Surface Plasmon Dispersion Relation Research Articles

Experimental observation of mode-selective anticrossing in surface-plasmon-coupled metal nanoparticle arrays

Surface plasmon excitation using resonant metal nanoparticles is studied experimentally. Geometry dependent reflection measurements reveal the existence of several optical resonances. Strong coupling of the in-plane nanoparticle plasmon resonance and propagating plasmons is evident from clear anticrossing behavior. Reflection measurements at high numerical aperture demonstrate the excitation of surface plasmons via out-of-plane particle polarization. The thus excited plasmons do not exhibit anticrossing in the considered frequency range. The results are explained in terms of the known surface plasmon dispersion relation and the anisotropic frequency dependent nanoparticle polarizability. These findings are important for applications utilizing surface-coupled nanoparticle plasmon resonances.

The Coherence Effect of Surface Plasmons on Optical Transmission in Silver Subwavelength Hole Arrays

We study the optical transmission through a silver film with subwavelength hole arrays, which is sandwiched by super-thin SiO2 layers. Based on finite-difference time-domain method, optical transmission and dispersion relation of surface plasmons are obtained. It is shown that surface plasmons are coherent in the top layer of the sandwich, which affects optical transmission in this subwavelength system. As a result, transmission modes can be tuned by changing the thickness of top layer. Resonant modes are also demonstrated by the electric field distribution. Besides, anti-resonances induced by Fano interference are also observed in this system. These properties may provide a peculiar approach to manipulate the propagation of electromagnetic wave in subwave-length microstructures.

Nonlinear dispersion relation for surface plasmon at a metal–Kerr medium interface

The dispersion relation for the plasmon at the interface of a metal and a nonlinear Kerr medium is studied by applying a semi-analytic theory established in the literature. Explicit analytical results are obtained and are compared to those from a certain approximate treatment appeared in the literature. It is found that for large electric field strengths, both the dispersion relation and the surface plasmon frequency from the approximate treatment deviate significantly from those obtained in the exact approach, especially for the case with a negative Kerr susceptibility.

Spontaneous emission of quantum dot excitons into surface plasmons in a nanowire

The spontaneous emission (SE) of quantum dot (QD) excitons into surface plasmons in a cylindrical nanowire is investigated theoretically. Maxwell's equations with appropriate boundary conditions are solved numerically to obtain the dispersion relations of surface plasmons. The SE rate of QD excitons is found to be greatly enhanced at certain values of the exciton bandgap. Application in generation of remote entangled states via superradiance is also pointed out and may be observable with current technology.

Plasmon hybridization in metallic nanotubes

We study theoretical formalism of the plasmon hybridization in a metallic nanotube and find an explicit form of the dispersion relation for surface plasmons, in terms of interaction between the bare plasmon modes of the individual surfaces of the nanotubes. In the special case when the longitudinal wave vector is zero ( q = 0 ) , the plasmon hybridization of a nanotube has a behavior similar to the spherical nanoshell.

Thermoplasmonic shift and dispersion in thin metal films

In 2004, the authors reported two coupling schemes based on the thermo-optic properties of thin metallic films and their associated sub- and superstrates, by utilizing surface plasmons. These studies showed a potential for all-optical modulation at low rates that may be used for sensing purposes. In this article, they continue by investigating thermal processes involved in thin metallic films with different approaches. They first experimentally imaged the shift of the surface plasmon dispersion relation in the visible spectrum, as the thin film temperature is externally varied. They then reinforce the previous observations by collecting the absorption curves at selected visible photon energies of excitation, as the film temperature in the excitation region increases. Utilizing the absorption measurements, they briefly address how one may obtain the real and imaginary parts of the index of refraction of the thin film as a function of temperature for each involved wavelength. Finally, they investigate the local physical state of the film by optically profiling the surface plasmon excitation region.

Dispersion and extinction of surface plasmons in an array of gold nanoparticle chains: influence of the air/glass interface

We investigate the dispersion relation and extinction properties of surface plasmons in an array of gold nanoparticle chains under s-polarized plane wave excitations, through experiment and simulation. Our results reveal that the dispersion and extinction properties of gold nanoparticle chains at an air/glass interface are significantly different from those in a uniform medium. Under total internal reflection, the dispersion is much larger than that above total internal reflection and 100% extinction can be reached. We show that the large dispersion under total internal reflection can be explained by dipole fields and coupling at the air/glass interface.

Plasmonic band gaps of structured metallic thin films evaluated for a surface plasmon laser using the coupled-wave approach

The behavior of plasmonic band gaps appearing in the dispersion relations of surface plasmons for periodically corrugated thin silver films is theoretically investigated by using the rigorous coupled-wave approach. The structures have one-dimensional rectangular corrugations with 25%, 50%, and 75% fill factors and support both long-range and short-range surface plasmon band gaps. A unified explanation for the necessary conditions for opening these band gaps, as well as intermode band gaps, is given. The radiation characteristics of the surface plasmons at the edges of these band gaps are also analyzed. Based on the findings, the optimal structure for a plasmonic band gap laser is presented.

Light scattering and plasmon resonances in a metal film with sub-wavelength nano-holes

We report on a theoretical study of optical extinction in a metal film of 15–230 nm in thickness patterned periodically with sub-wavelength nano-holes of 140 nm in diameter. The gold plate was on a thick SiO2 wafer and the nano-holes as well as the top side of the metal plate were filled with water or solvent. Light was sent in toward the plate from the SiO2 side. The simulations were performed by solving the Maxwell equations using the scattering matrix method. It was seen that the extinction can, depending on the periodicity of the hole array, show one or several peaks in the visible wavelength range. The positions of the peaks were redshifted when the thickness of the gold plate was decreased. It was found that the peak positions for a thick plate can be identified from a simple surface plasmon dispersion relation.

Influence of the shape of the particles covering the metal surface on the dispersion relations of surface plasmons

The Green function method was used for calculation of dispersion relations of surface plasmon generated at the metal surface covered by ellipsoidal particles. The influence of the shape of the particles on the surface plasmon dispersion relations was studied. It was established that both s- and p-polarized surface plasmons can be excited at the surface covered by the particles. It was shown that the shape of the particles covering the surface strongly influences on the surface plasmons dispersion.

Humidity Adsorption and Surface Plasmon Excitation of Poly(vinyl alcohol) Films with Fluorescent Microspheres

In this study, thin films of poly(vinyl alcohol) (PVA) mixed with 100 nm polystyrene (PS) microspheres were prepared, and changes in attenuated total reflection (ATR) utilizing surface plasmon (SP) excitation due to the adsorption of humidity were investigated. The PS microspheres contained luminescent dyes, and SP emission light due to these dyes was observed. The sample configuration was prism/Ag film (50 nm)/PVA film with sphere. ATR dip and SP emission peak angles shifted with the adsorption and desorption of humidity, and SP emission light intensity changed markedly. Furthermore, kinetic curves were plotted and humidity adsorption responses were repeatedly observed. Finally, the dispersion relations of SPs were obtained from ATR and SP emission light properties.

Effect of longitudinal excitations on surface plasmons

The influence of a longitudinal component in surface plasma waves propagating along the boundary between a plasma and vacuum has been investigated theoretically. It is found that the inclusion of the longitudinal component significantly modifies the dispersion relation for surface plasmons. In particular, it is shown that a surface plasmon can have any frequency in the interval from zero to the bulk plasma frequency.

Bandgap-assisted surface-plasmon sensing

Surface-plasmon resonance (SPR) is a sensing technique widely used for its label-free feature. However, its sensitivity is contingent on the divergence angle of the excitation beam. The problem becomes pronounced for compact systems when a low-cost LED is used as the light source. When the Kretschmann configuration with a periodically modulated surface is used, a bandgap appears in the surface plasmon dispersion relation. We recognize that the high density of modes on the edge of the surface-plasmon bandgap permits the coupling of a wider range of incidence angles of excitation photons to surface-plasmon polaritons than what is possible in the traditional Kretschmann configuration. Here, the numerical simulation illustrates that the sensitivity, detection limit, and reflectivity minimum of an amplitude-based SPR bandgap-assisted surface-plasmon sensor are almost independent of the divergence angle. Two different bandgap structures are compared with the Kretschmann configuration using the rigorous coupled-wave analysis technique. The results indicate that the bandgap-assisted sensing outperforms traditional SPR sensing when the angular standard deviation of the excitation beam is above 1 degree.

Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice

Extraordinary optical transmission through a two-dimensional Ag film in the far infrared region was demonstrated. The holes were rectangular and arranged in a square lattice. When either the width or the length size of the rectangular holes was close to the half of the lattice constant a∕2, the degenerate (±1,0) Ag∕Si or (0,±1) Ag∕Si modes split into two peaks. Additionally, the surface plasmon dispersion relations of the square hole array with different aspect ratios of holes were measured. As the aspect ratio increased, the surface plasmon tended to couple strongly with the local charge dipole oscillations in a direction perpendicular to the long edges. The charge dipole oscillation parallel to the long edges gradually disappeared. This is confirmed by experiments using the polarized light. The dynamic properties of the surface plasmon dispersion relations show the interaction among localized surface plasmons and its mechanism.

Band structure, Wiener bounds, and coupled surface plasmons in one dimensional photonic crystals

Recently metallic two and three dimensional photonic crystals (PCs) have been studied with the focus on using such structures in incandescent lighting and thermal photovoltaic applications. They exhibit a metallic band gap for low frequencies as well as structural band gaps. Especially the metallic band gap allows to block the infrared transmission respectively emission. In this letter we show that also the structural simpler one dimensional (1D) system has the same features; furthermore it builds an omnidirectional band gap for the Drude dispersion relation. For the case of a polaritonic system 1D PCs are able to exhibit angle of incidence as well as frequency dependent filter characteristics. The dispersion relation of surface plasmons, extending over adjacent layers is obtained. Propagating states must lie within the Wiener bounds.

Nonlocal surface plasmons by Poisson Green's function matching

The Poisson Green's function for all space is derived for the case in which an interface divides space into two separate semi-infinite media, using the Green's function matching method. Each of the separate semi-infinite constituent parts has its own dynamic, nonlocal polarizability, which is taken to be unaffected by the presence of the interface and is represented by the corresponding bulk response property. While this eliminates Friedel oscillatory phenomenology near the interface with p ∼ 2pF , it is nevertheless quite reasonable and useful for a broad range of lower (nonvanishing) wavenumbers, p < pF. The resulting full-space Poisson Green's function is dynamic, nonlocal and spatially inhomogeneous, and its frequency pole yields the surface plasmon dispersion relation, replete with dynamic and nonlocal features. It also accommodates an ambient magnetic field.

Dielectric optical elements for surface plasmons

Basic optical elements for surface plasmons are fabricated and their functionality (focusing, refraction, and total internal reflection) is demonstrated experimentally. The optical elements consist of dielectric structures of defined geometry on top of a gold film. The working principle of these structures is discussed on the basis of calculated surface plasmon dispersion relations.

Effect of non-locality on nanofocusing of surface plasmon field intensity in a conical tip

The propagation of a surface plasmon–polariton toward the tip of a conically shaped metal wire is investigated. The modification of the surface plasmon dispersion relation due to non-local effects is included by employing the hydrodynamic approximation. As found in previous, local calculations, the electric field intensity associated with the surface plasmon increases sharply as the wire becomes narrower. However, the rate of increase is somewhat slower than in the local case.

Curvature effects in surface plasmon dispersion and coupling

We have studied the resonant coupling of surface plasmons in curved thin-film tunneling geometries by obtaining the dispersion relations for the system. The surface plasmon dispersion relations are calculated for a metal-coated dielectric probe above a dielectric half space with and without metal coating. The system is modeled in the prolate spheroidal system, and the dispersion relations are studied as functions of the parameter that defines the boundaries of the tip and the corresponding coating, and as functions of the involved coating thicknesses. Using this type of probe-substrate configuration, the nonradiative surface plasmon coupling mechanism is investigated in the visible spectrum at frequencies relevant to scanning probe microscopy. The simulations of the results predict optical access to the resonant surface modes of the system.

Direct visualization of surface-plasmon bandgaps in the diffuse background of metallic gratings

When a surface plasmon propagates along a microrough grating, it interacts with the periodic plus the random roughness and emits light into the diffuse background, which can present intensity maxima called diffuse light bands. We reexamine previous studies on these bands within the framework of recent studies on photonic surfaces and show that the phenomenon of diffuse light provides an experimental technique for directly imaging the dispersion relation of surface plasmons, including the gap that, under appropriate circumstances, opens in the reciprocal grating space.