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J Opt Soc Am A Opt Image Sci Vis. 2006 Jun;23(6):1410-8.

Propagation of hollow Gaussian beams through apertured paraxial optical systems.

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1
Joint Research Center of Photonics of the Royal Institute of Technology and Zhejiang University, Zhejiang University, Hangzhou, China. yangjian_cai@yahoo.com.cn

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.

PMID:
16715160
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