Efficient coupling of light to graphene plasmons by compressing surface polaritons with tapered bulk materials

Surface-acoustic-wave-driven graphene plasmonic sensor for fingerprinting ultrathin biolayers down to the monolayer limit

Surface plasmon polaritons in graphene can enhance the performance of mid-infrared spectroscopy, which is key for the study of both the composition and the conformation of organic molecules via their vibrational resonances. In this paper, a plasmonic biosensor using a graphene-based van der Waals heterostructure on a piezoelectric substrate is theoretically demonstrated, where far-field light is coupled to surface plasmon-phonon polaritons (SPPPs) through a surface acoustic wave (SAW). The SAW creates an electrically-controlled virtual diffraction grating, suppressing the need for patterning the 2D materials, that limits the polariton lifetime, and enabling differential measurement schemes, which increase the signal-to-noise ratio and allow a quick commutation between reference and sample signals. A transfer matrix method has been used for simulating the SPPPs propagating in the system, which are electrically tuned to interact with the vibrational resonances of the analytes. Furthermore, the analysis of the sensor response with a coupled oscillators model has proven its capability of fingerprinting ultrathin biolayers, even when the interaction is too weak to induce a Fano interference pattern, with a sensitivity down to the monolayer limit, as tested with a protein bilayer or a peptide monolayer. The proposed device paves the way for the development of advanced SAW-assisted lab-on-chip systems combining the existing SAW-mediated physical sensing and microfluidic functionalities with the chemical fingerprinting capability of this novel SAW-driven plasmonic approach.

Excitation of Surface Plasmon Polariton Modes with Double-Layer Gratings of Graphene

A long-range surface plasmon polariton (SPP) waveguide, composed of double-layer graphene, can be pivotal in transferring and handling mid-infrared electromagnetic waves. However, one of the key challenges for this type of waveguide is how to excite the SPP modes through an incident light beam. In this study, our proposed design of a novel grating, consisting of a graphene-based cylindrical long-range SPP waveguide array, successfully addresses this issue using finite-difference time-domain simulations. The results show that two types of symmetric coupling modes (SCMs) are excited through a normal incident light. The transmission characteristics of the two SCMs can be manipulated by changing the interaction of the double-layer gratings of graphene as well as by varying various parameters of the device. Similarly, four SCMs can be excited and controlled by an oblique incident light because this light source is equivalent to two orthogonal beams of light. Furthermore, this grating can be utilized in the fabrication of mid-infrared optical devices, such as filters and refractive index sensors. This grating, with double-layer graphene arrays, has the potential to excite and manipulate the mid-infrared electromagnetic waves in future photonic integrated circuits.

Electrically controllable active plasmonic directional coupler of terahertz signal based on a periodical dual grating gate graphene structure

We propose a concept of an electrically controllable plasmonic directional coupler of terahertz signal based on a periodical structure with an active (with inversion of the population of free charge carriers) graphene with a dual grating gate and numerically calculate its characteristics. Proposed concept of plasmon excitation by using the grating gate offers highly effective coupling of incident electromagnetic wave to plasmons as compared with the excitation of plasmons by a single diffraction element. The coefficient which characterizes the efficiency of transformation of the electromagnetic wave into the propagating plasmon has been calculated. This transformation coefficient substantially exceeds the unity (exceeding 6 in value) due to amplification of plasmons in the studied structure by using pumped active graphene. We have shown that applying different dc voltages to different subgratings of the dual grating gate allows for exciting the surface plasmon in graphene, which can propagate along or opposite the direction of the structure periodicity, or can be a standing plasma wave for the same frequency of the incident terahertz wave. The coefficient of unidirectionality, which is the ratio of the plasmon power flux propagating along (opposite) the direction of the structure periodicity to the sum of the absolute values of plasmon power fluxes propagating in both directions, could reach up to 80 percent. Two different methods of the plasmon propagation direction switching are studied and possible application of the found effects are suggested.

Symmetric Graphene Dielectric Nanowaveguides as Ultra-Compact Photonic Structures

A symmetric graphene plasmon waveguide (SGPWG) is proposed here to achieve excellent subwavelength waveguiding performance of mid-infrared waves. The modal properties of the fundamental graphene plasmon mode are investigated by use of the finite element method. Due to the naturally rounded tips, the plasmon mode in SGPWG could achieve a normalized mode field area of ~10⁻⁵ (or less) and a figure of merit over 400 by tuning the key geometric structure parameters and the chemical potential of graphene. In addition, results show that the modal performance of SGPWG seems to improve over its circular counterparts. Besides the modal properties, crosstalk analysis indicates that the proposed waveguide exhibits extremely low crosstalk, even at a separation distance of 64 nm. Due to these excellent characteristics, the proposed waveguide has promising applications in ultra-compact integrated photonic components and other intriguing nanoscale devices.

Tunable anisotropic plasmon response of monolayer GeSe nanoribbon arrays

Recently, emerging two-dimensional (2D) germanium selenide (GeSe) has drawn lots of attention due to its in-plane anisotropic properties and great potential for optoelectronic applications such as in solar cells. However, methods are still sought to enhance its interaction with light to enable practical applications. Herein, we numerically investigate the localized plasmon response of monolayer GeSe nanoribbon arrays systematically, and the results show that localized surface plasmon polaritons in the far-infrared range with anisotropic behavior can be efficiently excited to enhance the light-matter interaction. We further show that the plasmon response of monolayer GeSe nanoribbons could be tuned effectively through the nanoribbon width, local refractive index, substrate thickness and carrier concentration, pointing out the ways for controlling the localized plasmon response. In the case of monolayer GeSe nanoribbons on a substrate of finite thickness, a Fabry-Pérot-like (FP-like) quantitative model has been proposed to explain the overall spectral response originating from overlapped FP and plasmon modes, and it matches well with the simulation results. All in all, we investigate the plasmon response of the novel 2D GeSe nanoribbons thoroughly for the first time, bringing opportunities for potential applications of novel polarization-dependent optoelectronic devices.

Surface plasmon dispersion engineering for optimizing scattering, emission, and radiation properties on a graphene spherical device

We present a dispersion engineering method based on the rigorous electromagnetic theory to study the scattering properties of a double graphene layer spherical structure. The localized surface plasmons (LSPs) supported by the structure provide resonance channels that lead to an enhancement of the electromagnetic cross section. The method is used to find conditions under which two different multipolar LSP resonances occur at the same frequency value. The superscattering feature under these conditions is revealed by an extraordinary enhancement of the scattering cross section when the structure is illuminated by a plane wave field. Moreover, by studying the behavior of a single emitter localized near the graphene sphere, we show that the spontaneous emission and radiation efficiencies are also largely enhanced when the two different LSP resonances overlap.

Graphene-Coated Nanowire Waveguides and Their Applications

In recent years, graphene-coated nanowires (GCNWs) have attracted considerable research interest due to the unprecedented optical properties of graphene in terahertz (THz) and mid-infrared bands. Graphene plasmons in GCNWs have become an attractive platform for nanoscale applications in subwavelength waveguides, polarizers, modulators, nonlinear devices, etc. Here, we provide a comprehensive overview of the surface conductivity of graphene, GCNW-based plasmon waveguides, and applications of GCNWs in optical devices, nonlinear optics, and other intriguing fields. In terms of nonlinear optical properties, the focus is on saturable absorption. We also discuss some limitations of the GCNWs. It is believed that the research of GCNWs in the field of nanophotonics will continue to deepen, thus laying a solid foundation for its practical application.

Mode Conversion of the Edge Modes in the Graphene Double-Ribbon Bend

In this paper, a new kind of graphene double-ribbon bend structure, which can support two edge graphene surface plasmons (EGSPs) modes, is proposed. In this double-ribbon bend, one edge mode can be partly converted into another one. We attribute the mode conversion mechanism to the interference between the two edge plasmonic modes. Based on the finite element method (FEM), we calculate the transmission and loss of EGSPs propagating along this graphene double-ribbon bend in the mid-infrared range under different parameters.

Chasing Plasmons in Flatland

Two-dimensional layered crystals, including graphene and transition metal dichalcogenides, represent an interesting avenue for studying light-matter interactions at the nanoscale in confined geometries. They offer several attractive properties, such as large exciton binding energies, strong excitonic resonances, and tunable bandgaps from the visible to the near-IR along with large spin-orbit coupling, direct band gap transitions, and valley-selective responses.

Real-space mapping of mid-infrared near-field of Yagi-Uda antenna in the emission mode

By using transmission-mode, scattering-type scanning near-field optical microscopy, we characterize the mid-infrared near-field properties of a Yagi-Uda antenna in the emission mode. The underlying near-field properties, including the near-field dipole-dipole coupling between antenna elements, are clearly observed. Moreover, even though most of the radiation energy is emitted into the substrate, by adopting two detector antennas, we managed to verify the unidirectionality and frequency-selectivity of the Yagi-Uda antenna in the air side. All the experimental results presented in this work are in good qualitative agreement with our numerical simulations. Our work on the Yagi-Uda antenna could help lead to novel methods for mid-infrared material analysis and bio-sensing. It should also be applicable in all-optical processing like radiation routers or a chromatic discriminator.

High-efficiency modulation of coupling between different polaritons in an in-plane graphene/hexagonal boron nitride heterostructure

Two-dimensional van der Waals (vdW) materials have a full set of highly confined polariton modes, such as low-loss phonon polaritons and dynamically tunable graphene plasmons, which provide a solution for integrated nanophotonic devices by combining the unique advantages of different polaritons. Highly efficient coupling between these complementary polaritons is key to realize the nanoscale optical integration. However, fluctuations of permittivity or geometry at the abrupt interfaces have been demonstrated as perturbations or scatters of polaritons. Here, in-plane plasmon-phonon polariton coupling in an in-plane graphene/hexagonal boron nitride (BN) heterostructure is studied using a full-wave electromagnetic numerical model. Transmittance between different polaritons is proportional to momentum matching, which can be tuned using the graphene Fermi energy. The transmittance between a graphene plasmon and a BN phonon polariton can be controlled between 0% and 100% within the upper Reststrahlen band of the BN. This is central to many photon devices, such as waveguides, wavefront shapers, filters, modulators and switches. Moreover, we simulate near-field interference patterns in an in-plane heterostructure based on the theoretical dispersion relation of polaritons, enabling scattering scanning near-field optical microscopy a potential experimental method to investigate the coupling between different polaritons. This study provides a theoretical basis for efficient coupling of propagation and modulation between different polaritons in in-plane heterostructures of vdW materials, which could pave a way to design nanoscale multi-functional waveguide devices in integrated photonic systems.

Conversion from terahertz-guided waves to surface waves with metasurface

Surface waves (SWs) have attracted a widespread attention due to the characteristic of subwavelength confinement and convenient manipulation in photonic integrated circuits. Though metasurface provides a powerful tool in realizing the conversion between freely propagating waves and surface modes in recent years, a gulf between guided waves (GWs) and SWs in terahertz (THz) range still exists as a bottleneck for on-chip photonic integrated devices. Here, we implemented the conversion from THz GWs to SWs through the coupling of a lithium niobate (LN) subwavelength waveguide and metasurface antennas on an all-feature on-chip THz integrated platform. The conversion process and transmission mode of the THz waves were directly visualized via a time-resolved imaging system. Based on the dynamic process, the formation of SWs could be clarified through analyzing the dispersion relation of propagating modes, which is in good agreement with numerical models. In further, relying on the numerical simulation, SWs were induced from the collective oscillations of the metasurface antenna array and the maximum coupling efficiency was around 62.6 percent. Our work provides an efficient approach to control of GWs, and promotes the practicability of THz surface integrated devices, including THz surface spectroscopy sensing.

Strong optical force and its confinement applications based on heterogeneous phosphorene pairs

We study the plasmonic properties of face-to-face phosphorene pairs, including their optical constraints and optical gradient forces. The symmetric and anti-symmetric plasmonic modes occur due to the strong anisotropic dispersion of phosphorene. Compared with the anti-symmetric mode, the symmetric mode has a stronger optical constraint and much larger gradient force. Especially, the optical constraint of the symmetric mode can even reach as high as 96% when the two phosphorene layers are along the armchair and zigzag direction respectively. We also propose a scheme of an ultra-small phase shifter using phosphorene-based photonic devices.

Mid-infrared subwavelength modulator based on grating-assisted coupling of a hybrid plasmonic waveguide mode to a graphene plasmon

This work reports a mid-infrared modulator based on a hybrid plasmonic waveguide with graphene on a grating in its slot region. The modulator utilizes a graphene plasmon for electro-optic tuning in a more practical and effective way than graphene-plasmon-based waveguide devices studied up to now. The hybrid plasmonic waveguide can be easily and efficiently integrated with input and output photonic waveguides. It supports a hybrid plasmonic waveguide mode and a graphene-plasmon-based waveguide mode. Grating-assisted coupling of the former to the latter in it is demonstrated to work successfully even though the two modes have significantly different propagation constants and losses. Theoretical investigation of the modulator shows that the coupling via the grating of length 5.92 μm generates a deep rejection band at a wavelength of 8.014 μm in the transmission spectrum of the output photonic waveguide of the modulator. With the graphene chemical potential tuned between 0.6 eV and 0.65 eV, the transmission at the wavelength is modulated between -27 dB and -1.8 dB. The subwavelength modulator, which may have a large bandwidth and small energy consumption, is expected to play a key role in free-space communications and sensing requiring mid-infrared integrated photonics.

Tunable graphene plasmonic Y-branch switch in the terahertz region using hexagonal boron nitride with electric and magnetic biasing

A tunable graphene plasmonic Y-branch switch at THz wavelengths is proposed. The effects of magnetic and electric biasing are studied to harness the transmission of the transverse electric and magnetic guided mode resonances. In the structure, hexagonal boron nitride is utilized as a substrate for graphene. The application of hexagonal boron nitride, with the advantages of high mobility and ultralow ohmic loss, introduces a promising alternative substrate for graphene. Analytical and numerical results show that, by slight variation of the doping level in graphene through magnetic and electric biasing, the characteristics of the propagation of the guided mode resonances can be manipulated. A large extinction ratio of 40 dB at a wavelength of 60 μm is obtained. Besides, the proposed switch shows a low insertion loss of about 1 dB and a relatively large optical bandwidth of 1 μm. The electric biasing is of the order of 0.1 mV. Additionally, with the presence of magnetic biasing, a compact switch with a size of 25 μm is achieved. Showing a high extinction ratio, low insertion loss, and compact size, the proposed switch can find potential applications in graphene plasmonics integrated devices.

Strong plasmonic confinement and optical force in phosphorene pairs

The plasmonic responses in the spatially separated phosphorene (single-layer black phosphorus) pairs are investigated, mainly containing the field enhancement, light confinement, and optical force. It is found that the strong anisotropic dispersion of black phosphorus gives rise to the direction-dependent symmetric and anti-symmetric plasmonic modes. Our results demonstrate that the symmetrical modes possess stronger field enhancement, higher light confinement, and larger optical force than the anti-symmetric modes in the nanoscale structures. Especially, the light confinement ratio and optical force for the symmetric mode along the armchair direction of black phosphorus can reach as high as >90% and >3000 pN/mW, respectively. These results may open a new door for the light manipulation at nanoscale and the design of black phosphorus based photonic devices.

Second harmonic generation in graphene-coated nanowires

We study second harmonic generation in a pair of graphene-coated nanowires. We show that the phase matching condition for harmonic generation can be engineered in a wide range of frequencies by tuning the spacing between graphene nanowires. We derive coupled mode equations describing the process of second harmonic generation using an unconjugated Lorentz reciprocity theorem. We show that the highest harmonic generation efficiency can be achieved by phase matching the fundamental mode with the two lowest order symmetric modes at the second harmonic frequency. Despite losses in graphene, we predict that the efficiency can be further enhanced by reducing the radius of nanowires due to larger mode overlap and lower propagation loss.

Modal evolution in asymmetric three- and four-layer plasmonic waveguides

Through the employment of a novel approach in solving the dispersion for the three-layer plasmonic waveguides, considering lossy metals, we demonstrate that, besides well-known modes, the complete dispersion always contains high-lossy periodic solutions. Consideration of these solutions is shown to be crucial for the understanding of every aspect of dispersion evolution at broad spectral range when the thickness of the middle layer is varied. In particular, we show that generally considered modes of the three-layer waveguide transform into the single interface modes via interaction with high-lossy periodic solutions. Furthermore, the negative index mode is shown to experience a transition between low- and high-lossy regimes depending on the waveguide's thickness. Our results, avoiding complicated analytical analysis, perfectly integrate and importantly complement past theoretical works.

Tunable tapered waveguide for efficient compression of light to graphene surface plasmons

Dielectric-graphene-dielectric (DGD) structure has been widely used to construct optical devices at infrared region with features of small footprint and low-energy dissipation. The optical properties of graphene can be manipulated by changing its chemical potential by applying a biased voltage onto graphene. However, the excitation efficiency of surface wave on graphene by end-fire method is very low because of large wavevector mismatch between infrared light and surface wave. In this paper, a dielectric-semiconductor-dielectric (DSD) tapered waveguide with magnetic tunability for efficient excitation of surface waves on DGD at infrared region is proposed and analyzed. Efficient excitation of surface waves on DGD with various chemical potentials in graphene layer and incident frequencies can be attained by merely changing the external magnetic field applied onto the DSD tapered waveguide. The electromagnetic simulations verify the design of the proposed structure. More importantly, the constituent materials used in the proposed structure are available in nature. This work opens the door toward various applications in the field of using surface waves.

Localized Surface Plasmons in Nanostructured Monolayer Black Phosphorus

Plasmonic materials provide electric-field localization and light confinement at subwavelength scales due to strong light-matter interaction around resonance frequencies. Graphene has been recently studied as an atomically thin plasmonic material for infrared and terahertz wavelengths. Here, we theoretically investigate localized surface plasmon resonances (LSPR) in a monolayer, nanostructured black phosphorus (BP). Using finite-difference time-domain simulations, we demonstrate LSPRs at mid-infrared and far-infrared wavelength regime in BP nanoribbon and nanopatch arrays. Because of strong anisotropic in-plane properties of black phosphorus emerging from its puckered crystal structure, black phosphorus nanostructures provide polarization dependent, anisotropic plasmonic response. Electromagnetic simulations reveal that monolayer black phosphorus nanostructures can strongly confine infrared radiation in an atomically thin material. Black phosphorus can find use as a highly anisotropic plasmonic devices.

Tunable Band-Stop Filters for Graphene Plasmons Based on Periodically Modulated Graphene

Tunable band-stop filters based on graphene with periodically modulated chemical potentials are proposed. Periodic graphene can be considered as a plasmonic crystal. Its energy band diagram is analyzed, which clearly shows a blue shift of the forbidden band with increasing chemical potential. Structural design and optimization are performed by an effective-index-based transfer matrix method, which is confirmed by numerical simulations. The center frequency of the filter can be tuned in a range from 37 to 53 THz based on the electrical tunability of graphene, while the modulation depth (−26 dB) and the bandwidth (3.1 THz) of the filter remain unchanged. Specifically, the bandwidth and modulation depth of the filters can be flexibly preset by adjusting the chemical potential ratio and the period number. The length of the filter (~750 nm) is only 1/9 of the operating wavelength in vacuum, which makes the filter a good choice for compact on-chip applications.

Terahertz and mid-infrared reflectance of epitaxial graphene

Graphene has emerged as a promising material for infrared (IR) photodetectors and plasmonics. In this context, wafer scale epitaxial graphene on SiC is of great interest in a variety of applications in optics and nanoelectronics. Here we present IR reflectance spectroscopy of graphene grown epitaxially on the C-face of 6H-SiC over a broad optical range, from terahertz (THz) to mid-infrared (MIR). Contrary to the transmittance, reflectance measurements are not hampered by the transmission window of the substrate, and in particular by the SiC Reststrahlen band in the MIR. This allows us to present IR reflectance data exhibiting a continuous evolution from the regime of intraband to interband charge carrier transitions. A consistent and simultaneous analysis of the contributions from both transitions to the optical response yields precise information on the carrier dynamics and the number of layers. The properties of the graphene layers derived from IR reflection spectroscopy are corroborated by other techniques (micro-Raman and X-ray photoelectron spectroscopies, transport measurements). Moreover, we also present MIR microscopy mapping, showing that spatially-resolved information can be gathered, giving indications on the sample homogeneity. Our work paves the way for a still scarcely explored field of epitaxial graphene-based THz and MIR optical devices.

Investigation of plasmonic properties of graphene multilayer nano-ribbon waveguides

In this paper, we investigate the plasmonic properties of a graphene-silica-silicon (G-SiO₂-Si) multilayer nano-ribbon waveguide in the mid-IR spectral range using the finite element method. Numerical results show that single-mode operation and modal cut-off properties of the G-SiO₂-Si are highly sensitive to the width and chemical potential. In particular, we demonstrate that by properly tuning the geometric and material parameters of the spacer layer or by decreasing the operation frequency, the graphene-based waveguide exhibits a propagation length higher than that of its metal-based counterpart. We believe that this study will provide a valuable reference for designing ultra-compact and low-loss graphene-based novel integrated plasmonic devices.

Plasmonically induced magnetic field in graphene-coated nanowires

In this Letter, we investigate a magnetic field induced by guiding plasmonic modes in graphene-coated nanowire via an inverse Faraday effect. Magnetic field distribution for different plasmonic modes has been calculated. It has been shown that a magnetic field has a vortex-like distribution for some plasmonic modes. The possibility of producing magnetic field distribution that rotates along the nanowire axis and periodically depends on azimuthal angle has been demonstrated.

Graphene circular polarization analyzer based on unidirectional excitation of plasmons

In this paper we propose a method of unidirectional excitation of graphene plasmons via metal nanoantenna arrays and reveal its application in a circular polarization analyzer. For nanoantenna pairs with orthogonal orientations, the graphene plasmons are excited through antenna resonances with the direction of propagation can be controlled by incident polarization. On the other hand, based on the spiral shape distribution of antenna arrays, a circular polarization analyzer can be obtained via the interaction of geometric phase effect of antenna arrays and the chirality carried by incident polarization. By utilizing the unidirectional excitation of plasmons, the extinction ratio of analyzer can be improved to over 10³, which is at least an order of magnitude larger than the result of antenna pairs with same orientations or antenna arrays with closed circular shape formation. The proposed analyzer may find applications in analyzing chiral molecules using different circularly polarized waves.

Graphene circular polarization analyzer based on spiral metal triangle antennas arrays

In this paper we propose a circular polarization analyzer based on spiral metal triangle antenna arrays deposited on graphene. Via the dipole antenna resonances, plasmons are excited on graphene surface and the wavefront can be tailed by arranging metal antennas into linetype, circular or spiral arrays. Especially, for spiral antenna arrays, the geometric phase effect can be cancelled by or superposed on the chirality carried within circular polarization incidence, producing spatially separated solid dot or donut shape fields at the center. Such a phenomenon enables the graphene based spiral metal triangle antennas arrays to achieve functionality as a circular polarization analyzer. Extinction ratio over 550 can be achieved and the working wavelength can be tuned by adjusting graphene Fermi level dynamically. The proposed analyzer may find applications in analyzing chiral molecules using different circularly polarized waves.

Plasmonic bandpass filter based on graphene nanoribbon

A plasmonic bandpass filter based on graphene is proposed and numerically investigated using the finite-difference time-domain method. The proposed filter has a very simple structure, including two graphene nanoribbon waveguides laterally coupled to a graphene ribbon resonator. The transmission efficiency can be tuned by altering the coupling distance between the ribbons. At the same time, the variation of the transmission spectra is investigated by tuning the size of the graphene resonant ribbon. Notably, due to the unique electronic tunability of graphene, the transmission spectra can be freely tuned in a broad frequency range by choosing the chemical potential, which exhibits more flexible tunability than that used in conventional metallic devices. Attributed to the standing wave distribution of different modes excited in the graphene resonant ribbon, the proposed filter can be used for the plasmonic device with the capability of band selection or power splitting by locating the output waveguide ports in the suitable positions.

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.

Analytical model for plasmon modes in graphene-coated nanowire

An analytical model for plasmon modes in graphene-coated dielectric nanowire is presented. Plasmon modes could be classified by the azimuthal field distribution characterized by a phase factor exp(imφ) in the electromagnetic field expression and eigen equation of dispersion relation for plasmon modes is derived. The characteristic of plasmon modes could be tuned by changing nanowire radius, dielectric permittivity of nanowire and chemical potential of graphene. The proposed model provides a fast insight into the mode behavior of graphene-coated nanowire, which would be useful for applications based on graphene plasmonics in cylindrical waveguide.