  Power induced wave collapse is one of the most fascinating phenomena in
optics as it provides extremely high intensities, thus stimulating a range of
nonlinear processes. For low power levels, propagation of beams in bulk media
is dominated by diffraction, while above a certain threshold self-focusing is
steadily enhanced by the action of a positive nonlinearity. An autocatalytic
blow-up occurs, which is only stopped by saturation of the nonlinearity,
material damage or the inherent medium discreteness. In the latter case, this
leads to energy localization on a single site. It is commonly believed that for
cubic nonlinearities, this intriguing effect requires at least two transverse
dimensions to occur and is thus out of reach in fiber optics. Following the
concept of synthetic dimensions, we demonstrate that mixing short and
long-range interaction resembles a two-dimensional mesh lattice and features
wave collapse at mW-power levels in a genuine 1D system formed by coupled fiber
loops.
