This paper proposes a new boundary integral equation (BIE) methodology based on the perfectly matched layer (PML) truncation technique for solving the electromagnetic scattering problems in a multi-layered medium. Instead of using the original PML stretched fields, artificial fields which are also equivalent to the solutions in the physical region are introduced. This significantly simplifies the study of the proposed methodology to derive the PML problem. Then some PML transformed layer potentials and the associated boundary integral operators (BIOs) are defined and the corresponding jump relations are shown. Under the assumption that the fields vanish on the PML boundary, the solution representations, as well as the related BIEs and regularization of the hyper-singular operators, in terms of the current density functions on the truncated interface, are derived. Numerical experiments are presented to demonstrate the efficiency and accuracy of the method.

翻译：本文提出一种基于完美匹配层截断技术的边界积分方程新方法，用于求解多层介质中的电磁散射问题。该方法引入人工场而非原始PML拉伸场，该人工场在物理区域同样等效于原问题的解，从而显著简化了所提方法的理论推导过程以导出PML问题。进一步定义了经PML变换的层势及其关联边界积分算子，并给出了相应的跳跃关系。在假定场量在PML边界处消失的条件下，推导了基于截断界面上电流密度函数的解表示公式、相关边界积分方程以及超奇异算子的正则化形式。数值实验验证了该方法的有效性与精度。