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Carving light beams

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..