Two-Frequency Mutual Coherence Function of a Gaussian Beam Pulse Propagated Through Non-Kolmogorov Turbulent Atmosphere

Over the past half century, satellite-laser-communication technology has been the focus in many countries and areas due to its higher data transmission rates, smaller terminals, low probability of intercept, etc. Much manpower and material and financial resources have been put into the development of this technology. Usually, longer pulses can be modeled as if they were continuous-wave pulses during the time when the pulse is transmitted. However, this is not the case for ultrashort pulses that are usually used as a carrier in satellite-laser communication. For satellite-to-ground or ground-to-satellite links, the atmospheric effects are more deleterious to the laser pulse and their analysis is also more complicated. For a long time, laser pulse propagation in the turbulent atmosphere were studied based on the Kolmogorov model. However, increasing experimental evidence and theoretical investigations have shown that the Kolmogorov model is not the only possible turbulent one in the atmosphere, and there exists another turbulence, namely, the non-Kolmogorov turbulence. So it is necessary to perform the analysis of the laser-pulse propagation in the non-Kolmogorov turbulence. The two-frequency mutual coherence function (MCF) plays an important pole in determining the basic characteristics associated with the laser-pulse propagating in the atmospheric turbulence. In this paper, we consider a theoretical power spectrum of the refractive-index fluctuations with a generalized power law, derive the two-frequency MCFs of a Gaussian-beam pulse in weak turbulence for a horizontal path, and analyze the influence of spectral power-law variations on the two-frequency MCFs. We present an analytical expression for a collimated-beam pulse.