The technique of applying form-invariant, spatial coordinate transformations of Maxwell's equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.

We describe the design of adaptive beam bends and beam splitters with arbitrary bend and split angles by use of finite embedded coordinate transformations. The devices do not exhibit reflection at the entrance or exit surfaces. It is shown that moderate and practically achievable values of the relative permittivity and permeability can be obtained for beam bends and splitters with both small and large bend radius. The devices are also discussed in the context of reconfigurable metamaterials, in which the bend and split angles can be dynamically tuned. The performance of adaptive beam bends and splitters is demonstrated in full wave simulations based on a finite-element method. Furthermore, the design of an adaptively adjustable transformation-optical beam expander/compressor is presented. It is observed that a pure transformation-optical design cannot result in a reflectionless beam expander/compressor.

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading generalization properties on clean data.