Statistical Theory of Relaxation in Disordered Nonlinear Multimoded Photonic Systems

Optical thermodynamics takes a statistical approach to the description of beam evolution towards its thermal state in multimoded nonlinear photonic platforms. We extend this theory to out-of-equilibrium systems to study the rates at which various optical systems relax towards equilibrium. We study systems that support modes with different spatial profiles and examine how a system's relaxation rates reflect its modes' profile. We find that systems with localized modes, whether they are power-law or exponentially localized, relax slower than those with extended modes. Examining the entire distribution of relaxation rates revealed a transition from a Porter-Thomas to a Log-Normal distribution in response to Anderson localization. Surprisingly, we find that systems that support fractal modes (e.g. disordered systems at the metal-to-insulator phase transition) relax faster than extended modes, due to correlations between energetically close fractal modes.