Statistical properties of pulsed Gaussian Schell-model vortex beams

In this paper, a theoretical framework is developed to investigate the far-field statistical properties of pulsed Gaussian Schell-model vortex (PGSMV) beams. A mathematical relation between the degree of cross-polarization (DoCP), electromagnetic degree of coherence (EMDoC), and the usual degree of coherence (DoC) is established. Unlike the usual DoC and degree of polarization (DoP), which solely characterize the coherence and polarization properties of a beam, respectively, the EMDoC and DoCP characterize both coherence and polarization of a PGSMV beam. The results reveal that the interplay among spatial coherence, spectral coherence, and polarization at the input plane determines the far-field statistical properties of the PGSMV beams. Notably, both the EMDoC and DoCP distributions preserve the vortex characteristics of the input beam even for low values of input spatial coherence lengths, whereas this information is lost in the spectral density distributions. Furthermore, the EMDoC of the PGSMV beams decreases more rapidly than that of stationary Gaussian Schell-model vortex beams with the same topological charge. We also observe that the values of both the DoCP and the EMDoC increase as the spatial and temporal coherence lengths of the input beam increase. In contrast to DoCP, which increases with both the pulse width and the spectral width, the EMDoC decreases as either the pulse width or the spectral width increases. The findings of the study could be valuable in various applications that rely on the correlation properties of the PGSMV beams, such as free-space optical communication, micromachining, and pulse generation.