Critical disorder inflating thermal relaxation in nonlinear multimoded systems

We establish a connection between the thermal relaxation rate of optical beams in weakly nonlinear multimoded systems and the spatial correlations among the system's linear supermodes. We implement this methodology for tailored network arrangements supporting various spatial mode profiles. For critical disorder configurations giving rise to metal-insulator transitions, fractal supermodes extremize the correlations, inflating the relaxation rates. Our results inform a design of the physical platforms (their topology, disorder, etc.) supporting targeted relaxation rates.