The von Neumann representation as a joint time–frequency parameterization for polarization-shaped femtosecond laser pulses

Abstract

We generalize the joint time–frequency von Neumann representation of femtosecond laser pulses for usage with time-dependent polarization states. The electric field is expanded in terms of Gaussian-shaped transform-limited subpulses located on a discrete time–frequency lattice, each with a specific polarization state. This formalism provides an intuitive picture for the time- and frequency-dependent polarization state. It can also serve as a basis for polarization pulse shaping. As an illustration, we define pulses for which polarization parameters (ellipticity and orientation) are given directly in time–frequency phase space. This approach has applications in quantum control and other areas for which time- and frequency-dependent light polarization is relevant.