Graphene Surface Plasmon Polaritons Research Articles

Propagating and Localized Graphene Surface Plasmon Polaritons on a Grating Structure

The general dispersion characteristics of the surface plasmon polariton (SPP) modes for graphene on a grating structure are studied. It is shown that the dispersion of the excited SPP modes highly depends on the size of the gap of the grating. The dispersion of the SPP modes for such a complex grating system can be well approximated by using the photonic crystal model, and therefore, a full simulation is not needed. The fact that for a large gap size the dispersion of the SPP modes can be found by regarding the grating structure as a series of Fabry–Perot cavities suggest strong reflection of propagating plasmons at the gap edges; the excited SPP modes become highly localized in contrast to the propagating SPPs when the gap is small.

Nanowires-assisted excitation and propagation of mid-infrared surface plasmon polaritons in graphene

We investigate the excitation and propagation of surface plasmon polaritons in a novel graphene hybrid photonic nanostructure, which consists of a graphene sheet and a dielectric layer with partly etched nanowires coated on the silicon substrate. The simulation and analytical results show that the mid-infrared plasmonic wave can be generated in the graphene sheet by normally incident light due to the satisfaction of the wavevector matching condition. Especially, we find that the plasmonic wavelength and spectral width are determined by the width, pitch, and refractive index of the dielectric nanowires, as well as the layer number and the Fermi level of graphene sheet. The analytical calculations agree well with the finite-difference time-domain simulations. These results would provide an new avenue toward the excitation of graphene plasmonics for the manipulation of mid-infrared light at nanoscale.

Family of graphene-assisted resonant surface optical excitations for terahertz devices.

The majority of the proposed graphene-based THz devices consist of a metamaterial that can optically interact with graphene. This coupled graphene-metamaterial system gives rise to a family of resonant modes such as the surface plasmon polariton (SPP) modes of graphene, the geometrically induced SPPs, also known as the spoof SPP modes, and the Fabry-Perot (FP) modes. In the literature, these modes are usually considered separately as if each could only exist in one structure. By contrast, in this paper, we show that even in a simple metamaterial structure such as a one-dimensional (1D) metallic slit grating, these modes all exist and can potentially interact with each other. A graphene SPP-based THz device is also fabricated and measured. Despite the high scattering rate, the effective SPP resonances can still be observed and show a consistent trend between the effective frequency and the grating period, as predicted by the theory. We also find that the excitation of the graphene SPP mode is most efficient in the terahertz spectral region due to the Drude conductivity of graphene in this spectral region.

A Dielectric-Thickness-Adjusting Method for Manipulating Graphene Surface Plasmon Polariton

We propose and numerically investigate a dielectric-thickness-adjusting method to manipulate the graphene surface plasmon polariton (SPP). The dispersion relationships of graphene SPP at different dielectric thickness are derived by solving the analytic equations. In addition, the SPP effective index at cutoff dielectric thickness is obtained according to different dielectric permittivity and working frequencies. As a typical application, a plasmonic Bragg reflector is designed by alternately depositing dielectric gratings along the transverse direction of the SPP propagation. The performance of the Bragg reflector is analyzed at different grating thickness, and the effective index at cutoff thickness is verified by numerical simulation. The proposed method will have important potential prospects in designing graphene-based wave trapping and slow wave devices in future.

Excitation of Surface Plasmon Polaritons in an Inhomogeneous Graphene-Covered Grating

Highly confined waves of surface plasmon polaritons (SPPs) in monolayer graphene are efficiently excited using an etched diffractive grating on silicon. In this paper, an inhomogeneous graphene-covered grating is proposed and the excitation of which is analyzed as an analogy with the two-level system in quantum mechanics. Based on the equivalent circuit theory, the excitation of plasmonic waves in an etched diffractive grating is equivalent to the resonance of an oscillator. Thus, according to the governing equation, the electric currents for the inhomogeneous graphene-covered grating is correspond to the ket of energy states in the two-level system. In addition, the excitation of SPPs in an inhomogeneous graphene-covered grating is numerically analyzed to validate the theoretical model. Our work offers a new inroad of the excitation of SPPs in an inhomogeneous graphene-covered grating in an analogy with the two-level system.

Free electromagnetic radiation from the graphene monolayer with spatially modulated conductivity in THz range

An infinite graphene layer is known to support graphene surface plasmon polariton (GSP) confined at the interface between the two dielectric half-spaces. In the case of finite width graphene stripe, the termination of the graphene layer acts both as a scattering source and as a “mirror”, thus producing Fabry–Perot (FP)-type resonance. These resonant wavelengths in the presence of free-standing graphene stripe are investigated using the homogeneous convolution-type integral equation approach. The capabilities of the suggested numerical method are illustrated with the results for the transmission spectrum of TM electromagnetic waves travelling in the direction perpendicular to the graphene stripe. Special attention is paid to the case of spatially modulated conductivity of the graphene monolayer, and thus the feasibility of controlling the GSP response.

Harmonics radiation of graphene surface plasmon polaritons in terahertz regime

This letter presents an approach to extract terahertz radiation from surface plasmon polaritons excited in the surface of a uniform graphene structure by an electron beam. A sidewall configuration is proposed to lift the surface plasmon mode to be close to the light line, so that some of its harmonics have chances to go above the light line and become radiative. The harmonics are considered to be excited by a train of periodic electron bunches. The physical mechanism in this scheme is analyzed with three-dimensional theory, and the harmonics excitation and radiation are demonstrated through numerical calculations. The results show that this technique could be an alternative to transform the surface plasmon polaritons into radiation.

Tunable Fano resonances of a graphene/waveguide hybrid structure at mid-infrared wavelength.

A planar graphene/dielectric multilayer structure is investigated, where the graphene surface plasmon polariton and the planar waveguide mode are coupled to realize Fano resonances. Few-layer graphene with high doping levels is used to excite surface plasmons at mid-infrared wavelength. Reflectance of the structure is calculated numerically by transfer-matrix method, and tunable Fano resonances with different line shapes are demonstrated by varying doping levels of graphene. Properties of the Fano resonances are discussed qualitatively by calculating electric field distribution in the structure and quantitatively by utilizing an analytical fitting equation. We also calculate Goos-Hänchen shift of the Fano resonances as an example for potential applications, and find that large Goos-Hänchen shift appears for optimized doping levels of graphene.

Period fold structure of graphene SPP waveguide

The field of plasmonics has experience a renaissance in recent years by providing a large variety of new physical effects and applications. Surface plasmon polaritons (SPPs), i.e. the collective electron oscillations at the interface of a metal/dielectric, may bridge the gap between electronic and photonic devices, provided a fast switching mechanism is identified. Here, we design folds graphene waveguide excited SPPs and full compensation structures with periodic array by graphene material. Theoretically, we analyzed the loss of the way by periodic array gain full compensation is analyzed. By the results of theoretically analysis, we discover period fold structure not only excites SPPs, which also we can control device parameters using SPPs wave relations. In addition, periodic array compensation can significantly increase the propagation distance of SPPs. Simulation results we further find by simulation results: structure of our design has the advantage of strong localized and subwavelength waveguide size; periodic array compensation can significantly improve the electric field strength of nanocavity; structure of graphene waveguide expresses high levels of population inversion and low spontaneous emission noise disturbance. The graphene waveguide devices which we design can be the key device for the micro-nano optics, photonic sensing and measurement.

Optical bistability induced by nonlinear surface plasmon polaritons in graphene in terahertz regime

We demonstrate optical bistability in a prism-air-graphene-dielectric structure. Under a moderate electric field in the terahertz frequency regime, the third order nonlinear optical conductivity is comparable to the linear conductivity. The nonlinear conductivity enhances the energy of surface plasmon polaritons. Both the energy and frequency of the surface plasmon polaritons depend on the strength of the nonlinear current in the graphene layer. When considering excitation in the Kretschmann configuration, the reflectance as a function of frequency exhibits bistability. The origin of the bistability is the field dependence of the plasmon mode. We have determined the parameter regime for the occurrence of bistability in this structure.

Graphene surface plasmon polaritons transport on curved substrates

We theoretically investigate the transport property of graphene surface plasmon polaritons (GSPPs) on curved graphene substrates. The dispersion relationship, propagation length, and field confinement are calculated by an analytical method and compared with those on planar substrates. Based on our theory, the bend of graphene nearly does not affect the property of GSPPs except for an extremely small shift to the lower frequency for the same effective mode index. The field distributions and the eigenfrequencies of GSPPs on planar and cylindrical substrates are calculated by the finite element method, which validates our theoretical analysis. Moreover, three types of graphene-guided optical interconnections of GSPPs, namely, planar to curved graphene film, curved to planar graphene film, and curved to curved graphene film, are proposed and examined in detail. The theoretical results show that the GSPPs propagation on curved graphene substrates and interconnections will not induce any additional losses if the phase-matching condition is satisfied. Additionally, the extreme tiny size of curved graphene for interconnection at a certain spectra range is predicted by our theory and validated by the simulation of 90° turning of GSPPs. The bending effect on the property of GSPPs is systematically analyzed and identified. Our studies would be helpful to instruct design of plasmonic devices involving curved GSPPs, such as nanophotonic circuits, flexible plasmonic, and biocompatible devices.

Graphene surface plasmon polaritons with opposite in-plane electron oscillations along its two surfaces

We predict the existence of a surface plasmon polariton (SPP) mode that can be guided by a graphene monolayer, regardless of the sign of the imaginary part of its conductivity. In this mode, in-plane electron oscillations along two surfaces of graphene are of opposite directions, which is very different from conventional SPPs on graphene. Significantly, coating graphene with dielectric films yields a way to guide the SPPs with both sub-wavelength mode widths and ultra-long propagation distances. In particular, the mode characteristics are very sensitive to the chemical potential of graphene, so the graphene-based waveguide can find applications in many optoelectronic devices.

Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial.

Hexagonal boron nitride (h-BN) is a natural hyperbolic material, in which the dielectric constants are the same in the basal plane (ε(t) ≡ ε(x) = ε(y)) but have opposite signs (ε(t)ε(z) < 0) in the normal plane (ε(z)). Owing to this property, finite-thickness slabs of h-BN act as multimode waveguides for the propagation of hyperbolic phonon polaritons--collective modes that originate from the coupling between photons and electric dipoles in phonons. However, control of these hyperbolic phonon polaritons modes has remained challenging, mostly because their electrodynamic properties are dictated by the crystal lattice of h-BN. Here we show, by direct nano-infrared imaging, that these hyperbolic polaritons can be effectively modulated in a van der Waals heterostructure composed of monolayer graphene on h-BN. Tunability originates from the hybridization of surface plasmon polaritons in graphene with hyperbolic phonon polaritons in h-BN, so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon-phonon polaritons. The hyperbolic plasmon-phonon polaritons in graphene/h-BN suffer little from ohmic losses, making their propagation length 1.5-2.0 times greater than that of hyperbolic phonon polaritons in h-BN. The hyperbolic plasmon-phonon polaritons possess the combined virtues of surface plasmon polaritons in graphene and hyperbolic phonon polaritons in h-BN. Therefore, graphene/h-BN can be classified as an electromagnetic metamaterial as the resulting properties of these devices are not present in its constituent elements alone.

Low-loss dielectric-loaded graphene surface plasmon polariton waveguide based biochemical sensor

We have modeled and numerically simulated the performance of a dielectric-loaded graphene surface-plasmon-polariton (DL-GSPP) waveguide as a biochemical sensing device. In our device, the conventionally used gold layer is replaced with a graphene microribbon for the detection of biochemical molecules. The graphene layer is incorporated to minimize ohmic losses and to enhance the adsorption of biomolecules so that the sensor sensitivity is increased significantly. The sensor performance is quantified through numerical simulations carried out by varying device parameters such as waveguide length, effective mode index, dimension of the dielectric ridge, and the length and the number of graphene layers. One of the prominent features of our DL-GSPP waveguide sensor is that its length is in the millimeter range, an essential requirement for realistic plasmonic waveguide sensors. The average sensitivity of DL-GSPP structure is found to be in the range of 3–6 μRIU (refractive index units), which is comparable to the values obtained using surface-plasmon resonance (1–10 μRIU) and long-range waveguide sensors (0.1–5 μRIU).

An all-optical modulation method in sub-micron scale.

We report a theoretical study showing that by utilizing the illumination of an external laser, the Surface Plasmon Polaritons (SPP) signals on the graphene sheet can be modulated in the sub-micron scale. The SPP wave can propagate along the graphene in the middle infrared range when the graphene is properly doped. Graphene's carrier density can be modified by a visible laser when the graphene sheet is exfoliated on the hydrophilic SiO2/Si substrate, which yields an all-optical way to control the graphene's doping level. Consequently, the external laser beam can control the propagation of the graphene SPP between the ON and OFF status. This all-optical modulation effect is still obvious when the spot size of the external laser is reduced to 400 nm while the modulation depth is as high as 114.7 dB/μm.

Terahertz generation from surface plasmon polaritons in graphene induced by a moving electron beam

We studied theoretically the THz radiation emission induced by an electron beam moving atop a graphene sheet based on a structure consisting of 2D square lattice of dielectric cylinders. Numerical evaluation result shows that the THz radiation frequency can be turned in a range of 10THz by adjusting the Fermi level or the filling fraction of the dielectric cylinders, and the peak radiation intensity, which largely depends on the velocity of the electron beam, is the order of 10−3μJ/cm2. These results indicate a promising application in developing the THz radiation source.

Electrically tunable graphene anti-dot array terahertz plasmonic crystals exhibiting multi-band resonances

Graphene-based plasmonic structures feature large tunability, high spatial confinement, and potentially low loss, and are therefore an emerging technology for unconventional manipulation of light. In this paper, we demonstrate electrically tunable terahertz plasmonic crystals consisting of square-lattice graphene periodic anti-dot arrays on a SiO2/Si substrate. Transmission spectroscopy reveals multiple distinct resonances arising from excitations of graphene surface-plasmon–polariton (SPP) modes on different branches of the SPP dispersion curves inherent to the periodic structures. The resonance frequencies are readily tuned electrostatically with the Si back-gate and exhibit the dependency on the carrier density unique to SPP in graphene. Simulations show excellent agreement with the experiments and further illustrate the symmetry-based selection rule for the excited graphene SPP modes. Such graphene plasmonic crystals may lead to a broad range of applications including plasmonic waveguide and transformation optics. Exploiting higher-order graphene SPP modes is an effective way to further facilitate field localization and enhancement.

Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene

The excitation of localized or delocalized surface plasmon polaritons in nanostructured or extended graphene has attracted a steadily increasing attention due to their promising applications in sensors, switches, and filters. These single resonances may couple and intriguing spectral signatures can be achieved by exploiting the entailing hybridization. Whereas thus far only the coupling between localized or delocalized surface plasmon polaritons has been studied in graphene nanostructures, we consider here the interaction between a localized and a delocalized surface plasmon polariton. This interaction can be achieved by two different schemes that reside on either evanescent near- field coupling or far-field interference. All observable phenomena are corroborated by analytical considerations, providing insight into the physics and paving the way for compact and tunable optical components at infrared and terahertz frequencies.

Phase-resolved surface plasmon interferometry of graphene.

The surface plasmon polaritons (SPPs) of graphene reflect the microscopic spatial variations of underlying electronic structure and dynamics. Here, we excite and image the graphene SPP response in phase and amplitude by near-field interferometry. We develop an analytic cavity model that can self-consistently describe the SPP response function for edge, grain boundary, and defect SPP reflection and scattering. The derived SPP wave vector, damping, and carrier mobility agree with the results from more complex models. Spatial variations in the Fermi level and associated variations in dopant concentration reveal a nanoscale spatial inhomogeneity in the reduced conductivity at internal boundaries. The additional SPP phase information thus opens a new degree of freedom for spatial and spectral graphene SPP tuning and modulation for optoelectronics applications.

Giant terahertz gain via surface plasmon polaritons in photoexcited graphene

Giant terahertz gain via surface plasmon polaritons in photoexcited graphene