It is well know that free-space laser system performance is limited by atmospheric turbulence. Most theoretical treatments have been described for many years by Kolmogorov's power spectral density model because of its simplicity. Unfortunately, several experiments have been reported recently that show that the Kolmogorov theory is sometimes incomplete to describe atmospheric statistics properly, in particular, in portions of the troposphere and stratosphere. We present a non-Kolmogorov power spectrum that uses a generalized exponent instead of constant standard exponent value 11/ 3, and a generalized amplitude factor instead of constant value 0.033. Using this new spectrum in weak turbulence, we carry out, for a horizontal path, an analysis of long-term beam spread, scintillation index, probability of fade, mean signal-to-noise ratio ͑SNR͒, and mean bit error rate ͑BER͒ as variation of the spectrum exponent. Our theoretical results show that for alpha values lower than ␣ = 11/ 3, but not for alpha close to ␣ = 3, there is a remarkable increase of scintillation and consequently a major penalty on the system performance. However, when alpha assumes a value close to ␣ = 3 or for alpha values higher than ␣ = 11/ 3, scintillation decreases, leading to an improvement on the system performance.
A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ς. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ς 2−α .
In this paper, the concept of anisotropy at different atmospheric turbulence scales is introduced. A power spectrum and its associated structure function with inner and outer scale effects and anisotropy are also shown. The power spectrum includes an effective anisotropic parameter ζ(eff) to describe anisotropy, which is useful for modeling optical turbulence when a non-Kolmogorov power law and anisotropy along the direction of propagation are present.
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