Electromagnetics and exotic media: a quest for the holy grail

During the past eight years, the authors have extensively studied the properties of linear homogeneous bianisotropic media. They have studied the Green's dyadics, the factorization of the Helmholtz determinant operator, the field and source decomposition, and plane-wave propagation in various classes of these media. We give an overview of our findings, and we place these findings in historical order. The results we found provide insight into the nature of Maxwell's equations, in general, and into the field propagation mechanisms in the different media, in particular. Finally, we mention that closed-form solutions are valuable as benchmarking results for numerical solutions.