  The object of this contribution is twofold. On one hand, it rises some
general questions concerning the definition of the electromagnetic field and
its intrinsic properties, and it proposes concepts and ways to answer them. On
the other hand, and as an illustration of this analysis, a set of quadratic
equations for the electromagnetic field is presented, richer in pure radiation
solutions than the usual Maxwell equations, and showing a striking property
relating geometrical optics to all the other Maxwell solutions.
