The field of nanophotonics, together with recent significant advances in nanofabrication techniques, sparks a lot of interest in artificial materials that are designed to have unique properties that cannot be found in nature. These materials are termed metamaterials or metasurfaces, and consist of at least two scales of structure, “micro” and “macro”. Interest in these types of structures is not only limited to nanophotonics, but also to microwave engineering, where, in fact, applications are more straightforward. Applications include perfect absorbers; high impedance surfaces for simulating magnetic conductors, specifically tailored surface impedance for anomalous manipulation of wave propagation, thin lenses, and more. However, unfortunately due to their high structural complexity, exact analysis of these structures is challenging. Exact analytic methods are typically rare, whereas numerical methods are typically too time consuming due to the multi-scale nature of the structures and, moreover, convey less physical insight, which is essential for design purposes.

In this course we will follow four main references [1-4] and try to convey a picture of the issues that the field of metamaterials is resolving together with approximated analytical approaches that have been developed to handle these types of complex structures. More specifically, the course will begin with presenting basic ideas that are especially relevant for composite media characterization, such as different types of constitutive relations, spatial dispersion vs temporal dispersion, Kramer Kroning's relations, etc, followed by different approaches to modelling thin layers and sheets, approximate analytical modeling of interfaces, periodic structures and composite materials (metamaterials), and basic homogenization techniques, and concluding with current and future applications.