A brief analysis on pulse front tilt in simultaneous spatial and temporal focusing

The spatial and temporal behavior of ultrashort pulses has drawn more and more attention. Especially in laser material processing, such spatio-temporal behavior has significant influences. In this paper we present a brief analysis on the pulse front tilt (PFT) in simultaneous spatial and temporal focusing (SSTF) mathematically and in simulations. We apply paraxial field tracing based on the Collins integral for modeling the spatio-temporal focusing process. Using the shift theorem of the Fourier transformation, we present an explanation of the PFT in focus for general input pulses. Next, by assuming a Gaussian lateral pulse shape, an analytical solution for the field distribution at any position in the region is obtained. In this work we take the influence of an initial PFT before focusing into considerations as well and find potential way to control the PFT during the focusing process. Finally with the optical modeling software VirtualLabTM we present rigorous simulations of the SSTF to verify our mathematical conclusions.