  We find new exact solutions of the Abelian-Higgs model coupled to General
Relativity, characterized by a non-vanishing superconducting current. The
solutions correspond to \textit{pp}-waves, AdS waves, and Kundt spaces, for
which both the Maxwell field and the gradient of the phase of the scalar are
aligned with the null direction defining these spaces. In the Kundt family, the
geometry of the two-dimensional surfaces orthogonal to the superconducting
current is determined by the solutions of the two-dimensional Liouville
equation, and in consequence, these surfaces are of constant curvature, as it
occurs in a vacuum. The solution to the Liouville equation also acts as a
potential for the Maxwell field, which we integrate into a closed-form. Using
these results, we show that the combined effects of the gravitational and
scalar interactions can confine the electromagnetic field within a bounded
region in the surfaces transverse to the current.
