Rectangular hard-edged aperture diffracted Laguerre–Gaussian beams

Based on the relations between Laguerre–Gaussian (LG) and Hermite–Gaussian (HG) modes and by introduced the complex Gaussian expansion method for two dimensional rectangular aperture, the approximate analytical propagation expressions of the rotational symmetrical LG beams along with their even and odd modes through a paraxial ABCD optical system with rectangular hard-edged aperture are derived. As special cases of the results, the corresponding closed-forms of the circular aperture diffracted LG beams and non-truncated LG beams are also given. Numerical examples are given to prove the validity of this approximate analytical method and illustrate the propagation properties of the rectangular hard-edged aperture diffracted LG beams.