  Some years after the appearance of the so-called non-diffracting beams, there
was the development of methods capable of structuring them spatially, being the
so called Frozen Waves method the first and, perhaps, the most efficient one.
That method allowed modelling the longitudinal intensity pattern of
non-diffracting beams, being, however, little efficient in controlling their
transverse spatial pattern, granting only the possibility of choosing their
transverse dimensions, which remain invariant throughout the propagation. In
this work, we have extended the Frozen Wave method in such a way to control, in
addition to the longitudinal pattern, the transverse beam structure along the
propagation. The new transversally and longitudinally structured beams can have
potential applications in areas such as photonics, optical manipulation,
optical atom guidance, lithography, etc..
