Propagation of complex-argument Laguerre-Gaussian beams through a rectangular hard-edged aperture

Using the relations between Hermite and Laguerre-Gaussian(LG) modes and expanding the window function of two-dimensional rectangular hard-edged apertures into a finite sum of complex Gaussian functions,the propagation of complex-argument Laguerre-Gaussian beams through a paraxial optical ABCD system with a rectangular hard-edged aperture is studied.An analytical propagation equation is derived and used to study the diffraction at the rectangular hard-edged aperture and the focusing properties of complex-argument LG beams.The method proposed is useful for studying the beam transformation through an apertured optical system with different geometrical symmetry.