  We find solutions $E:\Omega\to\mathbb{R}^3$ of the problem \begin{eqnarray*}
  \left\{
  \begin{aligned}
  &\nabla\times(\mu(x)^{-1}\nabla\times E) - \omega^2\epsilon(x) E = \partial_E
F(x,E) &&\quad \text{in }\Omega\\%\newline
  &\nu\times E = 0 &&\quad \text{on }\partial\Omega
  \end{aligned}
  \right. \end{eqnarray*} on a bounded Lipschitz domain
$\Omega\subset\mathbb{R}^3$ with exterior normal
$\nu:\partial\Omega\to\mathbb{R}^3$. Here $\nabla\times$ denotes the curl
operator in $\mathbb{R}^3$. The equation describes the propagation of the
time-harmonic electric field $\Re\{E(x)e^{i\omega t}\}$ in an anisotropic
material with a magnetic permeability tensor $\mu(x)\in\mathbb{R}^{3\times3}$
and a permittivity tensor $\epsilon(x)\in\mathbb{R}^{3\times3}$. The boundary
conditions are those for $\Omega$ surrounded by a perfect conductor. It is
required that $\mu(x)$ and $\epsilon(x)$ are symmetric and positive definite
uniformly for $x\in\Omega$, and that $\mu,\epsilon\in
L^{\infty}(\Omega,\mathbb{R}^{3\times 3})$. The nonlinearity
$F:\Omega\times\mathbb{R}^3\to\mathbb{R}$ is superquadratic and subcritical in
$E$, the model nonlinearity being of Kerr-type: $F(x,E)=|\Gamma(x)E|^p$ for
some $2<p<6$ with $\Gamma(x)\in GL(3)$ invertible for every $x\in\Omega$ and
$\Gamma,\Gamma^{-1}\in L^\infty(\Omega, \mathbb{R}^{3\times 3})$. We prove the
existence of a ground state solution and of bound states if $F$ is even in $E$.
Moreover if the material is uniaxial we find two types of solutions with
cylindrical symmetries.
