Spatio-temporal thermalization and adiabatic cooling of guided light waves

We propose and theoretically characterize three-dimensional spatio-temporal thermalization of a continuous-wave classical light beam propagating along a multi-mode optical waveguide. By combining a non-equilibrium kinetic approach based on the wave turbulence theory and numerical simulations of the field equations, we anticipate that thermalizing scattering events are dramatically accelerated by the combination of strong transverse confinement with the continuous nature of the temporal degrees of freedom. In connection with the blackbody catastrophe, the thermalization of the classical field in the continuous temporal direction provides an intrinsic mechanism for adiabatic cooling and, then, spatial beam condensation. Our results open new avenues in the direction of a simultaneous spatial and temporal beam cleaning.