Ultrashort light pulse propagation in optical systems: an analysis based on the Wigner distribution function

The expression of the field amplitude associated with ultra- short light pulses is analyzed using the phase-space formalism for the Wigner distribution function (WDF). By properly modifying the diffraction integral to take into account the dispersion effects, we derive a 2D WDF, from which the on-axis intensity is obtained for varying time and defocus. Thus, the behavior of the optical system can be visualized as a 3D irradiance display in a combined space- temporal domain. The performance of three different pupil functions are investigated, by comparing their imaging properties.