Abstract
We describe the simulations of the second harmonic generation of ultrashort laser pulses by numerically solving a system of wave propagation equations. The equations are solved by using a split-step method in twodimensional cyllindrically symmetric space and time coordinates. The diffraction part of a solution uses the Hopscotch type finite-difference scheme on a regular grid. The transport part is solved by using the cubic spline approximation. The obtained numerical results satisfactorily respect energy conservation constraints.
 The algorithm and program developed make it possible to optimize the process of the second harmonics generation and to identify the conditions where sufficiently high degree of the pulse compression with a relatively low degradation of their quality is achieved.
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