Optimized computation of tight focusing of short pulses using mapping to periodic space

When a pulsed, few-cycle electromagnetic wave is focused by optics with f-number smaller than two, the frequency components it contains are focused to different regions of space, building up a complex electromagnetic field structure. Accurate numerical computation of this structure is essential for many applications such as the analysis, diagnostics, and control of high-intensity laser-matter interactions. However, straightforward use of finite-difference methods can impose unacceptably high demands on computational resources, owing to the necessity of resolving far-field and near-field zones at sufficiently high resolution to overcome numerical dispersion effects. Here, we present a procedure for fast computation of tight focusing by mapping a spherically curved far-field region to periodic space, where the field can be advanced by a dispersion-free spectral solver. In many cases of interest, the mapping reduces both run time and memory requirements by a factor of order 10, making it possible to carry out simulations on a desktop machine or a single node of a supercomputer. We provide an open-source C++ implementation with Python bindings and demonstrate its use for a desktop machine, where the routine provides the opportunity to use the resolution sufficient for handling the pulses with spectra spanning over several octaves. The described approach can facilitate the stability analysis of theoretical proposals, the studies based on statistical inferences, as well as the overall development and analysis of experiments with tightly-focused short laser pulses.