Optical Phase Transitions in Photonic Networks: a Spin-System Formulation

We investigate the collective dynamics of nonlinearly interacting modes in multimode photonic settings. To this end, we have established a connection with the theory of spin networks. The emerging “photonic spins” are complex, soft (their size is not fixed), and their dynamics has two constants of motion. Our analysis sheds light on the nature of the thermal equilibrium states and reveals the existence of optical phase transitions which resemble a paramagnetic to a ferromagnetic and to a spin-glass phase transition occurring in spin networks. We show that, for fixed optical power, these transitions are driven by the type of the network connectivity, its coordination number, and the total energy of the optical signal. In strictly one-dimensional photonic networks we establish a universal one-parameter scaling that dictates the crossover from a (quasi)ferromagnetic phase to a paramagnetic phase.