Synergic action of linear dispersion, second-order nonlinearity, and third-order nonlinearity in shaping the spectral profile of a femtosecond pulse transporting in a lithium niobate crystal

We present a detailed theoretical and numerical analysis on the temporal-spectral-spatial evolution of a highpeak-power femtosecond laser pulse in two sets of systems: a pure lithium niobate (LN) plate and a periodically poled lithium niobate(PPLN) plate. We develop a modified unidimensional pulse propagation model that considers all the prominent linear and nonlinear processes and carried out the simulation process based on an improved split-step Fourier transformation method. We theoretically analyze the synergic action of the linear dispersion effect, the second-order nonlinearity(2nd-NL) second-harmonic generation (SHG) effect, and the third-order nonlinearity(3rd-NL) self-phase modulation(SPM) effect, and clarify the physical mechanism underlying the peculiar and diverse spectral broadening patterns previously reported in LN and PPLN thin plate experiments. Such analysis and discussion provides a deeper insight into the synergetic contribution of these linear and nonlinear effects brought about by the interaction of a femtosecond laser pulse with the LN nonlinear crystal and helps to draw a picture to fully understand these fruitful optical physical processes, phenomena, and laws.