Carving beams of light

Some years after the appearance of the so-called non-diffracting beams, there was the development of methods capable of structuring them spatially, with the so-called frozen wave method being the first and, perhaps, the most efficient one. That method allows for modelling the longitudinal intensity pattern of non-diffracting beams, but it is 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 the transverse beam structure along the propagation, in addition to the longitudinal pattern. The new transversally and longitudinally structured beams can have potential applications in areas such as photonics, optical manipulation, optical atom guidance, and lithography.