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 β 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 wR, β parameter and SRE versus the obscure ratio ε of annular beams are quite different, i.e., wR decreases monotonically as ε increases, while changes of β parameter and SRE versus ε are not monotonic. There exists a maximum of β for thick annular beams, and there exists a minimum of β for thin annular beams. But there only exists a maximum of SRE for thin annular beams. The values of ε at which β 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 β and the maximum of SRE may be used, but the maximum of β should be avoided.