Diffractive-refractive spatio-temporal shaping of ultrashort pulses

Ultrashort optical pulses play an important role in physics and engineering with applications in the life sciences, chemistry and data communications. Beam shaping has to take into consideration both, the spatial and temporal properties of a pulse. However, due to spatio-temporal dispersive coupling of the wave field, spatial beam shaping affects the temporal properties of the pulse and vice versa. In earlier work, it has been shown, that the combination of diffraction and refraction is a powerful tool for design and implementation. In this context, however, it is necessary to understand the relevant factors for this technique and to explore the limitations. Here, we present a comprehensive analysis of diffractive-refractive spatio-temporal pulse shaping and consider various examples.