  We show the existence of the so-called semiclassical states
$\mathbf{U}:\mathbb{R}^3\to\mathbb{R}^3$ to the following curl-curl problem $$
\varepsilon^2\; \nabla \times (\nabla \times \mathbf{U}) + V(x) \mathbf{U} =
g(\mathbf{U}), $$ for sufficiently small $\varepsilon > 0$. We study the
asymptotic behaviour of solutions as $\varepsilon\to 0^+$ and we investigate
also a related nonlinear Schr\"odinger equation involving a singular potential.
The problem models large permeability nonlinear materials satisfying the system
of Maxwell equations.
