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Abstract
The class of self-dual linear bi-anisotropic media can be defined in three different ways. It consists of media which are invariant in a duality transformation, allow factorization of the second-order dyadic Helmholtz operator in terms of two first-order dyadic operators and allow decomposition of fields and sources in a way that is an extension of the Bohren decomposition for chiral media. It is shown that the Green dyadic can be solved in closed analytic form for any self-dual bi-anisotropic medium and its general expression is given in terms of the self-dual decomposition. This generalizes previous results where special cases of self-dual media were considered.