Focusing properties of partially coherent dark hollow Gaussian beams through a thin lens system

This paper investigated the focal shift of partially coherent dark hollow Gaussian beams through a thin lens system. An analytic expression of the irradiance distribution of the focusing partially coherent dark hollow Gaussian beams in the back focal plane has been given by using the Collins formula. The focus shift of focused partially coherent dark hollow Gaussian beams in different parameters is studied in detail by numerical calculations. It is found that the absolute value of the focal shift of partially coherent dark hollow Gaussian beams decreases as the transverse coherence width or the order of the dark hollow Gaussian beams or a parameter of the dark hollow Gaussian beams increases.