Transformation of a femtosecond pulse upon focusing

Diffraction of a converging spherical wave from a circular aperture is studied by the delta-pulse method. Simple expressions are obtained which describe the influence of an edge wave on the signal shape at the symmetry axis of the system. The spatiotemporal structure of the signal is studied in the vicinity of the focal point. It is found that, irrespective of the value of the solid angle of the illuminated sector, a signal proportional to the first time derivative of the input-pulse amplitude is formed at the focus.