Shaping the beam profile of an elliptical Gaussian beam by an elliptical phase aperture

Based on the generalized Collins integral formula, an analytical paraxial propagation formula for an elliptical Gaussian beam (EGB) passing through an astigmatic ABCD optical system with an elliptical phase aperture is derived by use of a tensor method. As an application example, we study the propagation properties of an EGB passing through an elliptical aperture in free space. It is found that the elliptical phase aperture can be used for shaping the beam profile of an EGB, which is useful in many applications, such as free space optical communication and material thermal processing. The elliptical phase aperture induced changes of the propagation factors of an EGB are also analyzed.