Normal-incidence transmission measurements are commonly used for determining the real part of the in-plane optical conductivities σ1 （ω） of graphene layers. We present an accurate expression for σ1 （ω） in a cl...Normal-incidence transmission measurements are commonly used for determining the real part of the in-plane optical conductivities σ1 （ω） of graphene layers. We present an accurate expression for σ1 （ω） in a closed form for a multilayer graphene film supported on a finite-thickness transparent substrate. This form takes into account the coherent and incoherent multiple reflections of the system, whereas the traditional method assumes a semi-infinite substrate. The simulated results for graphene sheets with a layer number N ≤ 10 show that no matter what the transparent substrate is, the accuracy to which σ1 （ω） is determined by applying this expression is improved with no systematic error. Moreover, the layer number N can be exactly determined by simply dividing the σ1 （ω） value of N-layer graphene by the corresponding σ1 （ω） of monolayer graphene, where ωp is the peak frequency of the ordinary dielectric function＇s imaginary part ε1 （ω）of graphene.展开更多
We study shear-horizontal （SH） waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used...We study shear-horizontal （SH） waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used for the quartz plate and the elastic layer,respectively.A transcen-dental frequency equation that determines the dispersion relations of the waves is obtained.The dispersion relations are obtained and plotted by solving the frequency equation using MATLAB.Approximate dispersion relations are also obtained analytically for two special cases.One is for long waves whose wavelength is much larger than the plate thickness.The other is for the case of a very thin elastic layer.The effects of the elastic layer on the dispersion relations are exam-ined.The results obtained are fundamental and useful to acoustic wave sensors for measuring the mechanical and geometric properties of the elastic layer.展开更多
文摘Normal-incidence transmission measurements are commonly used for determining the real part of the in-plane optical conductivities σ1 （ω） of graphene layers. We present an accurate expression for σ1 （ω） in a closed form for a multilayer graphene film supported on a finite-thickness transparent substrate. This form takes into account the coherent and incoherent multiple reflections of the system, whereas the traditional method assumes a semi-infinite substrate. The simulated results for graphene sheets with a layer number N ≤ 10 show that no matter what the transparent substrate is, the accuracy to which σ1 （ω） is determined by applying this expression is improved with no systematic error. Moreover, the layer number N can be exactly determined by simply dividing the σ1 （ω） value of N-layer graphene by the corresponding σ1 （ω） of monolayer graphene, where ωp is the peak frequency of the ordinary dielectric function＇s imaginary part ε1 （ω）of graphene.
基金supported by the National Natural Science Foundation of China (Nos. 11072116,10772087 and 10932004)Key Team of Technological Innovation of Zhejiang Province (Grant 2009R50025)+2 种基金Key Industrial Project of Bureau of Science and Technology,City of Ningbo (No. 2005B100015)grants from the Bureau of Science and Technology,City of Ningbo,through the International Collaboration Initiative (Project 2007B10052)Sponsored by K.C.Wong MagnaFund in Ningbo University
文摘We study shear-horizontal （SH） waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used for the quartz plate and the elastic layer,respectively.A transcen-dental frequency equation that determines the dispersion relations of the waves is obtained.The dispersion relations are obtained and plotted by solving the frequency equation using MATLAB.Approximate dispersion relations are also obtained analytically for two special cases.One is for long waves whose wavelength is much larger than the plate thickness.The other is for the case of a very thin elastic layer.The effects of the elastic layer on the dispersion relations are exam-ined.The results obtained are fundamental and useful to acoustic wave sensors for measuring the mechanical and geometric properties of the elastic layer.
