  Since its introduction by Sir Michael Berry in 1984, geometric phase became
of fundamental importance in physics, with applications ranging from solid
state physics to optics. In optics, Pancharatnam-Berry phase allows the
tailoring of optical beams by a local control of their polarization. Here we
discuss light propagation in the presence of an intensity-dependent local
modulation of the Pancharatnam-Berry phase. The corresponding self-modulation
of the wavefront counteracts the natural spreading due to diffraction, i.e.,
self-focusing takes place. No refractive index variation is associated with the
self-focusing: the confinement is uniquely due to a nonlinear spin-orbit
interaction. The phenomenon is investigated, both theoretically and
experimentally, considering the reorientational nonlinearity in liquid
crystals, where light is able to rotate the local optical axis through an
intensity-dependent optical torque. Our discoveries pave the way to the
investigation of a new family of nonlinear waves featuring a strong interaction
between the spin and the orbital degrees of freedom.
