Topology preserving mappings in a self imaging photorefractively pumped ring resonator

We present a photorefractively pumped ring resonator for the formation of self-organized. topology-preserving mappings. The self-imaging ring resonator with saturable gain and loss supports localized cavity modes at arbitrary transverse locations. When the resonator is pumped by two uncorrelated signals, two spatially well separated modes form. Each mode is correlated temporally with one of the input signals. When the resonator is pumped by partially correlated inputs, modes with a partial spatial overlap form. The spatial distribution of the modes preserves the spatial topology of the input signals. An experimental demonstration and numerical simulations are presented.