Surface Plasmon Dispersion Research Articles

Transmission resonances in plasmonic metallic gratings

Using the Fourier modal method (FMM) we report our analysis of the transmission resonances of a plasmonic grating with sub-wavelength period and extremely narrow slits for wavelengths of the incoming, transverse magnetic (TM)-polarized, radiation ranging from 240nm to 1500nm and incident angles from 0 degree to 90 degree. In particular, we study the case of a silver grating placed in vacuo. Consistent with previous studies on the topic, we highlight that the main mechanism for extraordinary transmission is a TM-Fabry-Perot (FP) branch supported by waveguide modes inside each slit. The TM-FP branch may also interact with surface plasmons (SPs) at the air/Ag interface through the reciprocal lattice vectors of the grating, for periods comparable with the incoming wavelength. When the TM-FP branch crosses a SP branch, a band gap is formed along the line of the SP dispersion. The gap has a Fano-Feshbach resonance at the low frequency band edge and a ridge resonance with extremely long lifetime at the high frequency band edge. We discuss the nature of these dispersion features, and in particular we describe the ridge resonance in the framework of guided-mode resonances (GMRs). In addition, we elucidate the connection of the coupling between the TM-FP branch and SPs within the Rayleigh condition. We also study the peculiar characteristics of the field localization and the energy transport in two topical examples.

Equivalent-Circuit Modeling of Nonradiative Surface Plasmon Energy Transfer Along the Metallic Nanowire

An analytical methodology for establishing an equivalent-circuit network of nonradiative surface plasmon (SP) energy transport along the metallic nanowire (MNW) is presented. To find out the passive elements for MNW, the SP dispersion and damping relation through modified Bessel function electromagnetic (EM) field expansion was derived, thus demonstrating the low-pas transmission-line (TL) model. Specifically, the low-pass TL parameters, such as series impedance (Z) and shunt admittance ( Y) can be calculated based on the lumped-element model and harmonic-voltage (current) distribution. Furthermore, the equivalent-circuit parameters, such as resistance (R), inductance (L), capacitance (C) and conductance (G), are obtained by employing the finite difference (FD) discretization method such as T-cell RLCG networks. These equivalent-circuit elements can be verified by the HSPICE circuit simulation and 3-D scattered finite-difference time-domain (FDTD) method. Finally, the parallel MNWs are modeled as equivalent-circuit networks by using the electrostatic coupling.

Light extraction from surface plasmons and waveguide modes in an organic light-emitting layer by nanoimprinted gratings

Organic light-emitting diodes (OLEDs) usually exhibit a low light outcoupling efficiency because a large fraction of power is lost to surface plasmons (SPs) and waveguide modes. In this paper it is demonstrated that periodic grating structures with almost µm-scale can be used to extract SPs as well as waveguide modes and therefore enhance the outcoupling efficiency in light-emitting thin film structures. The gratings are fabricated by nanoimprint lithography using a commercially available diffraction grating as a mold which is pressed into a polymer resist. The outcoupling of SPs and waveguide modes is detected in fluorescent organic films adjacent to a thin metal layer in angular dependent photoluminescence measurements. Scattering up to 5th-order is observed and the extracted modes are identified by comparison to the SP and waveguide dispersion obtained from optical simulations. In order to demonstrate the low-cost, high quality and large area applicability of grating structures in optoelectronic devices, we also present SP extraction using a grating structure fabricated by a common DVD stamp.

Wavefront engineering for mid-infrared and terahertz quantum cascade lasers [Invited

We review our recent work on beam shaping of mid-infrared (mid-IR) and terahertz (THz) quantum cascade lasers (QCLs) using plasmonics. Essentials of QCLs are discussed; these include key developments, the operating principle based on quantum design, and beam quality problems associated with laser waveguide design. The bulk of the present paper is focused on the use of surface plasmons (SPs) to engineer the wavefront of QCLs. This is achieved by tailoring the SP dispersion using properly designed plasmonic structures, in particular, plasmonic Bragg gratings, designer (spoof) surface plasmon structures, and channel polariton structures. Using mid-IR and THz QCLs as a model system, various functionalities have been demonstrated, ranging from beam collimation, polarization control, to multibeam emission and spatial wavelength demultiplexing. Plasmonics offers a monolithic, compact, and low-loss solution to the problem of poor beam quality of QCLs and may have a large impact on applications such as sensing, light detection and ranging (LIDAR), free-space optical communication, and heterodyne detection of chemicals. The plasmonic designs are scalable and applicable to near-infrared active or passive optical devices.

Enhancement of extraction efficiency by metallic photonic crystal embedding in light-emitting diode

The bandgap effect of photonic crystals (PCs) and the effect of grating diffraction can be used to improve the extraction efficiency of light from the light-emitting diode (LED). The transmission of light at certain wavelength through periodic sub-wavelength hole arrays in metal films is extraordinary, surface plasmon (SP) effects effectively. In this letter, silver metallic photonic crystals with square lattice of cylinder unit cells are fabricated in GaN layer of GaN-based blue LED. We use the finite-difference time-domain (FDTD) method to investigate the optical transmission, the results show that the light extraction efficiency is enhanced by more than four times. Then we use the surface plasmon dispersion relation to analyze the mechanism of antireflection.

Localized surface plasmon resonance optical characteristics for hydrogen peroxide using polyvinylpyrrolidone coated silver nanoparticles

In this study, monitoring of localized surface plasmon resonance (LSPR) optical characteristics and dispersion condition change for hydrogen peroxide using polyvinylpyrrolidone (PVP)-coated silver nanoparticles (NPs) was described. PVP-coated silver NPs exhibit the specific light absorption in visible region. Hence, using LSPR optical characteristics, several applications such as optoelectronics, food control and life science can be realized. In addition, by introducing hydrogen peroxide solution into the PVP-coated silver NP dispersion, LSPR optical characteristics were drastically changed. From these LSPR optical characteristic changes of PVP-coated silver NPs for hydrogen peroxide, in this study, observation of dispersion kinetics of PVP-coated silver NPs was carried out. As a result, aggregation which is attributed by the radical polymerization of PVP layer could be observed by introduction of hydrogen peroxide. In addition, silver cluster structure which is included in the PVP layer was stably contained in the aggregated PVP layer. From these optical characteristic change and dispersion kinetics, this PVP-coated silver NPs have great potential for application to biosensing applications as a color indicator.

Time-dependent dynamical image screening at a metal surface

P.M.E. acknowledges partial support from the University of the Basque Country Grant No. 9/UPV 00206.215-13639/2001, the Basque Universitate eta Ikerketa Saila, and the Spanish Ministerio de Education y Ciencia MEC Grants No. FIS 2004-06490-C03-01 and No. CSD2006-53.

Quasiguided surface plasmon excitations in anisotropic materials

We present a theoretical study of surface plasmon polaritons in a configuration where a metal layer is bounded by a homogeneous anisotropic dielectric. We consider uniaxial and biaxial dielectrics with the optical axis lying in the plane defined by the metal/dielectric interface. Through a systematic study of the in-plane surface plasmon dispersion relation we confirm the existence of several propagation regimes for different values and signs of the birefringence. We report the discovery of the existence of quasiguided surface plasmon polaritons characterized by non-null radiative components. We identify the conditions for the existence of such modes, and explain their peculiar properties in terms of the hybridization of radiative and guided modes.

Plasmonic Modes Confined in Nanoscale Thin Silver Films Deposited onto Metallic Substrates

Collective electronic excitations in nanoscale thin Ag layers adsorbed on Cu(111) and Ni(111) at room temperature have been investigated by high-resolution electron energy loss spectroscopy. Surface plasmon was found to be confined within grains on Ag thin films on Cu(111) nanostructured in islands. Annealing removed surface plasmon confinement and induced a negative linear term of the dispersion relation. On the other hand, on flat thin films on Ni(111) the dispersion of Ag surface plasmon is fully quadratic. Landau damping processes of the plasmonic excitation were found to be dependent on the growth mode. Ag multipole surface plasmon at 7.7 eV was observed only under stringent kinematic conditions enhancing surface sensitivity.

Generation of electromagnetic waves in a spheroidal conductor by moving charges

The surface polarization fields generated by a charge moving near a spheroidal conductor are considered. The relations for surface plasmon dispersion are obtained. The polarization fields and energy losses of a moving charge are calculated.

Multimode Surface Plasmon Excitations on Organic Thin Film/Metallic Diffraction Grating

In this work, we demonstrate multimode surface plasmon (SP) excitations by white light irradiation on metallic diffraction grating/plastic substrates. Recordable compact discs were used as the diffraction grating substrates on which silver films were deposited by vacuum evaporation. Since the grating pitch (1.6 µm) was larger than that of diffraction gratings commonly used for the excitation of SPs, multimode SP excitations due to several diffraction orders were observed simultaneously in the wavelength region from 400 to 800 nm. The obtained SP excitations were then compared with the calculated SP dispersion on the grating. The multimode SP excitations were further studied on spin-coated poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) thin film/silver grating substrates. An increased photoluminescence intensity due to SP excitations was observed on MEH-PPV/silver grating surfaces.

Plasmonic States From Visible Light to Microwaves

Plasmonics is a phenomenon often considered in the visible light and near infrared, whereas typical metal waveguide modes are studied in the microwave regime. We demonstrate how plasmonic modes become conventional waveguide modes as the frequency varies from visible light to microwaves. In particular, given the metal permittivity at microwaves, the plasmonic dispersion becomes the conventional waveguide dispersion. Moreover, the surface plasmon dispersion at a single metal/insulator boundary can be extracted over a metal/insulator/metal (MIM) heterostructure if the metal-to-metal spacing is taken infinite. In doing so, the coupling effect of plasmonic modes is clearly revealed. As the symmetric coupled plasmon mode is known to correspond to the TEM (TM0) mode, we found that the antisymmetric coupled surface plasmon mode is essentially related to the TM1 mode.

Plasmonic superlattices: Hierarchical subwavelength hole arrays

This Letter describes the dispersion properties of plasmonic lattices consisting of near-infinite arrays and superlattices (patches) of nanoholes in thin gold films. Zero-order, optical transmission spectra of the plasmonic lattices revealed that compared to the near-infinite arrays, the superlattices showed new resonances that depended on the separation between patches. Theoretical calculations were in good agreement with the measurements and identified the origins of the additional transmission peaks. Surface plasmon dispersion diagrams were also measured, and the superlattices were found to exhibit satellite-bands around the primary (intra-patch) surface plasmon polariton modes that were not present in the near-infinite nanohole arrays.

Blue-shift of surface plasmon resonance in a metal nanoslit array structure

The adsorption of a self-assembled monolayer of molecules on a metal surface commonly causes a red-shift in its surface plasmon resonance. We report that the anomalous dispersion of surface plasmons in a Au nanoslit array structure can cause a blue-shift of optical transmission upon adsorption of a non-absorbing self-assembled monolayer of molecules. We develop a simple model that explains the blue-shift observed in the transmission spectra with monolayer adsorption in terms of the interplay of anomalous dispersion and the cavity resonance of surface plasmons in the nanoslit array.

Plasmonic Fabry-Pérot Nanocavity

We experimentally demonstrate a novel, all-plasmonic nanoscopic cavity exhibiting Q-factors up to 200 at visible frequencies. The Fabry-Pérot type resonator uses tall metallic fins that reflect up to 98% of incident surface plasmon to concentrate light within a subwavelength cavity mode. High aspect ratio metal fins, constructed using lithography and electroplating, reduce surface plasmon scattering out of the surface, while a short cavity length reduces the propagation loss. A simple Fabry-Pérot cavity model adapted for surface plasmon dispersion and reflection describes the underlying physics of the nanocavities and the results agree well with Johnson's and Christie's permittivity data. The occurrence of an optimum wavelength for plasmon storage in these cavities allows us to clearly visualize the fundamental trade-off between propagation loss and the spatial extent of surface plasmon polaritons. The subwavelength optical mode area within these cavities enables the enhancement of weak optical processes such as spontaneous emission and nonlinear optics at nanoscale dimensions.

Exact surface plasmon dispersion relations in a linear-metal-nonlinear dielectric structure of arbitrary nonlinearity

Exact analytic expression for obtaining the surface plasmon (SP) dispersion relations in a system consisting of a thin metallic film sandwiched between a linear dielectric and a nonlinear dielectric of arbitrary nonlinearity is derived, based on a generalized first integral approach. The changes in SP dispersion relations on film thicknesses and nonlinearity are studied by model calculations. The thick-film limit generalizes previous results on metal/Kerr-type nonlinear interface to arbitrary nonlinearity. An analytic expression is obtained for the limiting SP frequency at large wave vectors with previous result recovered as a special case.

Plasmon Dispersion of the Au(111) Surface with and without Self-Assembled Monolayers

The surface plasmon dispersion of gold films with and without chemisorbed, alkane thiol self-assembled monolayers (SAMs) has been investigated using high resolution electron energy loss spectroscopy (HREELS). For a bare Au(111) film, the surface plasmon energy (2.49 eV at the zone center) shows a positive dispersion. After adsorption of ethylbenzenethiol or dodecanethiol SAMs, the plasmon energy at the zone center blueshifts and the dispersion switches sign to become negative, thus mimicking the behavior of a free-electron system. This striking behavior represents a benchmark for models of the electronic structure of the gold-sulfur interface, as manifest both in SAMs and in monolayer-protected nanoparticles.

Surface plasmon polaritons on deep, narrow-ridged rectangular gratings

The dispersion diagrams of surface plasmon polaritons have been calculated for rectangular gratings, with very narrow wires, of varying depths. For gratings with a moderate height a family of vertical-standing-wave resonances may be excited, which consist of surface plasmons, oscillating on either vertical surface, coupling together through the metal wires. These modes evolve similarly to the manner in which shallow-grating surface-plasmon dispersion curves evolve into cavity modes in the grooves of the structure. However, on further increase in grating height these vertical standing waves evolve into a second resonant feature, which is independent of yet further increases in height. This new mode is shown to be equivalent to the resonances found on infinite multilayer metal/dielectric structures illuminated at normal incidence.

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.

COLLECTIVE ELECTRONIC EXCITATIONS IN SYSTEMS EXHIBITING QUANTUM WELL STATES

We present high-resolution electron energy loss spectroscopy (HREELS) measurements on surface plasmon (SP) dispersion in systems exhibiting quantum well states (QWS), i.e. Na / Cu (111), Ag / Cu (111), and Ag / Ni (111). Our results demonstrate that the dominant coefficient of SP dispersion for thin and layer-by-layer Ag films presenting QWS is quadratic even at small q||, in contrast with previous measurements on Ag semi-infinite media and Ag thin films deposited on Si (111). We suggest that this behavior is due to screening effects enhanced by the presence of QWS shifting the position of the centroid of the induced charge less inside the geometrical surface compared with Ag surfaces and Ag / Si (111). For ultrathin Ag films, i.e. two layers, the dispersion was found to be not positive, as theoretically predicted. Annealing of the Ag film caused an enhancement of the free-electron character of the QWS, thus inducing a negative linear term of the dispersion curve of the SP. Moreover, we report the first experimental evidence of chemical interface damping in thin films for K / Ag / Ni (111). As regards Na / Cu (111), we found a different dispersion curve compared with thick Na films, thus confirming the enhanced screening by Na QWS. Results reported here should shed light on the influence of QWS on dynamical screening phenomena in thin films.