Third- and fifth-order optical nonlinearities characterization using the D4σ-Z-scan method

We solved analytically the equations governing the evolution of the intensity and phase shift inside a nonlinear medium taking into account third- and fifth-order nonlinear susceptibilities. We give explicit expression of the propagation distance and the phase shift versus the output intensity. This solution is inverted numerically by means of Newton´s method. The result does not apply to some special cases due to the vanishing of coefficients, then analytical solutions are given, so that all the cases are covered. Combined with D4σ-Z-scan method, the third- and fifth-order nonlinear coefficients are measured at 532 nm and 1064 nm in the picosecond regime.