The propagation properties of transverse localized structures are studied experimentally and numerically, showing that their free-space behavior is determined by the features acquired during the nonlinear light-matter interaction at their origin. For a Kerr-like nonlinearity in the optical loop, localized structures show a focalization followed by the formation of a local minimum of the intensity, these features reappearing outside the loop in the near-field region of their free-space propagation.