Interplay of diffraction and nonlinear effects in propagation of ultrashort pulses

We investigate the interplay of diffraction and nonlinear effects during propagation of very short light pulses. Adapting the factorization approach to the problem at hand by keeping the transverse-derivative terms apart from the residual nonlinear contributions we derive an unidirectional propagation equation valid for weak dispersion and reducing to the slowly-evolving-wave-approximation for the case of paraxial rays. Comparison of numerical simulation results for the two equations shows pronounced differences when self-focusing plays important role. We devote special attention to modelling propagation of ultrashort terahertz pulses taking into account diffraction as well as Kerr type and second order nonlinearities. Comparing measured and simulated wave forms we deduce the value of the nonlinear refractive index of lithium niobate in the terahertz region to be three orders of magnitude larger than in the visible.