Polarization and angle-of-arrival fluctuations for a plane wave propagated through a turbulent medium

The correlation function of the fluctuations of the depolarized component of a plane wave as a function of the distance between two parallel line-of-sight paths is derived in terms of the index of refraction variations. A first-order solution to the wave equation is found using spectral analysis techniques. The mean square polarization fluctuation is predicted to have a dependence, in contrast to the work of another author which showed no wavelength dependence. Some numerical values are calculated and the restrictions on the solutions are discussed. At optical wavelengths the depolarized component is extremely small. From the point of view of minimizing the noise introduced by a turbulent atmosphere, polarization modulation seems attractive compared to amplitude or angle modulation. The problem of determining the angle-of-arrival fluctuations when using a wave optics formulation is discussed. If one accepts the statement that the angle-of-arrival is the normal to the wave front at any point, then the correlation function of the angle-of-arrival is simply related to the correlation function of the phase fluctuations and agrees with the ray optics results.