Plasmonic Band Structure Research Articles

Spectral fingerprints of electron-plasmon coupling

We investigate the spectroscopic fingerprints of electron-plasmon coupling in integrated (PES) and angle-resolved photoemission spectroscopy (ARPES). To account for electron-plasmon interactions at a reduced computational cost, we derived the plasmonic polaron model, an approach based on the cumulant expansion of many-body perturbation theory that circumvents the calculation of the GW self-energy. Through the plasmonic polaron model, we predict the complete spectral functions and the effects of electron-plasmon coupling for Si, Ge, GaAs, and diamond. Si, Ge, and GaAs exhibit well-defined plasmonic polaron band structures, i.e., broadened replica of the valence bands redshifted by the plasmon energy. Based on these results, (i) we assign the structures of the plasmon satellite of silicon (as revealed by PES experiments) to plasmonic Van Hove singularities occurring at the L, $\Omega$, and X high-symmetry points and (ii) we predict the ARPES signatures of electron-plasmon coupling for Si, Ge, GaAs, and diamond. Overall, the concept of plasmonic polaron bands emerges as a new paradigm for the interpretation of electronic processes in condensed matter, and the theoretical approach presented here provides a computationally affordable tool to explore its effect in a broad set of materials.

Plasmon-modulated photoluminescence from gold nanostructures and its dependence on plasmon resonance, excitation energy, and band structure.

Two distinct single-photon plasmon-modulated photo-luminescence processes are generated from nanostructured gold surfaces by tuning the spectral overlap of the incident laser source, localized surface plasmon resonance band, and the interband transitions between the d and sp bands, near the X- and L-symmetry points of the electronic band structure of gold. In the main section of the article, the characteristics of these photoluminescence processes are described and discussed. In the last section, the background continuum accompanying surface-enhanced Raman scattering (SERS) spectra from benzenethiol and 4-mercaptopyridine self-assembled monolayers chemisorbed on nanostructured gold surfaces is shown to originate from plasmon-modulated photoluminescence.

Lasing at the band edges of plasmonic lattices

This paper reports a comprehensive experimental study of silver and gold plasmonic crystal lasers. Such periodic plasmon particle systems have recently triggered large attention due to the fact that localized plasmons and collective lattice resonances conspire to give large light-matter interaction strength in narrow resonances. The authors provide a detailed report on the conditions required for lasing, and a complete analysis of the underlying plasmonic lattice band structure.

Band modulation and in-plane propagation of surface plasmons in composite nanostructures.

In this work, we have experimentally and theoretically studied band modulation and in-plane propagation of surface plasmons (SPs) in composite nanostructures with aperture arrays and metallic gratings. It is shown that the plasmonic band structure of the composite system can be significantly modulated because of coupling between the aperture and grating. By changing the relative positions between these optical components, the resonant modes would shift or split. And the resonant SP modes launched on the structure surface can be effectively modified by the geometric parameters. Further, we provide an experimental observation to directly show the SP in-plane propagation by using far-field measurements, which agree with the simulated results. Our study offers a convenient way for observing the SP propagation in far field, and provides unique composite nanostructures for possible applications in subwavelength optodevices, such as optical sensors and detectors.

Active terahertz plasmonic crystal waveguide based on double-structured Schottky grating arrays

An electrically controllable terahertz (THz) plasmonic crystal waveguide based on double-structured Schottky grating arrays has been fabricated and investigated. The experiment and simulation show two different resonance behaviors of a discrete jump and a continuous shift when applying positive and negative bias, respectively. THz modulations with a 15 dB modulation depth have been realized in the frequency range of 2.2−3.2 THz. Furthermore, these modulation behaviors have been interpreted as the generation and shift of the plasmonic band structures accompanying with the spatial modulations of the Schottky barriers in this device. This active THz device can be feasibly applied into THz application systems.

Tuning the dispersion relation of a plasmonic waveguide via graphene contact

In this work, we have investigated experimentally and theoretically the dispersion relation of a plasmonic slab waveguide, where the thin gold film with nano-aperature arrays is sandwiched by graphene and a silica layer on a silicon chip. It is shown that the plasmonic slab waveguides are compatible with silicon technology. We have found that when the light waves irradiate the nanostructured waveguides with or without graphene, surface plasmon polaritons are always excited at the metal-dielectric interface due to the interaction between the surface charge oscillation and the electromagnetic field of the light. But in the slab waveguide with graphene, the resonant dips definitely shift in the reflection spectra, which indicates that the contact of graphene can tune the dispersion relation of the waveguide in the visible regime. Experimental measurements on optical reflections are in good agreement with calculated plasmonic band structures. Further calculations show that the dispersion relation of plasmonic slab waveguides can be tuned by electron doping and the nonlinear effect of graphene. The investigations provide a way to actively control the dispersion relation of plasmonic waveguides on silicon chips and benefit the development graphene-related active optical devices.

Plasmonic lifetimes and propagation lengths in metallodielectric superlattices

We study the complex plasmonic band structure of nanoscopically thin metallodielectric layers. It is shown that the lifetime and propagation lengths can be obtained with excellent accuracy using a perturbation technique, thus establishing a quantitative connection between mode dissipation and its electromagnetic fields. Ultimately, the perturbation approach is shown to elucidate the physical origin of the orders-of-magnitude variation of lifetime and propagation lengths across the band structure. The symmetrical Brillouin zone center mode is dissipated the least because its electric field is efficiently screened from the metal layers. For a typical silver--titanium dioxide system at visible and infrared frequencies, maximum lifetimes have been found in the subpicosecond and picosecond range, while the longest propagation lengths are direction dependent and in the 10 to 100-micron range. We have also shown that the ratio of the propagation length for a given direction and the lifetime is equal to the corresponding group velocity component.

Probing the plasmonic band structure of an optical metamaterial

Knowledge of the plasmonic band structure is crucial for the fundamental understanding and better control of electromagnetic waves in periodic optical metamaterials. Here, we probe the plasmonic band structure of the important fishnet metamaterial by angle- and polarization-resolved optical spectroscopy. We show that multiple ``magnetic'' plasmon bands exist in the fishnet metamaterial, and they display interesting dispersion behavior. We can understand the plasmon bands qualitatively using a band-structure zone-folding picture. Interestingly, some plasmon resonances have wave-vector-dependent coupling, and the corresponding plasmon bands exhibit anticrossing behavior due to hybridization of the plasmonic waves.

Plasmonic Band Structure Controls Single-Molecule Fluorescence

Plasmonics and photonic crystals are two complementary approaches to tailor single-emitter fluorescence, using strong local field enhancements near metals on one hand and spatially extended photonic band structure effects on the other hand. Here, we explore the emergence of spontaneous emission control by finite-sized hexagonal arrays of nanoapertures milled in gold film. We demonstrate that already small lattices enable highly directional and enhanced emission from single fluorescent molecules in the central aperture. Even for clusters just four unit cells across, the directionality is set by the plasmonic crystal band structure, as confirmed by full-wave numerical simulations. This realization of plasmonic phase array antennas driven by single quantum emitters opens a flexible toolbox to engineer fluorescence and its detection.

Plasmonic energy transfer in periodically doped graphene

We predict unprecedentedly large values of the energy-transfer rate between an optical emitter and a layer of periodically doped graphene. The transfer exhibits divergences at photon frequencies corresponding to the Van Hove singularities of the plasmonic band structure of the graphene. In particular, we find flat bands associated with regions of vanishing doping charge, which appear in graphene when it is patterned through gates of spatially alternating signs, giving rise to intense transfer rate singularities. Graphene is thus shown to provide a unique platform for fast control of optical energy transfer via fast electrostatic inhomogeneous doping.

Transmission line theory of collective plasma excitations in periodic two-dimensional electron systems: Finite plasmonic crystals and Tamm states

We present a comprehensive theory of the one-dimensional plasmonic crystal formed in the grating gated two-dimensional electron gas (2DEG) in semiconductor heterostructures. To describe collective plasma excitations in the 2DEG, we develop a generalized transmission line theoretical formalism consistent with the plasma hydrodynamic model. We then apply this formalism to analyze the plasmonic spectra of 2DEG systems with step-like periodic changes of electron density and/or gate screening. We show that in a periodically modulated 2DEG, a plasmonic crystal is formed and derive closed-form analytical expressions describing its energy band spectrum for both infinite and finite size crystals. Our results demonstrate a non-monotonic dependence of the plasmonic band gap width on the electron density modulation. At so-called transparency points where the plasmon propagates through the periodic 2DEG in a resonant manner, the plasmonic band gaps vanish. In semi-infinite plasmonic crystals, we demonstrate the formation of plasmonic Tamm states and analytically derive their energy dispersion and spatial localization. Finally, we present detailed numerical analysis of the plasmonic band structure of a finite four-period plasmonic crystal terminated either by an Ohmic contact or by an infinite barrier on each side. We trace the evolution of the plasmonic band spectrum, including the Tamm states, with changing electron density modulation and analyze the boundary conditions necessary for formation of the Tamm states. We also analyze interaction between the Tamm states formed at the opposite edges of the short length plasmonic crystal. The validity of our theoretical approach was confirmed in experimental studies of plasmonic crystals in short modulated plasmonic cavities which demonstrated excellent quantitative agreement between theory and experiment.

Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies

We study theoretically optical properties of a graphene monolayer supported on subwavelength dielectric gratings (SWDGs) using a scattering-matrix method. It is found that due to the formation of band structure of graphene plasmons (GPs) on the SWDG, optical excitations of GPs can be controlled by GP bands above the light line, resulting in optical absorption enhancement in graphene. In particular, very flat GP bands can exist above the light line at midinfrared frequencies. As a result, high optical absorption in graphene can be realized over a wide angular range at these flat bands when using a metallic substrate. Our results could find applications in graphene-based opto-electronics.

Inducing an Incipient Terahertz Finite Plasmonic Crystal in Coupled Two Dimensional Plasmonic Cavities

We measured a change in the current transport of an antenna-coupled, multigate, GaAs/AlGaAs field-effect transistor when terahertz electromagnetic waves irradiated the transistor and attribute the change to bolometric heating of the electrons in the two dimensional electron channel. The observed terahertz absorption spectrum indicates coherence between plasmons excited under adjacent biased device gates. The experimental results agree quantitatively with a theoretical model we developed that is based on a generalized plasmonic transmission line formalism and describes an evolution of the plasmonic spectrum with increasing electron density modulation from homogeneous to the crystal limit. These results demonstrate an electronically induced and dynamically tunable plasmonic band structure.

Plasmonic band structures and optical properties of subwavelength metal/dielectric/metal Bragg waveguides

In this paper, we applied the band structure theory to investigate the plasmonic band (PB) structures and optical properties of subwavelength metal/dielectric/metal Bragg waveguides in the near infrared range with either dielectric or geometric modulation. The Bloch wave vector, density of states, slowdown factor, propagation length and transmittance are calculated and analyzed. Both the modulations are in favor of manipulating surface-plasmon-polariton (SPP) waves. For the dielectric modulation, the PB structure is mainly formed by SPP modes and possesses a "regular pattern" in which the bands and gaps have a relatively even distribution. For the geometric modulation, due to the strong transverse scattering, the contributions of higher modes have to be considered and the gap widths have a significant increase compared to the dielectric modulation. A larger slowdown factor may emerge at the band edge; especially for the geometric modulation, the group velocity can be reduced to 1/100 of light, and negative group velocity is observed as well. While inside the bands, the slowdown factor is smaller and the bands are flat. The contribution of each eigenmode to the PB structure is analyzed.

Analysis of plasmonic Bloch waves and band structures of 1D plasmonic photonic crystals

We consider such passbands that appear due to excitation of plasmons inside the one-dimensional photonic crystal with elementary cells containing layers of positive and negative permittivities. The corresponding Bloch waves can be regarded as surface plasmon chains that are subsequently excited at the layers’ boundaries. The band structure depends on the elementary cell composition that also determines the plasmon type. The excited plasmons can be similar to surface plasmons that propagate along a dielectric slab “sandwiched” between two semi-spaces with negative permittivity, or to surface plasmons that propagate along a negative permittivity slab sandwiched between two dielectric semi-spaces. It is shown that the existence of negative refraction does not depend on the frequency dispersion of permittivity. The latter fact permits us to distinguish six elementary cell compositions with qualitatively different band structures. The frequency evolution of the band structure of a plasmonic PC with a given frequency dispersion of the permittivity can be considered as a transition between various kinds of band structures.

One-dimensional long-range plasmonic-photonic structures

We have fabricated line gratings from periodically etched fused silica on which a thin silver film is deposited that is in turn covered with a silica index-matched fluid. This dielectrically symmetric geometry supports an independent long-range surface plasmon-polariton (LRSPP) and a short-range surface plasmon polariton, and the associated plasmonic band structure has been probed. Coupling to external light is achieved via the patterned grating, and an ultrasharp LRSPP linewidth of 4 nm is observed. The experimental results are compared with finite-difference time-domain simulations.

Optical properties of metallic meanders

A vertical metallic meander structure with a rectangular corrugated surface profile represents a frequency-selective surface in which the excitation and interaction of localized surface plasmon modes are controlled in a flexible fashion by its geometrical parameters over a large spectral range. In this report we investigate the optical properties of metallic meanders numerically. Although the structure is simple from both the structural geometry and the nanofabrication point of view, its plasmonic band structure manifests rich features that would be very attractive for plasmonic functional devices. In particular, the short-range surface plasmon mode can be tuned by changing the meander depth without altering the long-range surface plasmon mode. To obtain deeper physical insight into the relationship between the structural geometry and its optical response, a transmission line equivalent circuit model is used. It is revealed that circuit parameters that were fitted from numerical scattering parameters have physical relationships with the structural parameters, which can be described by quasi-static or radiative descriptions. In certain frequency ranges, enhanced transmission occurs due to the interaction of magnetic and electric dipole resonances. The calculated effective material parameters reveal that enhanced transmission occurs around the near-zero index frequencies. The application potential of these structures as frequency filters is discussed.

Surface plasmon resonance in two-dimensional nanobottle arrays

We report our recent work on surface plasmon polaritons manipulation of two-dimensional arrays of subwavelength bottle-shaped cavities on gold surface. By tuning the geometry of such "nanobottle" it is possible to control the resonant frequencies and near field patterns of different surface plasmon resonances. The plasmonic band structures are not sensitive to the sizes and depths of the nano-bottles, but depend strongly on the polarization. In particular, by using different polarizations, it is observed that different types of plasmonic resonances, whether propagating or localized, can be excited independently. Moreover, we find that the local field and field intensity can by fine-tuned by controlling the topology of the bottleneck of the nanobottle. As a result, we believe these nanobottle arrays are useful for making plasmonic devices.

Ultrafast dynamics of surface plasmon polaritons in plasmonic metamaterials

Using near-field scanning optical microscopy and ultrafast laser spectroscopy, we study the linear optical properties of subwavelength nanoslit and nanohole arrays in metal films, which are prototype structures for novel plasmonic metamaterials. Near-field microscopy provides direct evidence for surface plasmon polariton (SPP) excitation and allows for spatial imaging of the corresponding SPP modes. By employing spectral interferometry with ultrashort 11-fs light pulses, we directly reconstruct the temporal structure of the electric field of these pulses as they are transmitted through the metallic nanostructures. The analysis of these data allows for a quantitative extraction of the plasmonic band structure and the radiative damping of the corresponding SPP modes. Clear evidence for plasmonic band gap formation is given. Our results reveal that the coherent coupling between different SPP modes can result in a pronounced suppression of radiative SPP damping, increasing the SPP lifetime from 30 fs to more than 200 fs. These findings are relevant for optimizing and manipulating the optical properties of novel nano-plasmonic devices.

Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation

We calculate the surface plasmon dispersion relations for a periodic chain of spherical metallic nanoparticles in an isotropic host, including all multipole modes in a generalized tight-binding approach. For sufficiently small particles ($kd \ll 1$, where $k$ is the wave vector and $d$ is the interparticle separation), the calculation is exact. The lowest bands differ only slightly from previous point-dipole calculations provided the particle radius $a \lesssim d/3$, but differ substantially at smaller separation. We also calculate the dispersion relations for many higher bands, and estimate the group velocity $v_g$ and the exponential decay length $\xi_D$ for energy propagation for the lowest two bands due to single-grain damping. For $a/d=0.33$, the result for $\xi_D$ is in qualitative agreement with experiments on gold nanoparticle chains, while for larger $a/d$, such as $a/d=0.45$, $v_g$ and $\xi_D$ are expected to be strongly $k$-dependent because of the multipole corrections. When $a/d \sim 1/2$, we predict novel percolation effects in the spectrum, and find surprising symmetry in the plasmon band structure. Finally, we reformulate the band structure equations for a Drude metal in the time domain, and suggest how to include localized driving electric fields in the equations of motion.