Noncollinear and nonlinear pulse propagation.

A novel method for numerical modelling of noncollinear and nonlinear interaction of femtosecond laser pulses is presented. The method relies on a separate treatment of each of the interacting pulses by it's own rotated unidirectional pulse propagation equation (UPPE). We show that our method enables accurate simulations of the interaction of pulses travelling at a mutual angle of up to 140°. The limit is imposed by the unidirectionality principal. Additionally, a novel tool facilitating the preparation of noncollinear propagation initial conditions - a 3D Fourier transform based rotation technique - is presented. The method is tested with several linear and nonlinear cases and, finally, four original results are presented: (i) interference of highly chirped pulses colliding at mutual angle of 120°, (ii) optical switching through cross-focusing of perpendicular beams (iii) a comparison between two fluorescence up-conversion processes in BBO with large angles between the input beams and (iv) a degenerate four-wave mixing experiment in a boxcar configuration.