From transformation optics to topology: local and global methods for material design

There are two basic approaches for designing electromagnetic materials. The first approach is local, where the field is manipulated at each point in space to achieve a desired goal: transformation optics is of this kind. The second approach is global, where e.g. an integral of the material parameters governs certain characteristics of a device. Methods of topology are of this second kind. In this talk I shall show some new design techniques of this second kind, from designing reflectionless media, to applications of topology to design one-way devices and graded index waveguides.