Phase mask for spatial and temporal control of ultrashort light pulses focused by lenses

The field amplitude associated with ultrashort light pulses was analyzed by using the phase-space formalism of the Wigner distribution function (WDF). The diffraction integral was properly modified to take into account the dispersion effects (up to second order). A two-dimensional WDF associated with a reduced pupil function was derived, from which the on-axis irradiance was obtained for varying times. A two-dimensional and rotationally symmetric quartic-phase mask to control the temporal stretching of femtosecond light pulses passing through optical systems was proposed and analyzed. A Gaussian spatial and temporal pulse passing through a single lens with and without the phase mask was investigated.