## 1. Introduction

[2] The authors of the present analysis have been actively studying basic electromagnetic field solutions in bianisotropic media during the past decade [*Olyslager and Lindell*, 2002]. In a general bianisotropic medium, characterized by the constitutive relations

analytic field solutions such as plane waves or Green dyadics are difficult to obtain. However, certain subclasses of these media allow some progress in such analytic solutions. A well-known example is the uniaxial anisotropic medium where we can decompose the fields in TE and TM parts. These TE and TM parts experience the uniaxial bianisotropic medium as a simpler affine isotropic medium [*Lindell*, 1995]. We say that a uniaxial anisotropic medium is a decomposable medium. After some efforts we were able to obtain [*Olyslager and Lindell*, 2001a; *Olyslager and Lindell*, 2001b], the most general bianisotropic medium that allows a decomposition of the fields. In general the slowness surface that describes plane wave solutions in a medium is a fourth-order surface. However, media that allow a decomposition of the fields are also so-called factorizable media. In these media the slowness surface consists of two second-order surfaces, i.e., two quadrics. *Olyslager and Lindell* [2001c] have shown that in these decomposable media it is possible to introduce two scalar potentials from which the fields in sourceless regions can be derived. These potentials are generalizations of the Hertz potentials in isotropic media [*Jones*, 1986]. We have earlier studied these generalized Hertz potentials in decomposable anisotropic media [*Lindell*, 2000] and in simple decomposable bianisotropic media [*Lindell and Olyslager*, 2001].

[3] In the present contribution we focus on the most general decomposable bianisotropic medium as introduced by [*Olyslager and Lindell*, 2001a]. *Olyslager and Lindell* [2001a] argued that this medium was also factorizable but an explicit factorization was not given. The reason for that was that this would have been an extremely complex calculation. To illustrate this complexity we refer to *Lindell and Olyslager* [1999] where a “simpler” special case was treated. Throughout this paper we will use a six-vector formalism, i.e., a formalism where we group the electric and magnetic field in one vector. We will show that this six-vector formalism allows a very efficient treatment that allows us to solve the factorization problem for the most general decomposable medium. The decomposed parts of the field see the original medium as simpler media so-called equivalent media. We will derive the Green dyadics for these equivalent media in closed form. Again this can be done very elegantly using the six-vector formalism. We will also, unlike *Olyslager and Lindell* [2001c], use the six-vector formalism to introduce generalized Hertz potentials. Finally we will illustrate the whole theory by considering a particular medium. This medium will be an anisotropic medium with interesting properties that has never been studied before and that has not been known to be decomposable. Before reading this paper we refer the reader to Appendix A to get acquainted with the six-vector notations and rules.