Abstract

We frequently need to know the statistical properties of light propagated through a turbulent atmosphere either for receiving images or for precorrecting for turbulence in a projected beam. The most common approach to determining these properties approximates the unperturbed light by either a plane or spherical wave,¹ whichever is more appropriate; often, for extended (but not infinite) sources, neither is appropriate. Lutomirski and Yura² formulated the so-called extended Huygens principle which introduces an integration over the area of the beam, and Ishimaru³ showed that the fundamental Gaussian mode could serve as a source by using the Rytov approximation. We show that higher-order Gaussian modes of rectangular and circular (azimuthal) symmetry can all be analytically propagated through turbulence. This allows a modal expansion of beams with arbitrary profile.

© 1991 Optical Society of America