Theoretical study of arrays of graphene ribbons is currently of high interest due to its potential application in beam splitters, absorbers, and polarizers. In this paper, an analytical method is presented for diffraction analysis of graphene ribbon arrays. Previous analytical studies were carried out in the regime where the lateral separation between the ribbons is much smaller than the wavelength of the incident wave. As such, they cannot be used to calculate the reflection coefficients of higher diffracted orders. In contrast, the method proposed here can predict the electromagnetic response of graphene ribbon arrays even when the array constant is larger than the wavelength. To reach our results, we first derive an analytical expression for the surface density of the electric current induced on the ribbons by an incident, transverse-magnetic, plane wave. Next, closed-form and analytical expressions are obtained for the reflection coefficients of the zeroth and higher diffracted orders. The results are in excellent agreement with those obtained from full-wave simulations. The method presented facilitates the design of tunable gratings with many potential applications in the terahertz regime and optics.

中文翻译：

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亚波长石墨烯带衍射电磁波的解析方法

由于其在分束器，吸收器和偏振器中的潜在应用，目前对石墨烯带阵列的理论研究引起了极大的兴趣。本文提出了一种石墨烯带状阵列衍射分析的分析方法。以前的分析研究是在色带之间的横向间隔远小于入射波波长的情况下进行的。因此，它们不能用于计算更高衍射级的反射系数。相反，即使阵列常数大于波长，此处提出的方法也可以预测石墨烯带阵列的电磁响应。为了得出我们的结果，我们首先导出一个解析表达式，用于分析由于入射，横向磁场，平面波。接下来，获得零级和更高衍射级的反射系数的封闭形式和解析表达式。结果与从全波模拟获得的结果非常一致。提出的方法促进了可调谐光栅的设计，在太赫兹波段和光学领域具有许多潜在应用。