One of the rapid and efficient methods to calculate the interaction between electromagnetic fields and periodic surfaces with periodicity much less than the wavelength in the surrounding medium is the homogenization method. In this paper, the Hertzian potential Green’s functions corresponding to electric dipoles which excite a homogenized metasurface are presented. The metasurface includes a periodic array of planar scatterers and is replaced by a thin sheet with equivalent electric and magnetic surface polarization density dyads. The magnetic vector potentials are calculated using the generalized sheet transition conditions on the plane of the metasurface. Also the scalar electric potential corresponding to the structure is calculated with the aid of the Lorentz gauge. These potentials together are necessary to use in the mixed potential integral equation formulation of the method of moment in an electromagnetic problem. Two metasurfaces are investigated to calculate the electric fields; a perfect electric conductor square patch array whose surface polarization densities are calculated analytically, and a Jerusalem cross array whose surface polarization dyads are retrieved from reflection and transmission coefficients.

中文翻译：

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使用均质化方法计算由电偶极子激发的平面超表面的潜在格林函数

计算电磁场与周期性远小于周围介质波长的周期性表面之间相互作用的一种快速有效的方法是均质化方法。在本文中，提出了对应于激发均质超表面的电偶极子的赫兹势格林函数。超表面包括平面散射体的周期性阵列，并由具有等效电和磁表面极化密度二元组的薄片代替。使用超表面平面上的广义片材过渡条件计算磁矢量势。此外，借助洛伦兹规范计算与结构相对应的标量电势。这些势能一起用于电磁问题中矩量法的混合势积分方程公式。研究了两个超表面来计算电场；一个完美的电导体方形贴片阵列，其表面极化密度是通过解析计算的，以及一个耶路撒冷十字阵列，其表面极化二元组是从反射和透射系数中检索出来的。