Radially polarized twisted Multi-Gaussian Schell-model beams and their statistical properties

Abstract

A radially polarized twisted Multi-Gaussian Schell-model (RPT MGSM) beam based on the unified theory of coherence and polarization is introduced. The reliability conditions for the beams are also derived. We derive the analytical expressions for the elements of the cross-spectral density matrix of such beam propagating in free space and investigate the statistical properties, such as spectral density, degree of coherence, degree of polarization and state of polarization. It is found that the statistical properties of the RPT MGSM beams are closely related to the twist phase, e.g. the twist phase induces not only the rotation of the beam spot but also changes of the degree of coherence, degree of polarization and state of polarization on propagation. Specially, an interesting phenomenon is found. In the far field, when the beams without carrying twist factor, the state of polarization in the flat-top area of intensity distribution is azimuthally polarized rather than radially polarized. Our results may be useful in optical trapping and free-space optical communications.