Disentangling bright and dark plasmonic modes in hexagonal nanoprism oligomers

We develop a general quantum theory of the coupled plasmonic modes resulting from the near-field interaction between localized surface plasmons in a heterogeneous metallic nanoparticle dimer. In particular, we provide analytical expressions for the frequencies and decay rates of the bright and dark plasmonic modes. We show that, for sufficiently small nanoparticles, the main decay channel for the dark plasmonic mode, which is weakly coupled to light and, hence, immune to radiation damping, is of nonradiative origin and corresponds to Landau damping, i.e., decay into electron-hole pairs.

When two degenerate surface plasmon polariton (SPP) modes couple, in addition to the creation of plasmonic band gap, their respective decay rates are modified as well, resulting in the formation of a pair of dark and bright modes. We combine temporal coupled mode theory, finite-difference time-domain simulation, and angle- and polarization-resolved reflectivity spectroscopy to study the absorption and radiative decay rates of this pair in periodic system. One-dimensional metallic groove arrays are served as an example here. We find for arrays with small groove width, when approaching to the coupling of -1 and + 1 SPP modes, while the radiative decay rate of the high energy mode tends to become zero, the absorption rate decreases as well, forming a "cold" dark mode. At the same time, both the absorption and radiative decay rates of the low energy mode increase, yielding a "hot" bright mode. The situation is completely reversed when groove width increases, turning the high energy mode into a "cold" bright mode and vice versa for the low energy mode. We attribute such modifications to the interplay between the real and imaginary parts of the complex coupling constant, which are found to be highly geometry dependent. Further numerical simulations show the hybridized modes exhibits distinctive electric and magnetic field symmetries, giving rise to different surface charge distributions and Poynting vector profiles, which significantly affect the resulting absorption and radiation losses. Finally, we have measured the decay rates and the complex coupling constant of the hybridized modes and the experimental results are consistent with the analytic and numerical results.

Borophene, an emerging two-dimensional (2D) material platform, is capable of supporting highly confined plasmonic modes in the visible and near-infrared wavebands. This provides a novel building block for light manipulation at the deep subwavelength scale, thus making it well-suited for designing ultracompact optical devices. Here, we theoretically explore a borophene-based plasmonic hybrid system comprising a continuous borophene monolayer (CBM) and sodium nanostrip gratings (SNGs), separated by a polymer spacer layer. In such a structure, a dynamically tunable plasmon-induced transparency (PIT) effect can be achieved by strongly coupling dark and bright plasmonic modes, while actively controlling borophene. Here, the bright mode is generated through the localized plasmon resonance of SNGs when directly excited by TM-polarized incident light. Meanwhile, the dark mode corresponds to a propagating borophene surface plasmon (BSP) mode in the CBM waveguide, which cannot be directly excited, but requires phase matching with the assistance of SNGs. The thickness of the polymer layer has a significant impact on the coupling strength of the two modes. Owing to the BSP mode, highly sensitive to variations in the ambient refractive index (RI), this borophene-based hybrid system exhibits a good RI-sensing performance (643.8 nm/RIU) associated with a wide range of dynamically adjustable wavebands (1420–2150 nm) by tuning the electron density of borophene. This work offers a novel concept for designing active plasmonic sensors dependent on electrically gating borophene, which has promising applications in next-generation point-of-care (PoC) biomedical diagnostic techniques.

Plasmon hybridization modes are observed in the extinction spectra of a metal-insulator-metal (MIM) nanodisk array fabricated using nanospherical-lens lithography. Two distinct hybridization modes are observed in this vertically aligned configuration. Theoretical simulation indicates that the bonding mode located at a lower energy level exhibits an antiphase charge distribution and corresponds to the dark plasmon mode. This is vastly different compared to antibonding dark plasmon mode observed in the conventional dimer configuration. The observed mode is tunable over a wide spectral range simply by varying the insulator thickness and the diameters of the MIM nanodisks. Absorption is the dominating extinction process for the dark plasmon, while scattering dominates the bright plasmon mode. The ability to experimentally measure and tune dark plasmon modes using a MIM configuration should catalyze more novel studies that take full advantages of the absorption-dominated dark plasmon mode.

Plasmonic nanostructures are often used in surface-enhanced infrared absorption (SEIRA) spectroscopy to probe surface assembled molecules or the dielectric environment surrounding the metallic nanostructures. Here we fabricate metallic nanogap structures using self-aligned techniques on an intrinsic silicon substrate and correlate resulting SEIRA spectra with the choice of metal nanostructure geometry. A motivation is to compare the enhancement from hybridization of bright plasmon modes with the effect of hybridization between bright and dark plasmon modes. These structures provide a gap size below 10 nm and support strong field enhancements. The structures demonstrate their sensitivity through the enhanced absorption signature of the Si–O stretch in the native silicon oxide layer of nanometer thickness beneath the metal. Simulations reveal this thin layer plays a critical role in determining the plasmon modes of the nanostructures. Numerical simulations of the optical properties are consistent with the observations that stronger Si–O stretch signals are detected on self-aligned nanogap structures than nanorod arrays, highlighting the enhanced electromagnetic fields in the underlying native oxide.

We investigate the fluorescence properties of colloidal quantum dots attached to gold rod nanoantennas. These structures are fabricated by a two step electron beam lithography process in combination with a chemical linking method. By varying the nanoantenna length, the plasmon modes of the nanoantennas are successively tuned through the emission band of the quantum dots. We observe a pronounced fluorescence enhancement both for short and long nanoantennas. These findings can be attributed to the coupling of the quantum dots to bright and dark plasmon modes, respectively.

The plasmon hybridization model of electromagnetic coupling between plasmonic nanoparticles predicts the formation of lower energy “bonding” and higher energy “antibonding” modes in analogy with the quantum mechanical description of chemical bonding. For a symmetric metallic nanoparticle dimer excited by linearly polarized light, the hybridization picture predicts that in-phase coupling of the dipole moments is optically allowed, creating bright “modes”, whereas the out-of-phase coupling is dark due to the cancellation of the oppositely oriented dipole moments (in the quasistatic approximation). These bright modes are electric dipolar in nature and readily couple to scalar (i.e., linearly or circularly polarized) beams of light. We show that focused cylindrical vector beams, specifically azimuthally and radially polarized beams, directly excite dark plasmon modes in symmetric gold nanoparticle (AuNP) dimers at normal incidence. We use single-particle spectroscopy and electrodynamics simulations to study the resonance scattering of AuNP dimers illuminated by azimuthally and radially polarized light. The electric field distributions of the focused azimuthal or radial beams are locally polarized perpendicular or parallel to the AuNP dimer axis, but with opposite directions at each particle. Therefore, the associated combinations of single-particle dipole moments are out-of-phase, and the excitation (resonance) is of so-called “dark modes”. In addition, multipole expansion of the fields associated with each scattering spectrum shows that the vector beam excitation involves driving multipolar, e.g., magnetic dipolar and electric quadrupolar, modes, and that they even dominate the scattering spectra (vs electric dipole). This work opens new opportunities for investigating dark plasmon modes in nanostructures, which are difficult to selectively excite by conventional polarized light.

Dark and bright mode hybridization: From electric to magnetic Fano resonances

Plasmonic nanostructures enable the concentration of light to the deep subwavelength regime and, thus, are the topic of intense fundamental and application oriented research. Nanoparticles acting as optical antennas are well known for their nanoscale mode volumes, due to the excitation of localized plasmon modes. In this context electron energy‐loss spectroscopy (EELS) in a transmission electron microscope (TEM) became a powerful technique as it enables to map the full modal spectrum of plasmon eigenmodes with unprecedented high spatial resolution [1–3]. Beside EELS, Cathodoluminescence (CL) has also recently been used to gain information about the optical response taking advantage of the same high spatial resolution in a TEM [4]. While it is stated that EELS is linked to the full photonic local density of states (LDOS), the CL signal is related to the radiative LDOS [5]. In this work we present a combined EELS/CL study of plasmon eigenmodes on silver nanodisks, using fast electrons in a TEM. In particular we compare the differences of the EELS and CL response using experimental and simulated data. Precise variation of the disk size is achieved by means of electron beam lithography (Figure 1a), enabling a comprehensive study of plasmon excitations on silver nanodisks. From theoretical considerations it is known, that for certain particle geometries (and therefore for specific surface charge distributions) there exist so called dark modes, which are “invisible” to photons but “visible” to electrons, and therefore can be measured with EELS but not with light [6]. Here we discuss how dark these dark modes are comparing EELS and CL (figure 1b+c). In particular, radial breathing modes (C in figure 1b+c) were predicted to be dark modes [6], although we will show how comparison between EELS and CL can mitigate this statement. Additionally, limitations for the theoretical predictions will be discussed, when the particle size is increased and therefore retardation effects become more important. In this case we show that dark modes are getting brighter. Furthermore symmetry breaking by the excitation source itself, a focused fast electron beam, will be discussed.

Strong coupling between plasmons and excitons in transition metal dichalcogenides enables room-temperature plexciton formation, providing a crucial platform for investigating Bose-Einstein condensation, low-threshold nanolasers, and ultrafast optical switches. Plexcitons can be produced by far-field optical excitation and near-field electron beam excitation, while electron beam excitation enables the detection of dark plasmon modes and their spatial imaging. Using the boundary element method with a coupled harmonic oscillator model, electron energy loss spectroscopy of silver nanotriangles, WS2, and their composite system is simulated. Our numerical results are consistent with the corresponding experiments. From the charge distributions of silver nanotriangles in electron beam excitation, the dipole configurations corresponding to bright and dark plasmon modes are identified. The coupling mechanism of excitons and plasmons in the composite structure is analyzed. Additionally, the origin of asymmetry in spatial imaging maps of electron loss from plexcitons is clarified, and the proportions of plasmons and excitons in plexcitons produced by different detunings are analyzed theoretically. This study provides guidance for further experimental and theoretical research on strong coupling in analogous composite systems.

Surface plasmon resonances, the coherent oscillation of free electrons, can concentrate incident field into small volumes much smaller than the incident wavelength. The intense fields at these \textit{hot spots} enhance the light-matter interactions and may lead to the appearance of nonlinearity. Controlling such nonlinearities is significant for various practical applications. Here we report that by coupling dark modes to the first and the generated second harmonic modes separately, one can gain control over both fields. We find that by engineering path interferences (Fano resonances) between bright and dark plasmon modes it is possible to enhance the fundamental mode without increasing the nonlinear field, enhance the nonlinear field without modifying the fundamental mode, and enhance the second harmonic field with enhanced fundamental mode.

The plasmonic properties of two closely adjacent gold nanocones of different sizes have been investigated. The plasmon modes of the first nanocone couple with the plasmon modes of the second one due to which a broad peak and a narrow peak emerges in the extinction spectrum, which can be categorized as bright and dark plasmon modes. The destructive interference of the two modes results in a sharp Fano dip in the spectrum. Several configurations of the conical nanodimer have been considered, which suggests that the plasmon coupling in the nanocone dimer is not only dependent on the interparticle distance and size of the nanoparticles but also on their spatial arrangement. The localized high near-field energy in the nanodimer can be used for surface-enhanced Raman spectroscopy applications.

The presence of plasmonic Fano-like resonances in the optical response of isolated and dimer metal-dielectric-metal nanostructures are investigated theoretically. The nanostructures are engineered in such a way to support multiple Fano-like resonances that are induced by the interference of bright and dark plasmon modes. It is found that the dimer resonators exhibit different types of Fano resonances for both the transverse and longitudinal polarizations unlike conventional nanodimers. Several configurations of the dimer Fano resonator are analyzed with special emphasis on the Fano spectral line shape. Breaking the symmetry of the dimer nanostructure in various directions control the asymmetric line shape and provides different kinds of unique Fano resonances. In certain cases, the Fano resonators exhibit multiple Fano resonances that are particularly significant for plasmon line shaping and can serve as platforms for multi-wavelength sensing applications.

Enhanced photoelectron emission from dark plasmon mode in gold nanoring

We report on our numerical work concerning a 3D planar nano-structure metamaterial exhibiting classical electromagnetically induced transparency (Cl-EIT). The interaction between two different plasmonic modes of the unit cell, induced directly or indirectly by the incident electromagnetic wave, leads to a transparent window, resembling the Cl-EIT. Their interactions and coupling between plasmonic modes are investigated in detail by analyzing magnetic field distributions and spectral responses. Simply by introducing of symmetry broken of the proposed nano-structure, the Cl-EIT can be dynamically tuned. At one special asymmetric case, a sharp transparency window with the bandwidth of about 2.96 nm (corresponding to 0.6 THz in frequency regime) is obtained at 246.3 THz (corresponding to 1.218 μm). The corresponding quality factor (Q-factor) is 411. Also, we show that the Cl-EIT frequency position depended very sensitively on the used metal in the metamaterial. Furthermore, we demonstrate numerically that tunable slow light can be realized in our planar nano-structure metamaterial with the unit cell composed of dark and bright plasmonic modes in a broad terahertz regime. It is demonstrated that the increased Q-factor leads to large group index (of the order of 620), which is promising for efficient plasmonic sensing, optical switching, and slow-light devices design.