Evaluation of twisted Gaussian Schell model beams produced with phase randomized coherent fields

The twisted Gaussian Schell Model describes a family of partially coherent beams that present several interesting characteristics, and as such have attracted attention in classical and quantum optics. Recent techniques have been demonstrated to synthesize these beams from a coherent source using a discrete set of 'pseudo-modes', where the phase of each mode is randomized so that they are mutually incoherent. Here we investigate this technique and evaluate the resulting beam parameters, such as divergence, coherence length and twist phase. We show that for a finite set of modes there is also some residual coherence, which can have an observable effect. A theoretical model is developed for the output field that includes residual coherence and agrees very well with experimental data. In addition, we demonstrate a simple method to measure the twist phase using double slit interference.