Propagation of coherence-OAM matrix of an optical beam in vacuum and turbulence

Abstract

Propagation of the coherence-orbital angular momentum (COAM) matrix of partially coherent beams in homogeneous and isotropic turbulence, e.g., atmosphere, is formulated using the extended Huygens-Fresnel principle. It is found that under the effect of turbulence the elements in the COAM matrix will generally be affected by other elements, resulting in certain OAM mode dispersion. We show that if turbulence is homogeneous and isotropic, there exists an analytic “selection rule” for governing such a dispersion mechanism, which states that only the elements having the same index difference, say l – m, may interact with each other, where l and m denote OAM mode indices. Further, we develop a wave-optics simulation method incorporating modal representation of random beams, multi-phase screen method and the coordinate transformation to simulate propagation of the COAM matrix of any partially coherent beam propagating in free space or in turbulent medium. The simulation method is thoroughly discussed. As examples, the propagation characteristics of the most representative COAM matrix elements of circular and elliptical Gaussian Schell-model beams in free space and in turbulent atmosphere are studied, and the selection rule is numerically demonstrated.