Poincare representation of polarization-shaped femtosecond laser pulses

The usage of Poincare phase space for the representation of polarization-shaped femtosecond laser pulses is discussed. In these types of light fields the polarization state (i.e. ellipticity and orientation) changes as a function of time within a single laser pulse. Such deliberate variation can be achieved by frequency-domain femtosecond pulse shaping in which two polarization components are manipulated individually. Here it is shown how these light pulses can be represented as temporal trajectories through the ellipticity-orientation (Poincare) phase space, whereas conventional light (either continuous-wave or pulsed) is determined by only one specific Poincare location. General properties of parametric Poincare trajectories are discussed, and their relation to experimentally accessible pulse-manipulation parameters (i.e. amplitudes and phases) determined. Specifically, it is shown how the maximum rate by which a given polarization state can be turned into a different one (at significant intensity levels) is limited by the spectral laser bandwidth. Apart from their direct usage in polarization-shaped pulse representation, Poincare trajectories also form the basis for intuitive quasi-three-dimensional renderings of the electric field profile. There, the temporal evolution of polarization, intensity, and chirp is directly apparent in a single illustration.