Space–time Wigner functions and their application to the analysis of a pulse shaper

The space–time Wigner function is a powerful tool for the analysis of femtosecond optical devices that act on both the spatial and the temporal features of ultrashort pulses. The advantages of this approach and the properties of the space–time Wigner function are reviewed. The matrix formalism that can be used to describe the action of dispersive first-order devices on any femtosecond pulse is presented. The method is used to describe and understand the behavior of an ultrashort light pulse propagating through a pulse shaper. The consequences of the limited resolution in the spectral-to-spatial conversion for the output pulse are fully analyzed.