Coherence vortex properties of partially coherent flat-topped vortex beams

The analytical propagation expression of partially coherent flat-topped vortex beams through a paraxial optical ABCD system is derived, and it then is used to investigate the coherence vortex properties of partially coherent flat-topped vortex beams in the Fourier transform and fractional Fourier transform systems. It is shown that in the Fourier transform system the coherence vortex depends on the flat-topped beam order N, spatial coherence parameter α and position (x ₁,y ₁) of the reference point, whereas in the fractional Fourier transform system the flat-topped beam order N does not affect the spectral degree of coherence. Furthermore, in both transform systems, depending on the choice of the reference point, the zero value point of the spectral degree of coherence may be present or absent. In particular, if x ₁=y ₁=0 is selected, the phase at the zero value point of the spectral degree of coherence may be determinate; thus the coherence vortex does not exist.