Intensity images and statistics from numerical simulation of wave propagation in 3-D random media

Abstract

An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.

Orbital-angular-momentum entanglement in turbulence

“…(17). For a real-valued, asymmetric phase functionξ * (K) = ξ(−K), however, in the numerical simulation one normally uses a completely asymmetric two-dimensional random complex functionξ(K), which implies that the resulting phase function is complex [28,29] …”

“…These N runs are used to perform ensemble averaging for each of the elements in the evolution sequence, as expressed in Eq. (28), to obtain a sequence of density matrices that represent the evolution of the bi-photon state from an initial pure state to the mixed quantum state that one would observe at a particular point along the propagation path.…”

Open-loop GPS signal tracking at low elevation angles from a ground-based observation site

“…In order to interpret the observed C / N 0 fluctuations we performed a series of MPS simulations (Knepp, 1983;Martin and Flatté, 1988;Grimault, 1998). The propagation of a plane wave through the lower troposphere is modelled by a series of 500 non-equidistant phase screens covering the range from the receiver to a distance of 500 km.…”

Using stellar scintillation for studies of turbulence in the Earth’s atmosphere

“…For more general conditions (strong scintillations), the moment equations are so difficult that they are solved only for some special cases and approximations. A variety of techniques have been proposed such as the parabolic equation method [16,59], extended Huygens-Fresnel principle [16,60], multiple phase screen [61], the path integral [62,63] and numerical techniques [64,65]. Among these, the parabolic equation method with the Markov approximation [59,66] occupies an important place.…”