Boundary conditions in the modeling of the material modification by laser pulses

To modify transparent materials by femtosecond laser pulses sharply focused pulses are required. To model the modification process, it is necessary to compute the distribution of the electric field of the pulse in the vicinity of the order or less 100 microns from the focus. An often-used paraxial formulas in the case of sharp focus are not applicable. In the case, when a parabolic mirror is used as a focusing element, the desired field distribution can be obtained using Stratton-Chu integral (SCI). In the presented paper the generalization of SCI on the short in time pulses, the simplification of SCI in the limit of the mirror's focus length much larger 100 microns, and concrete formulas of SCI for the pulses of different polarizations are given. The main achievement of the paper is development of extremely effective numerical methods of SCI computation. The last one is a difficult problem. Using this method unexpected and intriguing properties of the field created by sharp focusing top-hat laser pulse are demonstrated.