Let V (t) = e tG b , t ≥ 0, be the semigroup generated by Maxwell's equations in an exterior domain Ω ⊂ R 3 with dissipative boundary condition We prove that if γ(x) is nowhere equal to 1, then for every 0 < 1 and every N ∈ N the eigenvalues of G b lie in the region Λ ∪ R N , where Λ = {z ∈ C : | Re z| ≤ C (| Im z| 1 2 + + 1), Re z < 0}, R N = {z ∈ C : | Im z| ≤ C N (| Re z| + 1) −N , Re z < 0}.