Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

In ultra-short laser pulses, small changes in dispersion properties before the final focusing mirror can
lead to severe pulse distortions around the focus and therefore to very different pulse properties at the
point of laser-matter interaction yielding unexpected interaction results. The mapping between far and
near-field laser properties intricately depends on the spatial and angular dispersion properties as well as the
focal geometry. For a focusing Gaussian laser pulse subject to angular, spatial, and group delay dispersion,
we derive analytical expressions for its pulse-front tilt, duration, and width from a fully analytic expression
for its electric field in time-space domain. This expression is not only valid in and near the focus but along
the entire propagation distance from the focusing mirror to the focus. Together with expressions relating
angular, spatial, and group delay dispersion before focusing at an off-axis parabola to the respective values
in the pulse’s focus, these formulas are used to show in example setups that pulse-front tilts of lasers
with small initial dispersion can become several ten degrees large in the vicinity of the focus while being
small directly in the focus. The formulas derived here provide the analytical foundation for observations
previously made in numerical experiments. By numerically simulating Gaussian pulse propagation and
measuring properties of the pulse at distances several Rayleigh lengths off the focus we verified the analytic
expressions.