A scintillation index formulation for annular beams in strong turbulence is developed that is also valid in moderate and weak turbulence. In our derivation, a modified Rytov solution is employed to obtain the small-scale and large-scale scintillation indices of annular beams by utilizing the amplitude spatial filtering of the atmospheric spectrum. Our solution yields only the on-axis scintillation index for the annular beam and correctly reduces to the existing strong turbulence results for the Gaussian beam—thus plane and spherical wave scintillation indices—and also correctly yields the existing weak turbulence annular beam scintillations. Compared to collimated Gaussian beam, plane, and spherical wave scintillations, collimated annular beams seem to be advantageous in the weak regime but lose this advantage in strongly turbulent atmosphere. It is observed that the contribution of annular beam scintillations comes mainly from the small-scale effects. At a fixed primary beam size, the scintillations of thinner collimated annular beams compared to thicker collimated annular beams are smaller in moderate turbulence but larger in strong turbulence; however, thinner annular beams of finite focal length have a smaller scintillation index than the thicker annular beams in strong turbulence. Decrease in the focal length decreases the annular beam scintillations in strong turbulence. Examining constant area annular beams, smaller primary sized annular structures have larger scintillations in moderate but smaller scintillations in strong turbulence.
© 2010 Optical Society of America
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