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In free space optical communication links, due to the fast divergence of orbital angular momentum (OAM) beam, the issue of aperture mismatch is very common. However, in order to realize the aperture adaptation, this problem can be solved by introducing a defocusing double-lens-system at transmitter-side to control the transmitting beam divergence. In this paper, the expression for equivalent radius of Laguerre–Gaussian (LG) beams through defocusing double-lens-systems after a certain propagation distance is derived using Collins' diffraction integral formula. The expression of defocus distance with a determined transformation beam size is also derived. We numerically analyze how the defocus distance changes with OAM modes, transmitting beam size and transmission distance in free space. The calculating results show that the divergence of high-order OAM-beams in free space transmission can be effectively restrained by setting proper defocus distance to realize the aperture adaptation at the receiver. The results also show that defocus distance decreases with topological charge number, transmitting beam size or transmission distance increasing when equivalent focal length is smaller than transmission distance. When equivalent focal length is larger than transmission distance, defocus distance increases with increasing topological charge number or transmitted beam size and decreases with increasing transmission distance, in the meanwhile the smaller the ratio of equivalent radius of OAM beam at the receiver to the transmitted beam size is, the larger the required defocus distance for same OAM modes is. This paper will be beneficial to the parameters choosing for the OAM-FSO communication system.
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