Theoretical analysis of supercontinuum and colored conical emission produced during ultrashort laser pulse interaction with gases

We use a conceptually new approach to theoretical modeling of self-focusing in which we integrated diffractive and geometrical optics in order to explain and predict emission of white light and colored rings observed in ultrashort laser pulse interaction. In our approach laser beam propagation is described by blending solution of linear Maxwell's equation and a correction term that represents nonlinear field perturbation expressed in terms of paraxial ray-optics (eikonal) equation. No attempt is made to create appearance of exhaustive treatment via use of complex mathematical models. Rather, emphasis is placed on elegance of the formulations leading to fundamental understanding of underlying physics and, eventually, to an accurate practical numerical model capable of simulating white light generation and conical emission of colored rings produced around the filament.