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

Collapse on the line -- how synthetic dimensions influence nonlinear effects