Energy focusability of annular beams propagating through atmospheric turbulence along a slanted path

The energy focusability of annular beams propagating through atmospheric turbulence along a slanted path is studied in detail by using numerical simulation method. The relative mean-squared beam width wR, the beta parameter and the energy Strehl ratio (SRE) are adopted to characterize the influence of turbulence on the energy focusability which defined by a certain energy and the energy within a given bucket radius, respectively. It is shown that, in general, the influence of turbulence on the energy focusability is large for thick annular beams, and is small for thin annular beams. However, it is found out that the laws of w(R), beta parameter and SRE versus the obscure ratio beta of annular beams are quite different, i.e., w(R) decreases monotonically as epsilon increases, while changes of beta parameter and SRE versus epsilon are not monotonic. There exists a maximum of beta for thick annular beams, and there exists a minimum of beta for thin annular beams. But there only exists a maximum of SRE for thin annular beams. The values of epsilon at which beta reaches its maximum or minimum and SRE reaches its maximum are nearly independent of the zenith angle of the slanted path. In practice, the minimum of beta and the maximum of SRE may be used, but the maximum of beta should be avoided. (C) 2015 Elsevier Ltd. All rights reserved.