Two types of superposition, i.e., the superposition of the intensity and the superposition of the cross-spectral density function of off-axis partially coherent beams propagating through atmospheric turbulence, are analytically and numerically studied. The Gaussian–Schell model beam is taken as a typical example of the partially coherent beam, and analytical propagation equations for the resulting beam in turbulence are derived. The mean-squared beam width, the power in the bucket, and the β parameter are taken as the characteristic parameters of beam quality to compare the results of the two types of superimposed partially coherent beams in turbulence. It is shown that for the two types of superposition the smaller the coherence parameter α is, the less the resulting beam is sensitive to the effects of turbulence. The resulting beam of off-axis partially coherent beams for the superposition of the intensity is less affected by the turbulence than that for the superposition of the cross-spectral density function. The results are physically interpreted.
© 2008 Optical Society of America
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