Nonlinear electromagnetic (EM) inverse scattering is a quantitative and super-resolution imaging technique, in which more realistic interactions between the internal structure of scene and EM wavefield are taken into account in the imaging procedure, in contrast to conventional tomography. However, it poses important challenges arising from its intrinsic strong nonlinearity, ill-posedness, and expensive computational costs. To tackle these difficulties, we, for the first time to our best knowledge, exploit a connection between the deep neural network (DNN) architecture and the iterative method of nonlinear EM inverse scattering. This enables the development of a novel DNN-based methodology for nonlinear EM inverse problems (termed here DeepNIS). The proposed DeepNIS consists of a cascade of multilayer complex-valued residual convolutional neural network modules. We numerically and experimentally demonstrate that the DeepNIS outperforms remarkably conventional nonlinear inverse scattering methods in terms of both the image quality and computational time. We show that DeepNIS can learn a general model approximating the underlying EM inverse scattering system. It is expected that the DeepNIS will serve as powerful tool in treating highly nonlinear EM inverse scattering problems over different frequency bands, which are extremely hard and impractical to solve using conventional inverse scattering methods.

A simple and systematic derivation of anisotropic perfectly matched layers (PML's) in cylindrical and spherical coordinates is presented. The derivation is based on the analytic continuation of Maxwell's Equations to complex space. Through field transformations, results for Cartesian anisotropic PML media are recovered and, more importantly, a generalization of the anisotropic PML to cylindrical and spherical systems is obtained, providing further clarification on the PML concept. As expected, these new PML media are cylindrically and spherically layered, respectively.link_to_subscribed_fulltex

Extensions of finite-difference time-domain (FDTD) and finite-element time-domain (FETD) algorithms are reviewed for solving transient Maxwell equations in complex media. Also provided are a few representative examples to illustrate the modeling capabilities of FDTD and FETD for complex media. The term complex media refers here to media with dispersive, (bi)anisotropic, inhomogeneous, and/or nonlinear properties present in the constitutive tensors.

The perfectly matched layer (PML) constitutive tensors that match more general linear media presenting bianisotropic and dispersive behavior are obtained for single interface problems and for two-dimensional (2-D) and three-dimensional (3-D) corner regions. The derivation is based on the analytic continuation of Maxwell's equations to a complex variables domain. The formulation is Maxwellian so that it is equally applicable to the finite-difference time-domain (FDTD) or finite-element (FEM) methods. It recovers, as special cases, previous anisotropic media formulations, and dispersive media formulations.