The directionality of general beams propagating in free space and in atmospheric turbulence is studied. Based on the partial-coherence theory, the analytical expressions for the mean-squared width and the angular spread of general beams are derived by using the integral transform technique. It is shown that the mean-squared width and the angular spread depend not only on the weighting factors of all basis modes but also on the weighting factors of the corresponding mode coherence coefficients of the ith and the (i+2)th if the Hermite-Gaussian modes are adopted. It is found that under a certain condition there exist the equivalent general beams which may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The result holds true, irrespective of the model of turbulence used.
© 2008 Optical Society of AmericaPDF Article