Propagation and focusing properties of partially coherent sinh-Gaussian beams

In order to study the propagation and focusing properties of partially coherent sinh-Gaussian (SHG) beams through an astigmatic lens, the analytical expression of the intensity was derived based on the transmission formula of partially coherent beams, and the analytical expression of the beam width, the far-field divergence angle and the M2 factor were deduced, the intensity and the beam width were calculated and analyzed. It is found that the intensity distributions of focused partially coherent ShG beams depend on the astigmatic coefficient C6, spatial coherence parameter, decentered parameter a, Fresnel number Nw and position (x, y, z) in general. The astigmatism results in a difference between the beam widths in the x and y directions, but the M2 factor is independent of the astigmatism and decreases as the coherence increases and the decentered parameter decreases. The spatial beam shaping is achievable at the geometrical focal plane and other positions by properly varying the astigmatism and spatial coherence.