## Abstract

The propagation effects of spatially pseudo-partially coherent Gaussian Schell-model beams in atmosphere are investigated numerically. The characteristics of beam spreading, beam wandering and intensity scintillation are analyzed respectively. It is found that the degradation of degree of source coherence may cause reductions of relative beam spreading and scintillation index, which indicates that partially coherent beams are more resistant to atmospheric turbulence than fully coherent beams. And beam wandering is not much sensitive to the change of source coherence. However, a partially coherent beam have a larger spreading than the fully coherent beam both in free space and in atmospheric turbulence. The influences of changing frequency of random phase screen which models the source coherence on the final intensity pattern are also discussed.

© 2009 Optical Society of America

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### Equations (9)

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(1)
$$U(\overrightarrow{\rho},0;\omega )=\frac{1}{2\pi}{\int}_{-\infty}^{\infty}u(\overrightarrow{\rho},0;t)\mathrm{exp}\left(i\mathrm{\omega t}\right)\mathrm{dt},$$
(2)
$$W({\overrightarrow{\rho}}_{1},{\overrightarrow{\rho}}_{2},{\omega}_{1},{\omega}_{2})=\u3008{U}^{*}({\overrightarrow{\rho}}_{1},0;{\omega}_{1})U({\overrightarrow{\rho}}_{2},0;{\omega}_{2})\u3009,$$
(3)
$$W({\overrightarrow{\rho}}_{1},{\overrightarrow{\rho}}_{2})=\sqrt{{I}_{0}\left({\overrightarrow{\rho}}_{1}\right)}\sqrt{{I}_{0}\left({\overrightarrow{\rho}}_{2}\right)}{\mu}_{0}\left({\overrightarrow{\rho}}_{2}-{\overrightarrow{\rho}}_{1}\right),$$
(4)
$${I}_{0}\left(\overrightarrow{\rho}\right)=A\mathrm{exp}\left(-2{\rho}^{2}/{W}_{0}^{2}\right),$$
(5)
$${\mu}_{0}\left(\overrightarrow{\rho}\right)=\mathrm{exp}\left(-{\rho}^{2}/{l}_{c}^{2}\right),$$
(6)
$$u\left(x,y,0;t\right)={u}_{0}\left(x,y,0\right)\mathrm{exp}\left[i\xi \left(x,y;t\right)\right],$$
(7)
$$\xi \left(x,y;t\right)=r\left(x,y;t\right)\otimes f\left(x,y\right),$$
(8)
$$f\left(x,y\right)=\frac{1}{2\pi {\sigma}_{f}^{2}}\mathrm{exp}\left(-\frac{{x}^{2}+{y}^{2}}{2{\sigma}_{f}^{2}}\right),$$
(9)
$${l}_{c}^{2}=\frac{16\pi {\sigma}_{f}^{4}}{{\sigma}_{r}^{2}}.$$