“…The extension of the scattering problem to a multi-layered background medium is straightforward since the analytical forms of the fundamental solution can be similarly obtained for the twodimensional Helmholtz equation in the multi-layered background medium. Scattering problems in layered medium are of important applications in broad scientific areas such as submarine detection, geophysical exploration, near-field optical microscopy, and near-field optics modeling [6,15,33]. Near-field optics has developed dramatically in recent years as an effective approach to breaking the diffraction limit and obtaining images with subwavelength resolution [16], which leads to various applications in biology, chemistry, material sciences, and information storage.…”