This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme.

翻译：本文涉及对厌食媒介的反电磁散射问题。 我们使用内部共振模式为散射器成像开发反向散射法。 整个程序由三个阶段组成。 首先, 我们通过线性取样法机制从远方数据组中确定散射器的内部马克斯韦尔传输源值。 下一步, 我们通过解决一个限制的优化问题来确定相应的传输源值。 最后, 我们根据传输源头的全球和地方几何特性, 设计一个成像功能, 可用于确定中散射器的形状。 我们为我们的方法提供了严格的理论基础。 数字实验可以验证拟议方案的有效性、 更好的准确性和超分辨率结果 。