  Following earlier works of Dereli and collaborators, we study a three
dimensional toy model where we extend the topologically massive gravity with
electrodynamics by the most general $RF^2$-type non-minimal coupling terms.
Here $R$ denotes the possible curvature terms and $F$ denotes the
electromagnetic 2-form. We derive the variational field equations and look for
exact solutions on constant negative curvature space-times with a constant,
self-dual electromagnetic field. The notion of self-dual electromagnetic fields
in three dimensions is introduced by Dereli and collaborators in the study of
exact solutions of models with gravity-electromagnetism couplings. We note the
conditions that the parameters of the model have to satisfy for these self-dual
solutions to exist.
