α-MoO_(3)/石墨烯异质叠层结构中的声子极化激元-等离极化激元杂化波导模式

Hybridized Phonon-Plasmon Polariton Waveguide Modes in Stackedα-MoO_(3)/Graphene van der Waals Heterostructure

在中红外至太赫兹的电磁场长波谱段,二维范德瓦耳斯晶体石墨烯和a-MoO_(3)能够分别支持等离极化激元和双曲声子极化激元,实现对长波电磁场的纳米尺度聚焦和调控。不同类型极化激元之间的杂化可以进一步丰富极化激元物理特性,为纳米尺度下的电磁场调控带来更多维度。为此开展了a-MoO_(3)薄片和单层石墨烯异质叠层结构声子极化激元-等离极化激元杂化研究。在理论上通过求解二维光波导麦克斯韦波动方程,分析了a-MoO_(3)/石墨烯异质叠层结构中声子极化激元-等离极化激元杂化激元波导模式的传播特性,计算了波导模式的色散关系,揭示了a-MoO_(3)/石墨烯异质叠层结构特有的电磁场传输机制。在实验上通过干法转移制备了a-MoO_(3)/单层石墨烯异质叠层结构,并采用散射式扫描近场光学显微镜对该异质结构的杂化极化激元特性进行了三维空间纳米光学成像表征,验证了理论结果。研究结果为计算范德瓦耳斯二维晶体叠层结构的杂化极化激元特性提供了定量模型,为研究二维晶体中不同类型的极化激元之间的相互作用及其机制提供了理论和实验参考。

Objective Two-dimensional(2D)van der Waals(vdW)crystals like graphene and a-MoO_(3)can support polaritons in the spectral range from terahertz to mid-/far-infrared regime,enabling nanoscale confining,focusing,and controlling of the electromagnetic fields.The hybridization between different polaritons can further enrich the properties of polaritons and bring more degrees of freedom for the regulation of electromagnetic fields at the nanoscale.In this paper,we studied the hybridization of plasmon polaritons and phonon polaritons in a heterostructure composed of an a-MoO_(3)vdW thin lamina stacking onto a monolayer graphene.An analytical waveguide model was developed to calculate the polariton propagation characteristics in the vdW heterostructure.The dispersion contours,dispersion relations,and localized electromagnetic field distributions of the hybridized polariton waveguide modes were derived.The theoretical results were then verified by real-space optical nano-imaging and numerical simulations.Our study can provide a quantitative model for the calculation of the hybridized polariton waveguide modes in vdW heterostructures,which can help further exploring the interactions between different types of polaritons in 2D vdW crystals.Methods In our theoretical model,the vdW heterostructure is treated as a 2D infinite waveguide supported onto SiO_(2) substrate,which consists of a monolayer graphene of 0.5-nm thickness and an a-MoO_(3)lamina of 115-nm thickness(Fig.1).The dielectric functions of the graphene and a-MoO_(3)are described using the Drude model and Lorentz model,respectively.Because in a-MoO_(3)the polaritons can approximately be treated as transverse magnetic(TM)mode,the electromagnetic modes and the associated dispersion relations of the heterostructure can then be obtained by solving the Maxwell’s equations upon the continuities of the electric and magnetic fields at interfaces.Monolayer graphene was grown by the chemical vapor deposition(CVD)method.Microfabrication technique combining electron beam lithography(EBL)and reactive ion etching(RIE)was employed to pattern the graphene into microstructures.The vdW a-MoO_(3)laminas were grown using a physical vapor deposition method.Dry transfer method was utilized to prepare the a-MoO_(3)/graphene(a-MoO_(3)/Gr)heterostructures,where the monolayer graphene microstructures were covered with a-MoO_(3)laminas of different thicknesses.Real-space nano-imaging was conducted using a scattering-type scanning near-field optical microscope(NeaSNOM,Neaspec GmbH,Germany).In a specific measurement,a metal-coated tip(Arrow-IrPt,Nanoworld,Switzerland)was illuminated using a mid-infrared laser(Access Laser,USA)with a wavelength range of 9.20-10.70μm(934.5-1087.0 cm-1).The tip was vibrated vertically with a frequency of about 280 kHz.The backscattered light from the tip was detected in a pseudo-heterodyne interferometric manner,where the scattered light was demodulated at the fourth harmonic of the tip vibration frequency.The optical and morphological images of the sample can be simultaneously obtained by scanning the heterostructure underneath the tip.For the numerical study,the real-space polariton waves were manifested as the real-part of the z-component of the electric field,Re(Ez),on the surface of the SiO_(2) substrate.They were calculated using the finite element method(FEM)simulations(COMSOL Multiphysics).A vertically-polarized electric dipole source was fixed above the a-MoO_(3)with a separation of 50 nm(Fig.S5,Supporting materials).The thicknesses of the air,a-MoO_(3),graphene and SiO_(2) layers were 500 nm,115 nm,0.5 nm and 500 nm,respectively.The permittivities along the three principle axes were calculated according to Eq.(1).The anisotropic dielectric tensors of the a-MoO_(3)layer are written as ε=[ε_(x),0,0;0,ε_(y),0;0,0,ε_(z)]andε=[ε_(xx),ε_(xy),0;ε_(yx),ε_(yy),0;0,0,ε_(zz)].These tensors were imported into the COMSOL package to solve the Maxwell’s equations.For the monolayer graphene and a-MoO_(3)lamina,the Re(Ez)was monitored respectively on the planes 5 nm away from their upper surfaces,while for the a-MoO_(3)/Gr heterostructure,the Re(E_(z))was monitored on the plane 4 nm away from the graphene upper surface.Results and Discussions In the theoretical model,the vdW heterostructure is modeled as a 2D infinite waveguide(Fig.1).The thicknesses of top(ε[1])and bottom layers(ε[2])are d_(1) and d_(2),respectively.It is sandwiched between two semi-infinite plates,which act as the substrate(ε_(s)=ε^([3]))and cover layer(ε_(c)=ε^([0])).The electromagnetic modes[Eqs.(S8)-(S10),Supporting materials]and the associated polariton dispersions[Eq.(4)]are obtained by solving the Maxwell’s equations upon the continuities of the electric and magnetic fields at interfaces.With the input of dielectric functions of monolayer graphene[Eq.(2)]and a-MoO_(3)[Eq.(1)],the calculated polariton dispersions and contours of the a-MoO_(3)/Gr heterostructure are shown in Fig.1 and Fig.S4 in the Supporting materials.In comparison with the pristine monolayer graphene and a-MoO_(3)lamina,due to the isotropic plasmon polariton in the graphene,the dispersion contours of the heterostructure are more complex and distorted along the[100]and[001]directions.Therefore,the hybridized plasmon-phonon polaritons can propagate along these directions that are forbidden respectively for the phonon polaritons in Restrahlen Band 1 and Band 2 in a-MoO_(3)lamina(Fig.2).The theoretical results are further corroborated by numerical simulations using FEM(Figs.1 and 2)and experimental nano-imaging measurements(Figs.3 and 4).Moreover,the influence of the thickness of a-MoO_(3)lamina on the polariton hybridizations in a-MoO_(3)/Gr heterostructure is also investigated.Because the polariton fields are of evanescent nature,by reducing the a-MoO_(3)thickness,the hybridized polaritons converge to the plasmon polariton in monolayer graphene,while with the increase in the a-MoO_(3)thickness,the polaritons in the heterostructure evolve into the phonon polaritons in the pristine a-MoO_(3)(Fig.4).The results are also corroborated by the nano-imaging measurements(Fig.4).Conclusions In conclusion,we have established a theoretical model to investigate the hybridizations of plasmon polaritons and phonon polaritons in a heterostructure consisting of an a-MoO_(3)lamina covering a monolayer graphene.The propagation characteristics,including the polariton dispersion relation,in-plane dispersion contour,and localized electromagnetic field distribution,were calculated and studied.It is revealed that due to the hybridization effect,the a-MoO_(3)/Gr heterostructure is able to support polariton propagation along the directions that are forbidden for the phonon polaritons in pristine a-MoO_(3)lamina.Additionally,the influence of the a-MoO_(3)thickness on the polariton hybridization in the heterostructure was also investigated,indicating that when the a-MoO_(3)lamina was thinner/thicker,the hybridized polaritons became more plasmon/phonon polariton-like.The theoretical results were corroborated respectively by the numerical simulations and experimental nano-imaging measurements.We strongly believe that the results obtained in our study can on one hand provide a theoretical model for analytically studying the polariton hybridizations in vdW heterostructures,and on the other hand help further our understanding on the polaritonic physics in low-dimensional materials.