  Let $V(t) = e^{tG_b},\: t \geq 0,$ be the semigroup generated by Maxwell's
equations in an exterior domain $\Omega \subset {\mathbb R}^3$ with dissipative
boundary condition $E_{tan}- \gamma(x) (\nu \wedge B_{tan}) = 0, \gamma(x) > 0,
\forall x \in \Gamma = \partial \Omega.$ We prove that if $\gamma(x)$ is
nowhere equal to 1, then for every $0 < \epsilon \ll 1$ and every $N \in
{\mathbb N}$ the eigenvalues of $G_b$ lie in the region $\Lambda_{\epsilon}
\cup {\mathcal R}_N,$ where $\Lambda_{\epsilon} = \{ z \in {\mathbb C}:\: |\Re
z | \leq C_{\epsilon} (|\Im z|^{\frac{1}{2} + \epsilon} + 1), \: \Re z < 0\},$
${\mathcal R}_N = \{z \in {\mathbb C}:\: |\Im z| \leq C_N (|\Re z| + 1)^{-N},\:
\Re z < 0\}.$
