Abstract
Easily accessible through tabletop experiments, paraxial fluids of light are emerging as promising platforms for the simulation and exploration of quantumlike phenomena. In particular, the analogy builds on a formal equivalence between the governing model for a Bose-Einstein condensate under the mean-field approximation and the model of laser propagation inside nonlinear optical media under the paraxial approximation. Yet, the fact that the role of time is played by the propagation distance in the analog system imposes strong bounds on the range of accessible phenomena due to the limited length of the nonlinear medium. In this Letter, we present an experimental approach to solve this limitation in the form of a digital feedback loop, which consists of the reconstruction of the optical states at the end of the system followed by their subsequent reinjection exploiting wavefront shaping techniques. The results enclosed demonstrate the potential of this approach to access unprecedented dynamics, paving the way for the observation of novel phenomena in these systems.