Abstract
Summary On the basis of the expansion of the hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression of Laguerre-Gaussian beams passing through an annular apertured paraxial ABCD optical system is derived. Meanwhile, the corresponding closed-forms for the unapertured or circular apertured or circular black screen cases have also been given. Numerical examples are given to illustrate the propagation characteristics of Laguerre-Gaussian beams.
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