Propagation expression for cosine-Gaussian beams through a hard edge aperture

Based on Collinsinteg ralformula,the propagation of cosine Gaussian beams passing through a first order paraxial optical system with rectangular aperture is studied.With the rectangular function converted to a sum of complex Gaussian functions,a closed for m propagation expression for Gaussian beams is derived.Take a thin lens system with hard edge aperture as an example,numerical calculation is performed.The computation result conforms to that obtained by the straightforward integration of Collins formula.The principal advantage of the method is the great reduction of computing time.The method can also be applied to the propagation of ot her types of laser beams passing an optical system with a hard edge aperture.