Thermalization-induced self-polarization of temporally incoherent light: A nonequilibrium wave turbulence kinetic approach

Conservative nonlinear waves generally undergo an irreversible process of thermalization toward the Rayleigh–Jeans (RJ) equilibrium state. Light thermalization has recently been experimentally investigated in the two-dimensional transverse spatial dynamics of multimode waveguides. Here, we consider the one-dimensional temporal dynamics of incoherent light propagating in a weakly birefringent single-mode fiber. We show that light thermalization is responsible for a self-polarization of the incoherent wave during its propagation. Within the framework of wave turbulence theory, we show that this phenomenon originates from a nonequilibrium process of adiabatic cooling: polarization fluctuations are continuously transferred toward the high-frequency tails of a local RJ equilibrium state, whose effective temperature decreases during propagation, thereby increasing the degree of light polarization. Moreover, in the absence of a high-frequency cut-off that would regularize the ultraviolet catastrophe in the temporal domain, the optical wave exhibits an ever-increasing degree of polarization, ultimately approaching unity. These results show that it is thermodynamically advantageous for the optical field to evolve toward a polarized state, which provides new insight into spontaneous self-organization phenomena in conservative Hamiltonian systems operating far from thermodynamic equilibrium.