Abstract
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.
Highlights
A novel method for numerical modelling of noncollinear and nonlinear interaction of femtosecond laser pulses is presented
Even more fundamental approach, which drops the paraxial approximation and treats nonlinear polarization in a general way can be derived from the vectorial Unidirectional Pulse Propagation Equation (UPPE)[2,3]
In the present paper we describe a novel method for numerical simulations of noncollinear pulse propagation and nonlinear interaction using just the unidirectionality approximation
Summary
A novel method for numerical modelling of noncollinear and nonlinear interaction of femtosecond laser pulses is presented. Even more fundamental approach, which drops the paraxial approximation and treats nonlinear polarization (and possibly free currents) in a general way can be derived from the vectorial Unidirectional Pulse Propagation Equation (UPPE)[2,3]. These models enable numerical simulation of nonlinear processes in the presence of frequency dependent diffraction, dispersion and spatial walk-off. They do not, immediately enable noncollinear beam propagation. To this day no propagation simulation approach to these problems have been attempted
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