We present f (ϕ)(F µν ) 2 -type non-canonical and non-polynomial interactions for an N = 1 vector multiplet in three dimensions. We couple a Yang-Mills multiplet (A µ I , λ I ) to a scalar multiplet (ϕ, χ), where ϕ appears in the arbitrary scalar function f (ϕ) in the coupling αf (ϕ)(F µν I ) 2 . Supersymmetric Chern-Simons terms for the vector multiplet and a potential term for the scalar multiplet can be also added. We first give the component lagrangian, and we give its superspace

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... ion. We also give exact solutions for the vector and scalar fields in the Abelian case with a finite total energy.