Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence
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The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the angular spread θsp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition of the intensity. However, the θsp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition of the cross-spectral density function. For the superposition of the cross-spectral density function, θsp of GSM array beams with smaller coherence length σ0, smaller waist width w0, smaller beam number N, and larger separation distance xd are less affected by turbulence than of those with larger σ0,w0,N, and smaller xd; while, for the superposition of the intensity, the effect of turbulence on θsp is independent of N and xd. In addition, the angular spread is nearly the same for the two types of superposition when σ0 or w0 is small enough, or xd is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence.
PACS42.25.Dd 42.25.Kb 42.25.Fx
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