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22 April 2010 Propagation of higher-order annular Laguerre-Gauss beams in atmospheric turbulence
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The extended Huygens-Fresnel integral, with a quadratic structure function approximation, was used to derive closed form analytical expressions for the mean irradiance and spot size of higher-order annular Laguerre-Gaussian beams propagating in atmospheric turbulence. Comparisons were made to free space propagation of Laguerre-Gaussian modes, in which the spatial distribution is preserved as the beam spreads due to natural diffraction. It was found that the central void in annular Laguerre-Gaussian beams of any order is filled in as the turbulence strength increases. Higher order modes are less sensitive to the turbulence distortions compared to lower order annular beams, since higher order beams have a smaller turbulence induced fractional increase in their spot size compared to the lower order modes.
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Frida E. Strömqvist Vetelino and Ricky J. Morgan "Propagation of higher-order annular Laguerre-Gauss beams in atmospheric turbulence", Proc. SPIE 7685, Atmospheric Propagation VII, 768503 (22 April 2010);

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