title: Propagation of hollow Gaussian beams through apertured paraxial optical systems.
abstract: On the basis of the generalized Collins formula and the expansion of the hard-aperture function into a finite sum of complex Gaussian functions, an approximate analytical formula for a hollow Gaussian beam propagating through an apertured paraxial stigmatic (ST) ABCD optical system is derived. Some numerical examples are given. Furthermore, by using a tensor method, we derive approximate analytical formulas for a hollow elliptical Gaussian beam propagating through an apertured paraxial general astigmatic ABCD optical system and an apertured paraxial misaligned ST ABCD optical system. Our results provide a convenient way for studying the propagation and transformation of a hollow Gaussian beam and a hollow elliptical Gaussian beam through an apertured general optical system.
authors.affiliation: Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University, Zhejiang University, Hangzhou, China. yangjian_cai@yahoo.com.cn
authors.forename: Yangjian
authors.initials: Y
authors.lastname: Cai
authors.forename: Sailing
authors.initials: S
authors.lastname: He