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

In this paper we analyze the pulse front tilt (PFT) in simultaneous spatial and temporal focusing 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 can explain 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. Compared with previous works, we take the influence of an initial PFT into considerations as well. The theoretical calculation is valid for incoming pulses with temporally chirp and/or initial PFT. Finally with the optical modeling software VirtualLab™ we presented rigorous simulations of the SSTF to verify our mathematical conclusions.