  The modulation instability is a focusing mechanism responsible for the
formation of strong wave localizations not only on the water surface, but also
in a variety of nonlinear dispersive media. Such dynamics is initiated from the
injection of side-bands, which translate into an amplitude modulation of the
wave field. The nonlinear stage of unstable wave evolution can be described by
exact solutions of the nonlinear Schr\"odinger equation (NLSE). In that case,
the amplitude modulation of such coherent extreme wave structures is connected
to a particular phase-shift seed in the carrier wave. In this letter, we show
that phase-shifts localization applied to the background, excluding any
amplitude modulation excitation, can indeed trigger extreme events. Such rogue
waves can be for instance generated by considering the parametrization of
fundamental breathers and thus, by seeding only the local phase-shift
information to the regular carrier wave. Our wave tank experiments show an
excellent agreement with the expected NLSE hydrodynamics and confirm that even
though delayed in their evolution, breather-type extreme waves can be generated
from a purely regular wave train. Such novel focusing mechanism awaits
experimental confirmation in other nonlinear media, such optics, plasma, and
Bose-Einstein condensates.
