Characterization of nonlinear phase shifts using the temporal transport-of-intensity equation

An equivalent of the transport-of-intensity equation is derived in the temporal domain to describe the evolution of the instantaneous power of the electric field in a dispersive medium. As its spatial counterpart, which can be used to measure wavefronts using intensity measurements after various amounts of diffraction, the temporal transport-of-intensity equation allows the measurement of temporal phase shifts using only intensity information in a direct non-interferometric way. The application to the measurement of nonlinear phase shifts induced by self-phase modulation and cross-phase modulation is presented, and the nonlinear coefficient of a highly nonlinear fiber is accurately determined.