Fig. 1: Liquid crystal light valve (LCLV) with reciprocal and nonreciprocal optical feedback.

a Schematic representation of a liquid crystal light valve and optical bistable system chain. Scale bar indicates the distance between cells. b Snapshot of the optical bistable system chain and schematic representation of dissipative bistable optical chain. Scale bar indicates bistable cell spacing. b1 Experimental snapshot of the optical bistable system chain. The red spots depict the cells that make up the chain of bistable systems. The colour intensity in these red spots (cells) accounts for different states of molecular orientation, which coexist for the same experimental parameters, a dark and bright one. The index i labels the different cells. The panels b2, b3, and b4 illustrate that each cell undergoes an experimental bistability cycle. The cells are nonreciprocally coupled with their nearest neighbours. The arrows represent the different magnitudes of the coupling, and red and black dots account for dark and bright cells, respectively. The panels b5, b6, and b7 schematise theoretically each bistable cell nonreciprocally coupled to its nearest neighbour. c, d represent a reciprocally and nonreciprocally coupled bistable system dimer. α measures the lateral shift of the optical feedback, producing nonreciprocal coupling. The panels c1, c3, d1, and d3 show the snapshots of the dimer’s initial states, and the panels c2, c4, d2, and d4 show the snapshots of the dimer’s final states when one of the cells is excited. The system evolves, exhibiting a clear nonreciprocal coupling. See the Supplementary Movie 1. The dashed circles account for the illuminated areas. The scale bars accurately show the distance between interacting cells.