Surface Plasmon Polaritons Dispersion Research Articles

Vector frequency-comb Fourier-transform spectroscopy for characterizing metamaterials

We determine infrared transmission amplitude and phase spectra of metamaterial samples at well-defined incidence and polarization with a vector (‘asymmetric’) frequency-comb Fourier-transform spectrometer (c-FTS) that uses no moving elements. The metamaterials are free-standing metallic hole arrays; we study their resonances in the 7–13 μm and 100–1000 μm wavelength regions due both to interaction with bulk waves (Wood anomaly) and with leaky surface plasmon polaritons (near-unity transmittance, coupling features and dispersion). Such complex-valued transmission and reflection spectra could be used to compute a metamaterial's complex dielectric function directly, as well as its magnetic and magneto-optical permeability functions.

Azimuthal dispersion and energy mode condensation of grating-coupled surface plasmon polaritons

The excitation conditions for surface plasmon polaritons (SPPs) on a silver-gold bilayer coated sinusoidal grating can be varied over a wide range by tuning the azimuthal grating orientation $(\ensuremath{\alpha})$. Grating coupling induces rotation of the SPP wave vector which, for specific conditions, can be directed perpendicular to the exciting light direction. Certain $\ensuremath{\alpha}$ orientations allow the excitation of two SPPs with the same frequency but different propagation directions. Other azimuthal orientations allow excitation of many SPP modes characterized by propagation over a large angular range. The kinematics of SPP propagation can be described by a model based on the wave-vector conservation law. Using this model, SPP dispersion relation, propagation direction, and mode density have been computed and shown to be in agreement with experimental measurements. The wave-vector dispersion is characterized by an energy threshold for the SPP excitation that increases as $\ensuremath{\alpha}$ increases. The angular spread is accompanied by an energy condensation of the SPP modes in correspondence to the energy threshold.

Lamb shift due to surface plasmon polariton modes

The Lamb shift of a hydrogen atom due to the surface plasmon polariton (SPP) modes is calculated and we observe both band edge and surface enhancement. The atom sits inside a thin metal slab which is sandwiched by two semi-infinite dielectrics. The SPP dispersion relation shows a band gap if the two dielectrics have different dielectric constants. We find the magnitude of the $2{P}_{1/2}$ level shift increases rapidly when the level separation is close to the high band edge. But the low band edge enhancement can be overwhelmed by the decreasing trend of the shift. If the atom is placed close to either surface or if the slab is narrow, all the level shifts would be large because of the surface enhancement. An interesting feature is that the $2{P}_{1/2}$ level shift can be larger than the $2S$ level shift due to the nonisotropic fields.

Plasmon-Assisted Phase-Matched Second- and Third-Harmonic Generation in Single-Negative Heterostructures

Dispersion relations of surface plasmon polaritons (SPPs) in sandwiched optical systems are studied. The system is actually a kind of SPP waveguides, with two kinds of single negative material (SNG) as core and cladding layers, respectively. Since both TM and TE polarized SPPs can be excited in the structure, the dispersion of SPPs becomes more abundant and leads to colorful nonlinear optical properties. The authors demonstrate the effective phase-matched second and third-harmonic generation (SHG, THG) assisted by the coupled SPPs. A cascaded second-order nonlinear process can also be achieved in the structure when the thickness of the core layer is properly selected, leading to the simultaneous SHG and THG. Further investigations show that much easier phase-matching can be fulfilled in the SNG waveguide array. Our results would be of potential use for surface-enhanced frequency conversion device such as light emitters or lasers.

Terahertz surface plasmon polaritons on periodically corrugated metal surfaces

Based on a modal expansion of electromagnetic fields, a rigorous method for analyzing surface plasmon polaritons (SPPs) on a periodically corrugated metal surface has been formulated in this paper. This method takes into account the finite conductivity of the metal as well as higher-order modes within the grooves of the surface structure, thus is able to accurately calculate the loss of these spoof SPPs propagating along the structured surface. In the terahertz (THz) frequency range, the properties of the dispersion and loss of spoof SPPs on corrugated Al surfaces are analyzed. For spoof SPPs at THz frequencies, the strong confinement of the fields is often accompanied with considerable absorption loss, but the performance of both low-loss propagation and subwavelength field confinement for spoof SPPs can be achieved by the optimum design of surface structure.

单负层状异质结构的表面等离激元耦合效应

Propagation characteristics of surface plasmon polaritons (SPPs) in the lamellar heterostructure, which is actually a SPP waveguide array, constructed by two kinds of single negative (SNG) material layers stacked alternatively are investigated. Based on the finite element method (FEM), the negative-refraction (NR) property is demonstrated when the electromagnetic wave penetrates through free space into such SNG lamellar structure. A clear view of the underlying physics of NR is presented qualitatively that is mainly related to the coupled SPPs. The strong coupling effect leads to the novel SPP dispersion curves and then the anomalous propagation characteristics.

Curve crossing and negative refraction in simulations of near-field coupled metallic nanoparticle arrays

We extend our previous results [R. Baer et al., J. Chem. Phys. 126, 014705 (2007).] to develop a simple theory of localized surface plasmon-polariton (LSPP) dispersion on regular arrays of metal nanoparticles in the weak-field and weak-damping limits. This theory describes the energy-momentum as well as the polarization-momentum properties of LSPP waves, both of which are crucial to plasmonic device design. We then explicitly compute the dispersion relation for isotropic and anisotropic two-dimensional square lattices, and show curve crossings between all three levels as well as negative refraction where the phase and group velocities (refractive indices), or at least their projection along the main axis, have different signs. The curve crossing implies that scattering between the different polarizations, and therefore different velocities, is easy at the curve crossing momenta, so that a quick change in wave packet direction can be achieved. Time-resolved wave packet dynamics simulations demonstrate negative refraction and the easy scattering over nanometer length scales. This paper also gives some computational schemes for future applications, such as a way to include source terms and how to efficiently treat dissipative effects.

Spectral sensitivity of two-dimensional nanohole array surface plasmon polariton resonance sensor

An analytical expression of spectral sensitivity derived from a surface plasmon polariton dispersion relation for a two-dimensional nanohole array surface plasmon polariton resonance sensor is presented. The sensitivity of the nanohole array sensor depends on the periodicity of the array and the order of the excited surface plasmon polariton modes. The analytical expression is further confirmed by rigorous electromagnetic simulation and validated by experimental results. Real-time monitoring of protein-protein specific bonding is performed to demonstrate the integrated microfluidic nanohole array surface plasmon resonance biosensor.

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.

Bragg scattering of surface plasmon polaritons on extraordinary transmission through silver periodic perforated hole arrays

Extraordinary optical transmission through a two-dimensional periodic perforated Ag film in the far infrared region was demonstrated. When the squared hole size is close to a half lattice constant a∕2, the split of the degenerate (±1,0) Ag∕Si and (0,±1) Ag∕Si modes into two peaks becomes apparent. Surface plasmon polaritons dispersion relations with variously sized square holes are measured to investigate the different surface charge fields at the periodic metal array. Strong scattering of the forward SPP waves, in the (1,0) Ag∕Si mode, leads to a much lower transmission than that of in the (−1,0) Ag∕Si mode. Experimental results demonstrate that the photonic band gap opens up when the size of the squared hole exceeds a half lattice constant a∕2.

Direct observation of surface plasmon-polariton dispersion

We describe a method to observe the directional emission of electromagnetic radiation produced by the radiative decay of surface plasmonpolaritons (SPPs) that allows the dispersion of the modes in k-space to be directly visualized. The method presented here opens up the possibility of characterizing the effect of a wide range of surface morphologies on SPP dispersion. As an example we show the formation of a stop-band for SPPs when the metal surface is modulated in the form of a diffraction grating.

Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces

A modelling study of the effect of coupled surface plasmon polaritons (SPPs) on the optical response of a thin metal film corrugated on both surfaces is presented. Initially the case of conformally corrugated metal films (the corrugations on each surface are identical and in phase with each other) is considered. Sinusoidal structures, and those having an additional first harmonic, $2{k}_{g}$ (where ${k}_{g}$ is the grating vector) component, are investigated. This $2{k}_{g}$ component opens up significant band gaps in the SPP dispersion curves, and also causes anticrossing behavior between the long range SPPs and short range SPPs. It is shown that this anticrossing, and the band gap, have a common explanation. Following this, nonconformally corrugated films are examined, and strongly enhanced resonant transmission is shown to occur, which can be almost independent of the in-plane wave vector. The results presented show that, though the enhanced transmission through hole arrays which has provoked extensive recent investigation is of great interest from a physics viewpoint, other structures which exhibit enhanced transmission may provide more benefits, including higher transmission, for some applications.

Surface plasmon polariton modified emission of erbium in a metallodielectric grating

The spectral shape and bandwidth of the emission of Er3+ ions in silica glass around 1.5 μm is strongly modified by the presence of a silver grating. The metallodielectric grating was made by a sequence of ion implantation in silica glass, dry etching, and silver sputter deposition. Spectral enhancements are observed that are attributed to near-field coupling of Er3+ ions to surface plasmon polaritons that subsequently reradiate at well-defined resonance conditions. Qualitative agreement is observed between these resonance conditions and calculations based on the surface plasmon polariton dispersion relation.

Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount.

Recent investigations into high-aspect-ratio short-pitch metal grating structures have shown that it is possible to excite surface plasmon polaritons (SPPs) even in the zero-order region of the spectrum. The predominant reason this is possible is that extremely large bandgaps occur in the SPP dispersion curves, which are caused by the large depths, and heights, of the structures. The form of the resultant dispersion curves has also been found to be highly dependent on the shape of the grating profile. We present an extension to a previously published paper that described the nature of the SPPs excited on narrow-ridged short-pitch metal gratings in the classical mount by considering the case in which the radiation is incident at nonzero azimuthal angles (the conical mount). In particular, we consider the case of 90 degrees and 45 degrees azimuthal angles and discuss the coupling to the SPP modes and the way in which polarization conversion is evident on such structures.

Dispersion of surface plasmon polaritons on short-pitch metal gratings

The dispersion of surface plasmon polaritons (SPPs) has been calculated for short-pitch metal gratings for various depths. For gratings with depths greater than their pitch very flat SPP bands are formed in the zero-order region of the spectrum which may be resonantly excited with radiation polarized with its electric field in the plane of incidence of the radiation, which also contains the grating vector. The dispersion curves of these modes evolve as deformations of the familiar shallow grating dispersion curve due to the opening of very large band gaps, and interactions of the SPP bands with both the light line and other SPP bands. Also presented are the dispersion curves for the equivalent modes excited by radiation having its plane of incidence perpendicular to the grating vector, but polarized with its electric field parallel to this grating vector. The full dispersion curve of these SPP bands for all orientations of the grating relative to the plane of incidence is also presented.

Polarization conversion from blazed diffraction gratings

We present experimental evidence for significant levels of surface plasmon-polariton mediated polarization conversion from a blazed surface relief diffraction grating, oriented in a geometry where the in-plane component of the incident wave-vector is normal to the grating Bragg vector. This is a configuration in which no polarization conversion would be expected from a diffraction grating with a profile exhibiting reflection symmetry in the plane normal to its surface. The experimental observations are shown to be consistent with model reflectivities calculated using rigorous conical diffraction theory. We go on to show how the presence of a gap in the surface plasmon-polariton dispersion curve perturbs the observed reflectivities, illustrating the splitting of the surface plasmon-polariton dispersion curve with reciprocal-space maps. Finally we use theoretical modelling codes to explore the effect of changing the blazed grating amplitude on the observed level of polarization mixing, also comparing experimental and theoretical predictions for the variation in polarization conversion as a function of the angle between the in-plane component of the incident wave-vector and the grating Bragg vector.

Surface-profile dependence of photon-plasmon-polariton coupling at a corrugated silver surface

The influence of the surface-profile Fourier decomposition on photon–surface-plasmon-polariton (SPP) coupling at a corrugated silver surface, as probed by changes in diffraction-order intensities, line shapes, and peak positions, is explored. The effect of higher spatial harmonics on diffraction orders is considered for coupling to the SPP in the vicinity of a grating-induced minigap as well as away from the minigap region. Numerical results are obtained with the reduced Rayleigh equations, which are accurate in the range of corrugation strengths that optimize photon–SPP coupling for silver. Under first-order-coupling conditions away from the minigap region the presence of a particular spatial harmonic in the surface profile enhances a specific diffraction order in an easily predictable way. The selectivity, sensitivity, and associated line-shape changes for enhancement are examined as a function of harmonic amplitude for several higher harmonics. In connection with recent experiments [ J. Opt. Soc. Am. B8, 1348 ( 1991)] we investigate the influence of the second and the third spatial harmonics on the propagating orders in the vicinity of the (+ 1, −2) minigap region of an 870-nm grating at 633 nm. The interaction between first- and second-order couplings to the opposite branches of the SPP dispersion relation is tuned by variation of the corrugation depth. It is found that changes in the profile Fourier decomposition with corrugation depth, which arise in the holographic fabrication of diffraction gratings, can explain the observed momentum gap in the −1 diffraction order in this case.

Surface‐plasmon optical characterisation of asymmetric soap films

AbstractStable water films covered by arachidic acid monolayers were prepared on vertically arranged glass/Ag/SiO2‐substrates, which were partially pulled out of a film balance trough. The thickness profiles were recorded by on‐line‐measurement, using the thickness dependence of the dispersion of surface plasmon polaritons. The surface plasmon imaging technique allows for a thickness resolution of 0.2 nm and a height resolution of ca. 20 μm. Variations of these profiles as a function of the lateral pressure of the horizontal arachidate layer on the film balance were observed.For the first time Raman studies were made on asymmetric soap films. The intensity ratio of the Δηa = 2800 cm−1 to the Δηs = 2850 cm−1 line in the CH‐stretching vibration range shows a dependence on the lateral pressure in the monolayer.

Investigation of electrode surfaces by surface plasmon polariton spectroscopy

The article is no introduction to the physics of the surface plasmon polaritons (SPP), but reviews experiments on the influence of SPP dispersion by the potential changes in the double layer regime, by the crystal structure of the surface, by overlayers and by roughness and the use of the attenuated total reflection SPP resonance in Raman scattering from adsorbates.