  Optical (or Robinson) structures are one generalisation of four-dimensional
shearfree congruences of null geodesics to higher dimensions. They are
Lorentzian analogues of complex and CR structures. In this context, we extend
the Goldberg-Sachs theorem to five dimensions. To be precise, we find a new
algebraic condition on the Weyl tensor, which generalises the Petrov type II
condition, in the sense that it ensures the existence of such congruences on a
five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci
tensor. This results in a significant simplification of the field equations. We
discuss possible degenerate cases, including a five-dimensional generalisation
of the Petrov type D condition. We also show that the vacuum black ring
solution is endowed with optical structures, yet fails to be algebraically
special with respect to them. We finally explain the generalisation of these
ideas to higher dimensions, which has been checked in six and seven dimensions.
