Graphene Surface Plasmon Polaritons Research Articles

Nonlinear Optical Bistability Based on Surface Plasmons with Nonlinear Dirac Semimetal Substrate

In this paper, we theoretically investigated the low-threshold and controllable optical bistability (OB) of a graphene-based Otto configuration with a nonlinear three-dimensional Dirac semimetal (3D DSM) as the substrate. The combined effect of the excitation of surface plasmon polaritons (SPPs) in graphene and the very high third-order nonlinear conductivity of the 3D DSM enabled this scheme to achieve a relatively low optical bistability threshold. At the same time, this simple multilayer structure showed the tunability of OB due to the fact that the reflectance could be modulated by regulating the Fermi energy of the 3D DSM. Furthermore, we also found that the OB hysteresis curve was closely related to the relaxation time of the 3D DSM and the thickness of the air layer. We believe that this multilayer configuration could provide a reference idea for devising a bistable device.

Electric and magnetic metal-insulator-metal metasurfaces in the mid-infrared based on Babinet’s, Lorentz’s, and Kirchhoff’s principles

Metasurfaces can extend the optical properties of conventional materials by structuring surfaces at a subwavelength scale. These artificial subwavelength surfaces mimic the physics of conventional materials and can, in principle, be designed to provide novel optical material properties. Metal-insulator-metal (MIM) antenna metasurfaces are among the most widely used as ideal absorbers and emitters. In this work, we present MIM metasurfaces in the mid-infrared that comply in the electric and magnetic forms of Babinet’s, Lorentz’s, and Kirchhoff’s principles. To verify the validity of Babinet's, Lorentz's, and Kirchhoff's MIM metasurfaces, we computed their reflection and absorption spectra as well as electric and magnetic field maps. We found that even in the presence of graphene on top of the electric and magnetic MIM metasurfaces, these principles still hold qualitatively. However, the excitation of gap surface plasmon polaritons (SPPs) and graphene SPPs fails to comply quantitatively. Additionally, we fabricated the MIM metasurfaces and used imaging Fourier transform infrared spectroscopy in the mid infrared spectrum to validate them. Finally, we explore the potentials and limits of the use of graphene as tunability material, with a tunability bandwidth up to 0.6 µm. Our findings can be applied to the development of electric and magnetic frequency selectivity metasurfaces, polarizers, coherent thermal sources, and detectors.

Propagating surface plasmon polaritons in graphene under applied uniform strain

In this work, we theoretically investigate the propagation length of plasmon waves in graphene layer under uniform strain surrounded by two dielectric media of dielectric constants ε1 and ε2, respectively. The plasmon losses (plasmon damping), plasmon propagation length and the penetration depth of the electric field associates with the charge fluctuations can be controlled by varying the direction and the strength of the applied strain and the direction of the plasmon wave propagation with respect to the direction of the applied strain. Because strain induces anisotropy in graphene optical conductivity, the strain-dependent orientation plays an important role to manipulate the direction and variations of the graphene plasmon energy, which may be useful to tune graphene properties in plasmonic devices to enhance light-matter interaction.

Analytical calculation of beam profile and orbital angular momentum spectrum of Laguerre Gaussian beams reflected from a graphene plasmonic structure.

In this paper, Laguerre Gaussian (LG) beams with different topological charges are used for excitation of surface plasmon polaritons (SPPs) through a graphene layer inserted in the Otto-configuration. By utilizing the angular spectrum representation (ASR) and Lorenz-gauge vector potential, an explicit analytical expression is derived for the electromagnetic fields of the reflected beam. At the optimal excitation state of graphene SPPs, the reflected beam exhibits a distinctive field profile characterized by two identical crescent-shaped lobes separated by a vertical strip with null intensity. Furthermore, in the absence of external magnetic field, the orbital angular momentum (OAM) spectrum of the reflected beam at the optimal excitation of SPPs reveals the annihilation of central OAM mode and the generation of two equal OAM sidebands, regardless of the incident OAM topological charge. Furthermore, the phase distributions of electric field of the reflected beam confirm the existence of OAM sidebands in the vicinity of optimal SPPs excitation. As the system is taken away from the optimal excitation of SPPs by introduction of an external magnetic field or increasing the chemical potential or increasing the incident angle, both central and sideband modes appear in the OAM spectrum of the reflected beam. In this case, when the topological charge of the incident wave increases, the weight of central OAM mode decreases while the weight of sidebands increases. In contrast, in the presence of external magnetic field, at the optimal excitation of SPPs, both central OAM and sidebands modes exist in the reflected beam such that the weight of central modes increases with the external magnetic field. This effect is also confirmed by plotting the phase distributions of the reflected beam at different external magnetic fields and for different incident topological charges. Therefore, the manipulation of graphene plasmons characteristics leads to the control of OAM sideband generation.

Dual-band, high sensitivity, angle-insensitive graphene—Perfect absorber based on surface plasmon resonance

We propose a perfect absorber of dual-band, high sensitivity and angle-insensitive based on surface plasmon polaritons (SPP) in monolayer graphene. The structure is composed of the metamaterial and graphene with stable performance. The absorption properties of the structure are theoretically investigated by simulation. Perfect absorption is achieved in the laser band range of 10.6 μm and the mid-infrared range of 7.54 μm. At the same time, the absorption peaks can be tuned by adjusting the structural parameters and the Fermi energy level of the graphene. In the simulation, the absorption performance of this structure is insensitive to angles, where both of the absorption peaks remain 95 % in the incident angle range of 0– 50°. Moreover, the refractive index sensitivity of M1 and M2 can reach 3000 nm/RIU and 2000 nm/RIU, respectively. This research provides an effective solution for the development of mid-infrared optical devices and compatible camouflage application based on graphene.

Significant Enhancement of Near-Field Radiative Heat Transfer by Misaligned Bilayer Heterostructure of Graphene-Covered Gratings

Abstract The near-field radiative heat transfer of heterostructure consisting of SiC gratings and graphene is investigated in this work. The rigorous coupled-wave analysis is employed to calculate the spectral heat flux. Nevertheless, monolayer heterostructure and nonmisaligned bilayer heterostructure consistently suffer from a lack of spectral heat flux. In this work, we investigate the prominent effect of misaligned bilayer heterostructure in enhancing near-field radiative heat transfer by plotting energy transmission coefficients and electromagnetic fields. The results show that when the misalignment reaches half a period, the bilayer heterostructure exhibits optimal performance with a total heat flux of 3.5 × 104 W/m2. Besides the well-known coupled surface phonon polaritons supported by SiC gratings, the surface plasmon polaritons supported by graphene dominate the enhancement of heat flux from 0.01 × 1014 rad/s to 1.5 × 1014 rad/s. Due to the spatial misalignment of the upper and lower gratings, the lower layer graphene surface plasmon polaritons are intensified, compensating for the lack of spectral heat flux. Meanwhile, the graphene surface plasmon polaritons and SiC surface phonon polaritons can be hybridized to form surface plasmon-phonon polaritons. In addition, the dynamic modulation of near-field radiative heat transfer in the misalignment state is achieved by manipulating the Fermi level of graphene. We finally show that the superiority of misaligned heterostructure is robust with respect to the frequency shift in the phonon band, providing an effective way to improve the near-field radiative heat transfer in different configuration.

Magnetically Tunable Goos–Hänchen Shift of Reflected Beam in Multilayer Structures Containing Anisotropic Graphene

In this paper, the magnetically tunable Goos–Hänchen (GH) shift of a reflected beam at terahertz frequencies is achieved by using a multilayer structure where three layers of anisotropic graphene are inserted. The enhanced GH shift phenomenon results from the local field enhancement owing to the excitation of graphene surface plasmon polaritons at the interface between two dielectric materials. By considering the quantum response of graphene, the GH shift can be switched from negative to positive by harnessing the anisotropic conductivity of graphene, and the GH shift can be actively tuned through the external magnetic field or by controlling the structural parameters. By setting appropriate magnetic field and structural parameters, we can obtain GH values of −140 microns to 220 microns in the terahertz band. This enhanced and tunable GH shift is promising for fabricating graphene-based terahertz shift devices and other applications in nanophotonics.

Role of Local Conductivities in the Plasmon Reflections at the Edges and Stacking Domain Boundaries of Trilayer Graphene.

We employed infrared scattering-type scanning near-field optical microscopy (IR-sSNOM) to study surface plasmon polaritons (SPPs) in trilayer graphene (TLG). Our study reveals systematic differences in near-field IR spectra and SPP wavelengths between Bernal (ABA) and rhombohedral (ABC) TLG domains on SiO2, which can be explained by stacking-dependent intraband conductivities. We also observed that the SPP reflection profiles at ABA-ABC boundaries could be mostly accounted for by an idealized domain boundary defined by the conductivity discontinuity. However, we identified distinct shapes in the SPP profiles at the edges of the ABA and ABC TLG, which cannot be solely attributed to idealized edges with stacking-dependent conductivities. Instead, this can be explained by the presence of various edge structures with local conductivities differing from those of bulk TLGs. Our findings unveil a new structural element that can control SPP, and provide insights into the structures and electronic states of the edges of few-layer graphene.

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.

Strong plasmon − phonon coupling for graphene/ hBN thermal emitter atomic system

The surface plasmon polaritons of graphene coupled with hyperbolic phonon polaritons of hexagonal boron nitride (hBN) have been considered as the ideal platform to enhance thermal emitter, which provides a powerful tool to implement energy conversion and thermal management. The conventional approaches for the strong plasmon − phonon coupling rely on the bulk hBN materials, which usually have a large footprint and display little tunability. Recently, hBN atomic emitter has been demonstrated that its peak emissivity is hopefully as high as the bulk hBN emitters. Here, we propose a graphene/hBN thermal emitter atomic system to flexibly modify the spectral emissivity by the strong plasmon − phonon coupling effect, which can be separately manipulated by the graphene width, chemical potential of graphene, number of hBN atomic layers and hBN width. Our scheme is hopefully realizing a comparable function with the bulk graphene/hBN system. Furthermore, we employ coupled oscillator model involving three oscillators to investigate the energy exchange and mode evolution between three plasmon − phonon hybridized modes, providing an excellent agreement with simulated and theoretical results. Consequently, optically manipulating plasmon − phonon interaction opens a broad design space for the spectral emissivity control, which explores the mid-infrared applications of advanced graphene thermo-optoelectronics and electrically driven thermal emitters.

Tunable Fano resonance and optical switching in the one-dimensional topological photonic crystal with graphene

A hybrid structure composed of a grating coupled graphene structure and two one-dimensional photonic crystals (PhCs) is investigated, where the topological edge state (TES) and the graphene surface plasmon polariton (GSPP) are coupled to generate Fano resonances. The grating coupled graphene structure is used to excite the GSPP and provides a broad resonance. The two PhCs are designed to possess opposite topological properties; thus, the TES appears at the interface and exhibits a narrow resonance. The constructive and destructive interference between the GSPP and the TES results in the Fano resonance. By analyzing the resonant behaviors, it is found that the line shape of Fano resonance can be actively tuned by the graphene Fermi energy. We apply our results to the optical switching, a high-performance optical switch is achieved, and the modulation depth can reach as high as 23.31 dB. In addition, owing to the characteristic of Fano resonance with steep dispersion and asymmetric profile, our designs might offer an alternative strategy to achieve potential applications in sensors, filters, optical switches, and slow-light devices.

Modified dispersion for graphene plasmon polariton in hydrodynamic model without potential notation

A hydrodynamic model, which discards potential notation but couples with the full Maxwell's equations and boundary conditions, was proposed. The method took into account magnetic field but ascertained the type of surface plasmon-polaritons in the monolayer graphene. Utilizing the method, we investigated the spectrum of surface plasmon-polariton with or without the external magnetic field and found that the plasmon-polariton spectrum was suppressed compared with the traditional method. In the infrared and ultraviolet region, the fluence of external magnetic field can be ignored. There was an uplift in the transition region, which is roughly around q0∼1, which is attributed to the external magnetic field. Finally, the surface plasmon-polariton spectrum in the ultraviolet region was dominated by the nonlocal effect.

Near-field radiative heat transfer between on-substrate graphene sheets

A promising material for applications in near-field radiative heat transfer is graphene, due to large heat flux values and the capability to actively control the heat flux using various mechanisms such as applying a bias voltage. Theoretical studies have shown that a heat transfer coefficient as large as ∼1500 W/m2K can be modulated with a ratio of ∼100 for two graphene sheets at 300 K, free-standing in vacuum, with a gap of 100 nm. However, it is not clear how the heat transfer coefficient and the modulation ratio are affected in the presence of a substrate which needs to be used in practice. We study the effect of the presence of substrates on near-field radiative heat flux among two single-layer sheets of graphene. We determine the complex dielectric function that corresponds to maximal heat flux for an emitted electromagnetic mode. We compute the heat flux and modulation ratio for 41 different substrates selected from common dielectric, metallic and semiconducting materials and show that the heat flux and the modulation ratio both reduce in the presence of a substrate. The dielectric substrates such as BaF2, KCl, NaF, RbCl and RbBr have the largest modulation ratio and heat flux among the selected substrates. The low-frequency and high-frequency dielectric functions of these substrates are closest to the free space, and their dispersion occurs at low frequencies far from the spectral location of the surface plasmon polaritons of graphene. For low and high graphene sheet temperatures of 300 K and 400 K, respectively, and a separation gap of 100 nm, the largest heat coefficient (= 1436 W/m2K) is obtained for BaF2 with a modulation ratio of 20.3. The largest modulation ratio at the same temperatures and gap size is 22.5, which is obtained for NaF with a heat transfer coefficient of 1406 W/m2K.

Multi-channel THz perfect absorber using graphene-based Fibonacci photonic crystals

A graphene-based multi-channel THz perfect absorber is proposed in this paper. The absorber consists of a graphene layer, a Fibonacci quasi-periodic layer, a spacer, and a substrate. We demonstrate that the structure we proposed can lead to multi-channel perfect THz absorption because of the graphene surface plasmon polaritons and multiple photonic stop bands in this structure. The multi-channel working frequencies and absorption peaks can be flexibly tuned by controlling the incidence angle, size of component materials, and Fermi energy. Moreover, by adjusting the Fibonacci quasi-period orders of the structure, the number of working channels can be flexibly expanded without reoptimizing the structure size. Moreover, by adjusting the Fibonacci quasi-period orders of the structure, the number of working channels can be flexibly expanded without reoptimizing the structure size. Using existing technology, our design scheme is easy to realize, which will be helpful to promote the development and application of novel tunable optoelectronic devices.

Performance improvement of three-body radiative diodes driven by graphene surface plasmon polaritons.

As an analogue to an electrical diode, a radiative thermal diode allows radiation to transfer more efficiently in one direction than in the opposite direction by operating in a contactless mode. In this study, we demonstrated that within the framework of three-body photon thermal tunneling, the rectification performance of a three-body radiative diode can be greatly improved by bringing graphene into the system. The system is composed of three parallel slabs, with the hot and cold terminals of the diode coated with graphene films and the intermediate body made of vanadium dioxide (VO2). The rectification factor of the proposed radiative thermal diode reaches 300% with a 350 nm separation distance between the hot and cold terminals of the diode. With the help of graphene, the rectification performance of the radiative thermal diode can be improved by over 11 times. By analyzing the spectral heat flux and energy transmission coefficients, it was found that the improved performance is primarily attributed to the surface plasmon polaritons (SPPs) of graphene. They excite the modes of insulating VO2 in the forward-biased scenario by forming strongly coupled modes between graphene and VO2 and thus dramatically enhance the heat flux. However, for the reverse-biased scenario, the VO2 is at its metallic state, and thus, graphene SPPs cannot work by three-body photon thermal tunneling. Furthermore, the improvement was also investigated for different chemical potentials of graphene and geometric parameters of the three-body system. Our findings demonstrate the feasibility of using thermal-photon-based logical circuits, creating radiation-based communication technology and implementing thermal management approaches at the nanoscale.

Slow-light effects based on the tunable Fano resonance in a Tamm state coupled graphene surface plasmon system.

We theoretically realize the tunable Fano resonance in a hybrid structure that allows the coupling between Tamm plasmon-polaritons (TPPs) and graphene surface plasmon-polaritons (SPPs). In this coupling system, a distributed Bragg reflector (DBR)/Ag structure is designed to generate the TPP with a narrow resonance, and the graphene SPP is excited by grating coupling with a broad resonance. The overlap of these two kinds of resonances results in the Fano resonance with a high-quality factor close to 1500. The behaviors of the Fano resonance are discussed carefully, and the results show that both the graphene Fermi level and the incidence angle can actively tune the profile of the Fano resonance. Owing to the ultrasharp spectrum of the tunable Fano resonance, our design may offer an alternative strategy for developing various optoelectronic devices such as filters, sensors, and nonlinear and slow-light devices. Finally, as an example of the potential applications, we apply the tunable Fano resonance to the slow-light effect, a high performance slow-light effect can be achieved, and the group delay can reach up to 52 ps.

Active tuning hBN phonon polaritons and spontaneous emission rates based on VO<sub>2</sub> and graphene

<sec>Active tunability of phonon dispersion and spontaneous emission (SE) are still open problems due to their exciting potential applications. In view of the fact that polaritons are very sensitive to the dielectric environment, in this study, with the help of the differences in optical property between the phase change material vanadium dioxide (VO<sub>2</sub>) during the phase transition from the insulating state to metallic state and the tunable surface plasmon polaritons (SPPs) in graphene, a heterostructure composed of hyperbolic material hexagonal boron nitride (hBN) and graphene and VO<sub>2</sub> is proposed to investigate the active tunability of hBN phonon polaritons (PhPs). In order to illustrate the underlying physical mechanism of the above heterostructures, the dispersion distributions of the above heterostructures are calculated and represented by the imaginary part of the p-polarized Fresnel reflection coefficient of the heterostructure, meanwhile the dispersion relation of the hBN/VO<sub>2</sub> heterostructure in hyperbolic region is verified by the quasi-static approximation method.</sec><sec>Results indicate that the active tunability of hBN PhPs inside type-I and type-II hyperbolic bands can be achieved by controlling VO<sub>2</sub> phase transition in hBN/VO<sub>2</sub> heterostructure. The PhP dispersion change of the hBN/VO<sub>2</sub> heterostructure is mainly caused by the change of the VO<sub>2</sub> dielectric function when VO<sub>2</sub> substrate changes from the insulating state into metallic state, which affects the total Fresnel reflection coefficient of the heterostructure, finally resulting in the PhP dispersion change of hBN/VO<sub>2</sub> heterostructure. When graphene is introduced into the hBN/VO<sub>2</sub> heterostructure, coupled hyperbolic plasmon-phonon polaritons (HPPPs) are obtained within type-I and type-II hyperbolic band of hBN, while the surface plasmon-phonon polaritons (SPPPs) are generated outside its hyperbolic bands. Moreover, comparative analysis of SE rates is presented for a quantum emitter positioned with the hBN/VO<sub>2</sub> and graphene/hBN/VO<sub>2</sub> heterostructure, revealing that the SE rates of these heterostructures can be modulated by the passive means including changing the hBN thickness and distance between the dipole emitter and the proposed heterostructure, and also by the active means including tuning VO<sub>2</sub> phase states and graphene chemical potential without changing structural configurations. This study provides a theoretical guidance in realizing active tunability of both phonon dispersion and SE rate of the natural or artificial anisotropic optical materials by using functional materials including phase change materials and graphene.</sec>

An electrical/thermal dual-controlled quad-functional terahertz metasurface absorber.

Although the design of graphene-based tunable broadband terahertz (THz) absorbers has attracted much attention, improving the functionality of the absorbers to adapt to different scenarios is still worth studying. This paper presents an innovative design of a quad-functional metasurface absorber (QMA) in the THz region, which can switch the absorption frequency/band by means of dual voltage/thermal manipulation. By electrically manipulating the chemical potential of graphene, the QMA can switch freely between the narrowband absorption mode ("NAM") and the broadband absorption mode ("BAM"), while thermally manipulating the phase transition of VO2 allows switching between the low-frequency absorption mode ("LAM") and the high-frequency absorption mode ("HAM"). Detailed mechanistic analysis shows that the "NAM" and "BAM" are due to the switching of the fundamental and second order graphene surface plasmon polariton (SPP) resonances, respectively, and the switching between "LAM" and "HAM" is due to the phase transformation of VO2. Furthermore, the QMA is polarization insensitive in all absorption modes and maintains excellent absorption performance at large angular incidence of TE- and TM-polarized waves. All the results indicate that the proposed QMA has great potential for stealth, sensing, switching, and filtering applications.

An Innovative method for adjustable broadband THz to Mid-IR optical modulator using Graphene Gratings surface plasmon Fabry–Perot resonances with low insertion loss, high speed and modulation depth

Through numerical modeling, we present an ultrasensitive tunable Terahertz (THz) to Mid-IR modulator composed of single-layer graphene-based gratings combined with a Fabry–Perot (FP) cavity. The perpendicular-polarized incident light on gratings causes the grating edges to act as an electrical dipole, resulting in an FP interferometer of induced plasmonic waves on the graphene surface. The electric field in the cavity is substantially limited by the activation of standing-waves (SWs) graphene surface plasmon polaritons. The multi-mode SWs formation inside the gratings provides an excellent platform for THz to Mid-IR light modulation with promising features. We have demonstrated a modulation depth of 100% in desired frequencies with near zero insertion loss via full-wave electromagnetic simulations at the normal incident in the THz to Mid-IR range. The light reflection and absorption of the proposed structure have a multi-band profile due to the FP behavior. Therefore, it can be easily tuned by electrically directing the chemical potential of graphene. Due to multi-resonance-based reflected light, each resonance represents different behavior with different modulation parameters. In other words, not only any desired frequency can be chosen, but also at the constant frequency of interest; by choosing the appropriate mode, the desired linewidth, FWHM, and modulation depth can be easily obtained. Finally, we investigated the device bandwidth. The THz modulator requires a large device area for an average number of gratings, and the device area at the 3 dB frequency reaches as high as 1.5 THz, which depicts the high modulation speed in the proposed modulator. The proposed graphene plasmonic grating scheme is a promising candidate for developing the on-chip integrated THz to Mid-IR optical telecommunications. Moreover, the perfect absorption of graphene opens an opportunity to design photodetectors with high responsivity and quantum efficiency, which gives the proposed structure a multi-function capability.

HBN-based enhancement and regulation of radiative heat transfer between two monolayer graphene sheets

Near-field radiative heat transfer (NFRHT) in many-body systems has opened pathways for enabling novel thermal-radiation applications. In this Letter, we investigate hBN-based enhancement and regulation of NFRHT between two monolayer graphene sheets. On the one hand, we predict that adding an intermediate hBN plate can greatly compensate the exponential damping of evanescent waves due to its hyperbolic modes, thus leading to 1.5 times enhancement of the NFRHT without introducing additional thermal source compared to the graphene-graphene system. On the other hand, we find that adjusting the shift frequency of hBN can greatly change the coupling of its hyperbolic modes and graphene surface plasmon polaritons, thus enabling the remarkable thermal regulation with a ratio of 3.5. We hope that our work may facilitate nanoscale thermal management in many-body systems and benefit the comprehension of hBN-based photon tunneling.