  We study Lorentzian manifolds $(M, g)$ of dimension $n\geq 4$, equipped with
a maximally twisting shearfree null vector field $p_o$, for which the leaf
space $S = M/\{\exp t p_o\}$ is a smooth manifold. If $n = 2k$, the quotient $S
= M/\{\exp t p_o\}$ is naturally equipped with a subconformal structure of
contact type and, in the most interesting cases, it is a regular Sasaki
manifold projecting onto a quantisable K\"ahler manifold of real dimension $2k
-2$. Going backwards through this line of ideas, for any quantisable K\"ahler
manifold with associated Sasaki manifold $S$, we give the local description of
all Lorentzian metrics $g$ on the total spaces $M$ of $A$-bundles $\pi: M \to
S$, $A = S^1, \mathbb R$, such that the generator of the group action is a
maximally twisting shearfree $g$-null vector field $p_o$. We also prove that on
any such Lorentzian manifold $(M, g)$ there exists a non-trivial generalized
electromagnetic plane wave having $p_o$ as propagating direction field, a
result that can be considered as a generalization of the classical
$4$-dimensional Robinson Theorem. We finally construct a 2-parametric family of
Einstein metrics on a trivial bundle $M = \mathbb R \times S$ for any
prescribed value of the Einstein constant. If $\dim M = 4$, the Ricci flat
metrics obtained in this way are the well-known Taub-NUT metrics.
