Two-point nonlocality

Different kinds of nonlocal couplings in extended systems are at the center of an
increasing research activity. This seminar is about a nonlocality characterized
by the coupling of each point of the field with a shifted one. I will present two
broad classes of diffusive and optical systems with a two-point nonlocality that
can arise in presence of an off-axis feedback loop. Important consequences on the
spatio-temporal dynamics and new regions of instability are predicted
analytically and confirmed by numerical simulation of some selected models. In
particular, two-point nonlocality opens large windows of control parameters in
laser devices where weak light spots can be strongly amplified while the
background radiation remains very low. Furthermore, transverse phase and group
velocities of a signal can be independently tuned and this enables to steer it
non mechanically, to control its spatial chirping and to split it into two
counter-propagating ones.