According to the surface equivalence theorem [1], any enclosed surface with electric and magnetic current densities enforced on it can generate exactly the same fields as the original problem. The problem is how to construct the current sources. In this paper, an efficient and accurate unified approach with an equivalent current density enforced on the outermost boundary is proposed to solve transverse magnetic (TM) scattering problems by objects embedded in multilayers. In the proposed approach, an equivalent current density is derived after the surface equivalence theorem is recursively applied on each boundary from innermost to outermost interfaces. Then, the objects are replaced by the background medium and the equivalent electric current density only on the outermost boundary is derived. The scattering problems by objects embedded in multilayers can be solved with the electric field integral equation (EFIE). Compared with the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and other dual source formulations, the proposed approach shows significant benefits: only the surface electric current density instead of both the electric and magnetic current densities is required to model the complex objects in the equivalent problem. Furthermore, the electric current density is only enforced on the outermost boundary of objects. Therefore, the overall count of unknowns can be significantly reduced. At last, several numerical experiments are performed to validate its accuracy and efficiency. Although overhead is required to construct the intermediate matrices, the overall performance improvement is still significant as numerical results are shown. Therefore, it shows great potential useful in the practical engineering applications.

根据表面等效定理[1]，任何封闭的表面都具有强电磁电流密度，可以产生与原始问题完全相同的场。问题是如何构建当前资源。本文提出了一种有效且准确的统一方法，即在最外层边界上施加等效电流密度，以解决嵌入多层物体的横向磁（TM）散射问题。在提出的方法中，在从最​​内到最外界面递归地将表面等效定理应用于每个边界之后，得出等效电流密度。然后，将物体替换为背景介质，并得出仅在最外层边界上的等效电流密度。嵌入在多层中的物体的散射问题可以通过电场积分方程（EFIE）解决。与Poggio-Miller-Chang-Harrington-Wu-Tsai（PMCHWT）和其他双源公式相比，所提出的方法显示出显着的好处：仅表面电流密度而不是电流和磁流密度都需要建模。复杂对象中的等效问题。此外，电流密度仅在对象的最外边界上施加。因此，未知数的总数可以大大减少。最后，进行了几次数值实验以验证其准确性和效率。尽管构建中间矩阵需要开销，数值结果表明，总体性能改进仍然很显着。因此，在实际工程应用中显示出巨大的潜力。