5-DoF-transformation-based statistical characterization of optical-wave fluctuations arising from propagation in atmospheric turbulence with arbitrarily orientated anisotropy ellipsoids

Turbulence in certain portions of the atmosphere is anisotropic and its anisotropy ellipsoids may exhibit an arbitrary orientation with respect to a given propagation coordinate system. To explore various statistics of optical-wave fluctuations arising from propagation in atmospheric turbulence with arbitrarily oriented anisotropy ellipsoids, a new Markov-approximation-based spectrum model is developed by introducing five independent parameters, specifically, the three Euler angles and two anisotropic coefficients, which thus bring 5 degrees of freedom (DoF) to the model. With the help of such a spectrum model, a 5-DoF-transformation-based approach is proposed to derive analytical expressions for the wave structure function (WSF), log-amplitude-fluctuation spatial covariance function (SCF), and phase-fluctuation SCF of the optical plane and spherical waves propagating in atmospheric turbulence with arbitrarily oriented anisotropy ellipsoids. Insightful relations between various optical-wave fluctuation statistics and certain recognized special refractive-index fluctuation statistics are found and elucidated according to the developed analytical expressions. Various optical-wave fluctuation statistics are numerically examined with different anisotropic coefficients and orientation parameters of anisotropy ellipsoids. The obtained results show that variations in either the anisotropic coefficients or orientation parameters of anisotropy ellipsoids may lead to obvious changes in the statistical behavior of turbulence-induced optical-wave fluctuations, and hence the said five independent parameters are necessary for analytically dealing with various statistics of optical-wave fluctuations caused by atmospheric turbulence featuring an arbitrary orientation of anisotropy ellipsoids.