Dispersion Relation Of Surface Plasmon Polaritons Research Articles

Volume fractional change of nano-particle for enhanced localization probability in surface plasmon polariton dispersion relation at AgSiO2-cesium atomic interface

Volume fractional change of nano-particle for enhanced localization probability in surface plasmon polariton dispersion relation at AgSiO2-cesium atomic interface

Surface plasmon polaritons of higher-order mode and standing waves in metallic nanowires.

The surface plasmon polaritons (SPPs) of higher-order mode propagating along a plasmonic nanowire (NW) or an elongated nanorod (NR) are studied theoretically. The dispersion relations of SPPs in NWs of different radii, obtained from a transcendental equation, show that the propagation lengths of SPPs of mode 1 and 2 at a specific frequency are longer than that of mode 0. For the higher-order mode, the spatial phase of the longitudinal component of electric field at a cross section of a NW exhibits the topological singularity, which indicates the optical vortex. Of importance, the streamlines of Poynting vector of these SPPs exhibit a helical winding along NW, and the azimuthal component of orbital momentum density exists in the nearfield of NW to produce a longitudinal orbital angular momentum (OAM). Two types of standing wave of counter-propagating SPPs of mode 1 and 2 are also studied; they perform as a string of beads or twisted donut depending on whether the handedness of two opposite-direction propagating SPPs is same or opposite. In addition, a SPP of mode 1 propagating along an elongated NR can be generated by means of an end-fire excitation of crossed electric bi-dipole with 90° phase difference. If the criterion of a resonator for a mode-1 standing wave (string of beads) is met, the configuration of a plasmonic NR associated with a pair of bi-dipoles with a phase delay (0° or 180°) at the two ends can be applied as a high-efficiency nanoantenna of transmission. Our results may pave a way to the further study of SPPs of higher-order mode carrying OAM along plasmonic waveguides.

Absorption Enhancement in Hyperbolic Metamaterials by Means of Magnetic Plasma

The main features of surface plasmon polaritons (SPPs) that can propagate in a metamaterial–magnetic plasma structure are studied from theoretical perspectives. Both the conventional and imaginary parts of the dispersion relation of SPPs are demonstrated considering transverse magnetic (TM) polarization. We examine and discuss the influence of the external magnetic field. The results demonstrate that this factor dramatically alters the nature of SPPs. It is concluded that the positions and propagation lengths of SPPs can be engineered. Moreover, we present an approach allowing for an absorption enhancement that is a pivotal factor in antenna design. A unified insight into the practical methods aiming to attain hyperbolic dispersion by means of nanostructured and nanowire metamaterials is demonstrated.

Plasmon's Fizeau‐dragging effect at the interface of atomic and nano‐composites media

AbstractThe velocity uncertainty by Fizeaus plasmon dragging‐effect is investigated at the interface of four level atomic medium and Silver Silica (AgSiO2) nano‐composites material by using surface plasmon polaritons(SPPs) waves. We measured the real part of the dispersion relation Re(Ksp) = 1.5K0 with probe and control field detunings and Re(Ksp) = 1.36K0 with control field Rabi frequencies ∣Ω1,2 ∣ /γ. Furthermore, Re(Ksp/K0) = 1.8 with damping rate γ42/γ and volume frictional change fm. A large kink in the real part of dispersion relation of SPPs was measured in the large interaction region. The group index is in the range of ±20. The maximum dragging coefficient is ±20. The relative phase difference due to dragging is enhance by factor of −1.5 × 10−8rad. The propagation time is measured to be 0.8 ns with both control field Rabi frequencies. The volume fractional change of nano particles, probe/control field detuning and Rabi frequency of control field significantly influence the dragging coefficient, relative phase difference and velocity uncertainty. Including Fizeau‐Dragging effect in the given configuration the velocity uncertainty is measured to be 15 μm/s which is much larger than the velocity width of Kuan et al, used Δva = (8kBTln2/m)1/2 = 176 mm/s. The velocity uncertainty could be improved to 0.1 μm/s by taking large ensemble of atomic coherence and large delay/advance in time due to SPPs.

Using Active Surface Plasmons in a Multibit Optical Storage Device to Emulate Long‐Term Synaptic Plasticity

Artificial intelligence takes inspiration from the functionalities and structure of the brain to solve complex tasks and allow learning. Yet, hardware realization that simulates the synaptic activities realized with electrical devices still lags behind computer software implementation, which has improved significantly during the past decade. Herein, the capability to emulate synaptic functionalities by exploiting surface plasmon polaritons (SPPs) is shown. By depositing photochromic switching molecules (diarylethene) on a thin film of gold, it is possible to reliably control the electronic configuration of the molecules upon illumination cycles with UV and visible light. These reversible changes modulate the dielectric function of the photochromic film and thus enable the effective control of the SPP dispersion relation at the molecule/gold interface. The plasmonic device displays fundamental functions of a synapse such as potentiation, depression, and long‐term plasticity. The integration of such plasmonic devices in an artificial neural network is deployed in plasmonic neuroinspired circuits for optical computing and data transmission.

Electron energy loss of ultraviolet plasmonic modes in aluminum nanodisks.

We theoretically investigated electron energy loss spectroscopy (EELS) of ultraviolet surface plasmon modes in aluminum nanodisks. Using full-wave Maxell electromagnetic simulations, we studied the impact of the diameter on the resonant modes of the nanodisks. We found that the mode behavior can be separately classified for two distinct cases: (1) flat nanodisks where the diameter is much larger than the thickness and (2) thick nanodisks where the diameter is comparable to the thickness. While the multipolar edge modes and breathing modes of flat nanostructures have previously been interpreted using intuitive, analytical models based on surface plasmon polariton (SPP) modes of a thin-film stack, it has been found that the true dispersion relation of the multipolar edge modes deviates significantly from the SPP dispersion relation. Here, we developed a modified intuitive model that uses effective wavelength theory to accurately model this dispersion relation with significantly less computational overhead compared to full-wave Maxwell electromagnetic simulations. However, for the case of thick nanodisks, this effective wavelength theory breaks down, and such intuitive models are no longer viable. We found that this is because some modes of the thick nanodisks carry a polar (i.e., out of the substrate plane or along the electron beam direction) dependence and cannot be simply categorized as radial breathing modes or angular (azimuthal) multipolar edge modes. This polar dependence leads to radiative losses, motivating the use of simultaneous EELS and cathodoluminescence measurements when experimentally investigating the complex mode behavior of thick nanostructures.

Surface plasmon polaritons in plasma-dielectric-magnetic plasma structure

The properties of surface plasmon polaritons (SPPs) excited in the plasma-dielectric-magnetic plasma structure are investigated theoretically. Both the normal and the absorbing dispersion relations of SPPs are derived and presented for transverse-magnetic polarization. The influences of the external magnetic field, collision frequency of plasma, background material dielectric constant, and thickness on the characteristics of SPPs are explored and discussed. Results show that these factors greatly alter the properties of SPPs. The results imply that the locations and propagation length of SPPs can be tuned. In addition, the results also show that a one-way dispersion relation of SPPs can be realized in the low-frequency regions when the external magnetic field is introduced.

Understanding the Electromagnetic Response of Graphene/Metallic Nanostructures Hybrids of Different Dimensionality

Plasmonic excitations such as surface-plasmon-polaritons (SPPs) and graphene-plasmons (GPs), carry large momenta and are thus able to confine electromagnetic fields to small dimensions. This property makes them ideal platforms for subwavelength optical control and manipulation at the nanoscale. The momenta of these plasmons are even further increased if a scheme of metal-insulator-metal and graphene-insulator-metal are used for SPPs and GPs, respectively. However, with such large momenta, their far-field excitation becomes challenging. In this work, we consider hybrids of graphene and metallic nanostructures and study the physical mechanisms behind the interaction of far-field light with the supported high momenta plasmon modes. While there are some similarities in the properties of GPs and SPPs, since both are of the plasmon-polariton type, their physical properties are also distinctly different. For GPs we find two different physical mechanism related to either GPs confined to isolated cavities, or large area collective grating couplers. Strikingly, we find that although the two systems are conceptually different, under specific conditions they can behave similarly. By applying the same study to SPPs, we find a different physical behavior, which fundamentally stems from the different dispersion relations of SPPs as compared to GPs. Furthermore, these hybrids produce large field enhancements that can also be electrically tuned and modulated making them the ideal candidates for a variety of plasmonic devices.

Evaluation of surface roughness of metal films using plasmonic Fano resonance in attenuated total reflection

Attenuated total reflection (ATR) by surface plasmon polariton (SPP) is a method for evaluating the dispersion relation of SPP from the position of a dip in the reflection spectrum. However, recent studies have shown that the dips are displaced from SPP resonance because they are produced by a type of Fano resonance, i.e., the interference between the resonant reflection process accompanied by resonant excitation of SPP and the direct reflection process without resonant excitation. This result suggests that the system properties difficult to be achieved in the dispersion relation of SPP can be characterized using the ATR method. In this study, we investigate the effect of surface roughness due to nanosized dimples created in the initial stage of pitting corrosion on the ATR spectrum, from the viewpoint of Fano resonance. Using the temporal coupled-mode method, it is shown that the Fano resonance in ATR is caused by the phase change of direct reflection because of the absorption on the metal surface, and the spectral shape is determined by this phase, along with the ratio of the external (radiative) decay rate to the total decay rate of the resonant mode. Moreover, it is clarified that the internal and external decay rates extracted from the ATR spectrum provide information on corrosion, such as the effective thickness of the metal film and the randomness in dimple distribution.

Surface Plasmon Coupling in GaN:Eu Light Emitters with Metal-Nitrides

Metal-nitrides of hafnium nitride (HfN), zirconium nitride (ZrN) and titanium nitride (TiN) are investigated as plasmonic materials to enhance the internal quantum efficiency of a GaN:Eu red light emitter. Theoretical calculations are performed to evaluate the surface plasmon polariton dispersion relation and Purcell enhancement factor for a single metal-nitride layer on top of the GaN:Eu emitter. Our findings suggest that among the metal-nitrides investigated in this study, TiN is the most promising candidate for use as plasmonic material to increase the internal quantum efficiency in GaN:Eu red light emitters.

Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness

Surface plasmon polariton (SPP) resonance spectra for noble metals (Au, Ag, and Cu) were comprehensively studied in the Kretschmann attenuated total reflection (ATR) geometry, in the wavelength (λ) range from 300 to 1000 nm with the angle of incidence (θ) ranging from 45 to 60° and the film thickness (d) ranging from 41 to 76 nm. The experimental plasmon resonance spectra were reproduced by a calculation that included the broadening effects as follows: (1) the imaginary part of the bulk dielectric constant, (2) the thickness-dependent radiative coupling of the SPP at the metal–air interface to the prism, (3) the lack of conservation of the wavevector parallel to the interface kx(k||) caused by the surface roughness, (4) scanning λ at a fixed θ (changing both energy and kx at the same time) over the SPP dispersion relation. For Au and Ag, the experimental results were in good agreement with the calculated results using the bulk dielectric constants, showing no film thickness dependence of the plasmon resonance energy. A method to extract the true width of the plasmon resonance from raw ATR spectra is proposed and the results are rigorously compared with those expected from the bulk dielectric function given in the literature. For Au and Ag, the width increases with energy, in agreement with that expected from the relaxation of bulk free electrons including the electron–electron interaction, but there is clear evidence of extra broadening, which is more significant for thinner films, possibly due to relaxation pathways intrinsic to plasmons near the interface. For Cu, the visibility of the plasmon resonance critically depends on the evaporation conditions, and low pressures and fast deposition rates are required. Otherwise, scattering from the surface roughness causes considerable broadening of the plasmon resonance, resulting in an apparently fixed resonance energy without clear incident angle dependence. For Cu, the observed plasmon dispersion agrees well with that expected from the bulk dielectric function even with nominal oxidation of the surface, but the widths at long wavelengths are much larger than those theoretically expected.

Extraordinary terahertz transmission through a double-layer metal array with closed ring resonators

In this paper, we numerically investigate the transmission properties of a terahertz metamaterial. This metamaterial is composed of metal-dielectric-metal, which consists of metallic layers with an air hole array and one coaxial closed ring resonator in the air hole. The metamaterial in the THz range of 0.2–1THz has three transmission peaks. We provide an explanation of the transmission peaks by means of the surface plasmon polaritons and magnetic polaritons resonance based on the distribution of the surface current. Then according to the magnetic polaritons resonance, the equivalent circuit model of the metamaterial is established. The effects of geometric parameters on the transmission peaks are discussed and studied by an equivalent circuit model and surface plasmon polaritons dispersion relation. Our metamaterial promises dual-band potential applications such as filters.

Enhanced light emission from top-emitting organic light-emitting diodes by optimizing surface plasmon polariton losses

We demonstrate enhanced light extraction for monochrome top-emitting organic light-emitting diodes (OLEDs). The enhancement by a factor of 1.2 compared to a reference sample is caused by the use of a hole transport layer (HTL) material possessing a low refractive index (1.52). The low refractive index reduces the in-plane wave vector of the surface plasmon polariton (SPP) excited at the interface between the bottom opaque metallic electrode (anode) and the HTL. The shift of the SPP dispersion relation decreases the power dissipated into lost evanescent excitations and thus increases the outcoupling efficiency, although the SPP remains constant in intensity. The proposed method is suitable for emitter materials owning isotropic orientation of the transition dipole moments as well as anisotropic, preferentially horizontal orientation, resulting in comparable enhancement factors. Furthermore, for sufficiently low refractive indices of the HTL material, the SPP can be modeled as a propagating plane wave within other organic materials in the optical microcavity. Thus, by applying further extraction methods, such as micro lenses or Bragg gratings, it would become feasible to obtain even higher enhancements of the light extraction.

Surface Plasmon-Modulated Fluorescence on 2D Metallic Silver Gratings

The emitting properties of fluorophores can be tailored by surface plasmon polaritons (SPPs), which offers the potential to understand the light-matter interactions at the nanoscale, and lays the groundwork for many future applications. As one of the useful features in SPPs-surface plasmon-coupled emission (SPCE) based on the metal gratings; however, the study on its underlying modulation mechanism remains far from satisfactory. That is, how it is affected by the morphology of the grating surfaces. In this letter, we have addressed this question in the dye-coated corrugated silver gratings that possess different periods and depths. It is found that the properties of SPCE are strongly dependent on the dispersion relations of SPPs modulated by the grating periods.

Surface plasmon polaritons at linearly graded semiconductor interfaces.

New results are reported on investigation of dispersion curves for surface plasmon polaritons (SPPs) at an inhomogenously doped semiconductor/dielectric interface whereby the dielectric is represented by the same undoped semiconductor. The doped semiconductor is described by its frequency-dependent permittivity that varies with the depth. It is shown that a transition layer (TL) with a linear change in carrier concentration supports one branch dispersion curve regardless of the TL thickness. The obtained dispersion curves reach a maximum at a finite frequency depending on the TL thickness, and subsequently asymptotically approach the zero frequency in the shortwave limit. Therefore two surface plasmon modes are supported at a given frequency: a long-wave mode with a positive group velocity and a short-wave mode with a negative group velocity. A condition of a zero group velocity can be satisfied by tuning the TL layer. It is shown that the conventional dispersion relation for SPPs at a TL with a zero thickness is an asymptotic solution, and the convergence of real dispersion curves is point-wise instead of an expected uniform convergence.

Dynamics of quasiparticles in graphene under intense circularly polarized light

A monolayer of graphene irradiated with circularly polarized light suggests a unique platform for surface electromagnetic wave (plasmon-polariton) manipulation. In fact, the time periodicity of the Hamiltonian leads to a geometric Aharonov-Anandan phase and results in a photovoltaic Hall effect in graphene, creating off-diagonal components of the conductivity tensor. The latter drastically changes the dispersion relation of surface plasmon-polaritons, leading to hybrid wave generation. In this paper we present a systematic and self-contained analysis of the hybrid surface waves obtained from Maxwell equations based on a microscopic formula for the conductivity. We consider a practical example of graphene sandwiched between two dielectric media and show that in the one-photon approximation there is formation of propagating hybrid surface waves. From this analysis emerges the possibility of a reliable experimental realization to study Zitterbewegung of charge carriers of graphene.

Temperature dependence of exciton-surface plasmon polariton coupling in Ag, Au, and Al films on InxGa1−xN/GaN quantum wells studied with time-resolved cathodoluminescence

The optical properties and coupling of excitons to surface plasmon polaritons (SPPs) in Ag, Au, and Al-coated InxGa1−xN/GaN multiple and single quantum wells (SQWs) were probed with time-resolved cathodoluminescence. Excitons were generated in the metal coated SQWs by injecting a pulsed high-energy electron beam through the thin metal films. The Purcell enhancement factor (Fp) was obtained by direct measurement of changes in the temperature-dependent radiative lifetime caused by the SQW exciton-SPP coupling. Three chosen plasmonic metals of Al, Ag, and Au facilitate an interesting comparison of the exciton-SPP coupling for energy ranges in which the SP energy is greater than, approximately equal to, and less than the excitonic transition energy for the InGaN/GaN QW emitter. A modeling of the temperature dependence of the Purcell enhancement factor, Fp, included the effects of ohmic losses of the metals and changes in the dielectric properties due to the temperature dependence of (i) the intraband behavior in the Drude model and (ii) the interband critical point transition energies which involve the d-bands of Au and Ag. We show that an inclusion of both intraband and interband effects is essential when calculating the ω vs k SPP dispersion relation, plasmon density of states (DOS), and the dependence of Fp on frequency and temperature. Moreover, the “back bending” in the SPP dispersion relation when including ohmic losses can cause a finite DOS above ωsp and lead to a measurable Fp in a limited energy range above ωsp, which can potentially be exploited in plasmonic devices utilizing Ag and Au.

Dynamical Casimir-Polder interaction between an atom and surface plasmons

We investigate the time-dependent Casimir-Polder potential of a polarizable two-level atom placed near a surface of arbitrary material, after a sudden change in the parameters of the system. Different initial conditions are taken into account. For an initially bare ground-state atom, the time-dependent Casimir-Polder energy reveals how the atom is "being dressed" by virtual, matter-assisted photons. We also study the transient behavior of the Casimir-Polder interaction between the atom and the surface starting from a partially dressed state, after an externally induced change in the atomic level structure or transition dipoles. The Heisenberg equations are solved through an iterative technique for both atomic and field operators in the medium-assisted electromagnetic field quantization scheme. We analyze in particular how the time evolution of the interaction energy depends on the optical properties of the surface, in particular on the dispersion relationof surface plasmon polaritons. The physical significance and the limits of validity of the obtained results are discussed in detail.

Direct measurement of dispersion relation for surface plasmon-polaritons on silver nanoantennas

We investigated the degree to which the dispersion relation of surface plasmon-polaritons excited on silver nanoantennas depends on length. To accomplish this, dispersion measurements for individual silver nanoantennas with lengths from 220 nm to 2.5 μm were performed using angle-resolved electron energy-loss spectroscopy (AREELS) and spatially resolved EELS (SREELS). AREELS enabled measurements of the dispersion relation extending into the high-energy region of 2.6 eV for a 2.5-μm-long silver nanoantenna, without the need to excite Fabry-Perot-type resonances. Our experiments showed that the dispersion relation of silver nanoantennas that have the same diameter is independent of their individual lengths.

Switching and propagation of magnetoplasmon polaritons in magnetic slot waveguides and cavities

The dispersion relations for surface plasmon-polaritons propagating in the Voigt geometry in a metal-insulator-metal waveguide with a magneto-optically active dielectric medium are derived. The symmetry between the upper and lower interfaces is broken by the introduction of the magnetic field; the balance between the field distributions on the two interfaces can be controlled by the applied field. This control is illustrated by finite-element method numerical simulations of the field distributions around a point dipole placed in the centre of the short waveguide; it is shown that both the total emission of radiation from the cavity and the distribution of the far-field radiation can be strongly modified by tuning the magnetisation of the waveguide. This raises the novel possibility of using magnetic fields to control light propagation in nanostructures.