Homogenisation theory for deterministic and random bianisotropic media

Homogenisation theory may play an important role in the understanding, modelling and design of multifunctional materials. A homogenisation theory for periodic and random bianisotropic electromagnetic media is presented. Starting with a formal two-scale approach we motivate an auxiliary elliptic homogenisation problem which plays a crucial role in the construction of the homogenised bianisotropic medium which is subsequently supported by rigorous mathematical arguments based on the notion of weak convergence. Comments on the potential implementation of this theory in the modelling of complex electromagnetic media are provided.