To characterize electromagnetic metamaterials at the level of an effective medium, nonlocal constitutive relations are required. In the most general sense, this is feasible using a response function that is convolved with the electric field to express the electric displacement field. Even though this is a neat concept, it bears little practical use. Therefore, frequently the response function is approximated using a polynomial function. While in the past explicit constitutive relations were derived that considered only some lowest order terms, we develop here a general framework that considers an arbitrary high number of terms. It constitutes, therefore, an approximation to the initially considered response function of arbitrary precision. The reason for the previously self-imposed restriction to only a few lowest order terms in the expansion has been the unavailability of the necessary interface conditions with which these nonlocal constitutive relations have to be equipped. Otherwise one could not make practical use of them. Therefore, besides the introduction of such higher order nonlocal constitutive relations, it is at the heart of contribution to derive the necessary interface conditions to pave the way for the practical use of these advanced material laws.

为了在有效介质水平上表征电磁超材料，需要非局部本构关系。在最一般的意义上，使用与电场卷积的响应函数来表达电位移场是可行的。尽管这是一个简洁的概念，但它几乎没有实际用途。因此，通常使用多项式函数来近似响应函数。虽然在过去推导出的显式本构关系仅考虑一些最低阶项，但我们在这里开发了一个考虑任意数量项的通用框架。因此，它构成了最初考虑的任意精度响应函数的近似值。之前对扩展中的几个最低阶项进行自我强加限制的原因是这些非局部本构关系必须配备的必要界面条件不可用。否则就无法实际使用它们。因此，除了引入这种高阶非局部本构关系外，推导出必要的界面条件为这些先进的材料定律的实际应用铺平道路也是其贡献的核心。