In this paper, some optical properties of a two-walled carbon nanotube are studied. The system is represented by two infinitely long and infinitesimally thin coaxial cylindrical shells, each containing a two-dimensional electron nano-fluid. The quasi-static approximation and the quantum hydrodynamic model are adopted in order to obtain the optical response of the system. General expressions for polarizability, dispersion of dipole surface plasmons and induced surface charges of the system are derived, by solving the Laplace and fluid equations with appropriate boundary conditions. Also, by using the polarizability formula, scattering, absorption and extinction spectra are computed and expressed in terms of widths, which are defined as the cross sections per unit length of the system. Furthermore, the Maxwell-Garnett theory for the effective medium approximation of composite materials is developed to the effective dielectric function of a composite of aligned two-walled carbon nanotubes.

中文翻译：

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两壁碳纳米管的光学性质：准静态近似

本文研究了两壁碳纳米管的一些光学性质。该系统由两个无限长且无限薄的同轴圆柱壳表示，每个壳都包含二维电子纳米流体。为了获得系统的光学响应，采用了准静态近似和量子流体动力学模型。通过在适当的边界条件下求解拉普拉斯方程和流体方程，可以得出极化率，偶极子表面等离子体激元的弥散和系统的感应表面电荷的一般表达式。同样，通过使用极化率公式，可以计算并以宽度表示散射，吸收和消光光谱，这些宽度定义为系统每单位长度的横截面。此外，