmodes for nano-oligomers containing up to six monomers. Our study includes tables with selection rules for cylindrical vector beams, for beams with orbital angular momentum, and for field retardation along the propagation direction. We discuss multiphoton processes of nonlinear optics in addition to one-photon absorption. Structured light will unlock a broad range of excitations in nano-oligomers and other nanostructures that are currently inaccessible to optical studies

Selective excitation of localized surface plasmons by structured light

We investigated the selective excitation of localized surface plasmons by structured light. We derive selection rules using group theory and propose a fitting integral to quantify the contribution of the eigenmodes to the absorption spectra. Based on the result we investigate three nano oligomers of different symmetry (trimer, quadrumer, and hexamer) in detail using finite-difference time-domain simulations. We show that by controlling the incident light polarization and phase pattern we are able to control the absorption and scattering spectra. Additionally, we demonstrate that the fitting between the incident light and the oligomer modes may favor a number of modes to oscillate. Dark modes produce strong changes in the absorption spectrum and bright modes in the scattering spectrum. The experimental precision (axial shift error) may be on the same order as the oligomer diameter making the orbital angular momentum selection rules robust enough for experimental observation

Dark plasmon modes for efficient hot electron generation in multilayers of gold nanoparticles

The excitation of dark plasmons, i.e., coupled plasmon modes with a vanishing net dipole, is expected to favor Landau damping over radiative damping. Dark plasmon excitation might, therefore, lead to an increased absorption of energy within gold nanoparticles, resulting in a strong generation of hot electrons compared to the generation via bright plasmons. We performed transient-absorption spectroscopy on gold nanoparticle films to assess the initial electronic temperature before thermalization. We observe a significant increase in the electron–phonon coupling time when dark plasmon modes are excited in these films. The results indicate an efficient energy absorption due to the suppressed radiative decay of dark plasmon modes and a subsequent energy transformation into hot electrons

Probing the local dielectric function of WS2 on an Au substrate by near field optical microscopy operating in the visible spectral range

The optoelectronic properties of nanoscale systems such as carbon nanotubes (CNTs), graphene nanoribbons and transition metal dichalcogenides (TMDCs) are determined by their dielectric function. This complex, frequency dependent function is affected by excitonic resonances, charge transfer effects, doping, sample stress and strain, and surface roughness. Knowledge of the dielectric function grants access to a material’s transmissive and absorptive characteristics. Here we use the dual scanning near field optical microscope (dual s-SNOM) for imaging local dielectric variations and extracting dielectric function values using a pre-established mathematical inversion method. To demonstrate our approach, we studied a monolayer of WS2 on bulk Au and identified two areas with differing levels of charge transfer. The experiments highlight a further advantage of the technique: the dielectric function of contaminated samples can be measured, as dirty areas can be easily identified and excluded for the calculation, being important especially for exfoliated 2D materials (Rodriguez et al., 2021). Our measurements are corroborated by atomic force microscopy (AFM), Kelvin force probe microscopy (KPFM), photoluminescence (PL) intensity mapping, and tip enhanced photoluminescence (TEPL). We extracted local dielectric variations from s-SNOM images and confirmed the reliability of the obtained values with spectroscopic imaging ellipsometry (SIE) measurements

Plasmon-Polaritons in Nanoparticle Supercrystals: Microscopic Quantum Theory Beyond the Dipole Approximation

Crystals of plasmonic metal nanoparticles have intriguing optical properties. They reach the regimes of ultrastrong and deep strong light-matter coupling, where the photonic states need to be included in the simulation of material properties. We propose a quantum description of the plasmon polaritons in supercrystals that starts from the dipole and quadrupole excitations of the nanoparticle building blocks and their coupling to photons. Our model excellently reproduces results of finite difference time domain simulations. It provides detailed insight into the emergence of the polariton states. Using the example of a face centered cubic crystals we show that the dipole and quadrupole states mix in many high symmetry directions of the Brilouin zone. A proper description of the plasmon and plasmon-polariton band structure is only possible when including the quadrupole-derived states. Our model leads to an expression of the reduced coupling strength in nanoparticle supercrystals that we show to enter the deep strong coupling regime for metal fill fractions above $0.8$. In addition to the plasmon-polariton energies we analyse the relative contributions of the dipole, quadrupole, and photonic states to their eigenfunctions and are able to demonstrate the decoupling of light in the deep strong coupling regime. Our results pave the way for a better understanding of the quantum properties of metallic nanoparticle supercrystals in the ultrastrong and deep-strong coupling regime.Comment: 30 pages, 6 figure

Moving beyond the electromagnetic enhancement theory

The electromagnetic enhancement theory describes surface-enhanced Raman scattering (SERS) as a Raman effect that takes place in the near-field of a plasmonic nanostructure. The theory has been very successful in explaining the fundamental properties of SERS, modelling the performance of different metals as enhancing materials and optimizing SERS hotspots for strongest possible enhancement. Over the last decade, a number of carefully designed experimental studies have examined predictions of the electromagnetic theory like the size and shape of SERS hotspots, the absolute magnitude of the enhancement and the width of the SERS resonance. Although the overall picture was quite satisfactory, the theory failed to predict key aspects of SERS, for example, the absolute magnitude of the plasmonic enhancement. We scrutinize these experiments and review them focusing on the results that require going beyond the electromagnetic enhancement theory. We argue that the results of these experiments create the need to develop the theory of SERS further, especially the exact role of plasmonic enhancement in inelastic light scattering

Dark interlayer plasmons in colloidal gold nanoparticle bi- and few-layers

We demonstrate the excitation of dark plasmon modes with linearly polarized light at normal incidence in self-assembled layers of gold nanoparticles. Because of field retardation, the incident light field induces plasmonic dipoles that are parallel within each layer but antiparallel between the layers, resulting in a vanishing net dipole moment. Using microabsorbance spectroscopy we measured a pronounced absorbance peak and reflectance dip at 1.5 eV for bi- and trilayers of gold nanoparticles with a diameter of 46 nm and 2 nm interparticle gap size. The excitations were identified as dark interlayer plasmons by finite-difference time-domain simulations. The dark plasmon modes are predicted to evolve into standing waves when further increasing the layer number, which leads to 90% transmittance of the incident light through the nanoparticle film. Our approach is easy to implement and paves the way for large-area coatings with tunable plasmon resonance