Effective radius of curvature of spatially partially coherent beams propagating through non-Kolmogorov turbulence

The laser beam propagation through atmospheric turbulence is of importance for both theoretical study and practical applications. Taking the Gaussian Schell-model (GSM) beam as a typical example of spatially partially coherent beams, based on the non-Kolmogorov spectrum and generalized Huygens-Fresnel principle, the analytical expression for the effective radius of curvature of GSM beams propagating through non-Kolmogorov turbulence is derived. The effects of turbulence parameters (including generalized exponent parameter alpha, inner scale l(0), and outer scale L-0) and propagation distance z on the effective radius of curvature of GSM beams are stressed. It is shown that the effective radius of curvature of GSM beams increases with outer scale L-0 decreasing for 3.6 < alpha < 4 and the inner scale l(0) increasing, but dose not monotonically vary with the increases of exponent parameter alpha and propagation distance z. The results are explained physically.