Boundary Conditions in Modeling the Modification of Materials by Laser Pulses

Sharply focused pulses are required to modify transparent materials by femtosecond laser pulses. To model the modification process, it is necessary to compute the distribution of the electric field of the laser pulse at distances of the order of hundreds of microns from the focus. The frequently used paraxial approximation in the case of a sharp focus is not applicable. It is necessary to calculate a specific optical system. In the case when a parabolic mirror is used as a focusing element, the desired field distribution can be obtained using the Stratton–Chu integral (SCI). In this paper the generalization of the SCI to the case of a finite-time (femtosecond) pulse and a simplification of the SCI for the case of a large mirror located far from the focus are presented. This is typical for a wide range of practical problems. In addition, specific formulas of the SCI for frequently used polarizations of laser pulses are given. The main achievement of this paper is the development of extremely effective numerical methods of computing the SCI, which is the integral of a rapidly oscillating function. As an example, the calculation of the field of a focused laser pulse with a cylindrical intensity distribution along the radius (top-hat pulse) is given.