Formulation of the on-axis scintillation index of a focused Gaussian beam in weak oceanic turbulence is derived by using the Rytov method, and using this formulation, the average bit error rate (BER) is evaluated. The scintillation indices of collimated, focused Gaussian, plane, and spherical beams are compared. The scintillation index and BER versus the average signal-to-noise ratio is found by using the log-normal distributed intensity for the collimated and focused Gaussian beams, which are exhibited for various source sizes α(s), focal lengths F(s), rates of dissipation of the mean squared temperature χ(T), and rates of dissipation of the turbulent kinetic energy per unit mass of fluid ε. Focused beams are found to have important advantages over collimated beams. For the focused beam, as the source size increases, the scintillation index and BER decrease. When the focal length is equal to the propagation length, the BER is found to possess the smallest value. The BER is proportional to χ(T), but inversely proportional to ε.
We find the equivalence of the structure constants in non-Kolmogorov and Kolmogorov spectra in a turbulent atmosphere. As the reference point, the spherical wave scintillation index in a non-Kolmogorov medium is used. Relations of the structure constants are found to be functions of the power law of the turbulence spectrum and the Fresnel zone. It will be useful to employ the equivalence of the structure constants in making performance comparisons found with non-Kolmogorov and Kolmogorov spectra.
Results obtained on the intensity fluctuations of flat-topped Gaussian beams in weakly turbulent non-Kolmogorov horizontal atmospheric optics links are represented. Effects on the scintillation index of the power law α that describes the non-Kolmogorov spectrum are examined. Our results correctly reduce to the existing intensity fluctuations of flat-topped beams in Kolmogorov turbulence. Variation of the scintillation index against non-Kolmogorov power law α exhibits a peak at the worst power law α(w), which happens to be smaller than the Kolmogorov power law of 11/3. If the power law is smaller (larger) than α(w), increase in α will increase (decrease) the intensity fluctuations. Evaluation of the scintillation index at the worst power law results in smaller fluctuations for a Gaussian beam at short propagation distances; however, at long propagation distances flatter beams happen to possess smaller fluctuations. The scintillation change versus the source size follows a similar trend regardless whether the flat-topped beam propagates in a Kolmogorov or non-Kolmogorov medium.
A scintillation index formulation for annular beams in strong turbulence is developed that is also valid in moderate and weak turbulence. In our derivation, a modified Rytov solution is employed to obtain the small-scale and large-scale scintillation indices of annular beams by utilizing the amplitude spatial filtering of the atmospheric spectrum. Our solution yields only the on-axis scintillation index for the annular beam and correctly reduces to the existing strong turbulence results for the Gaussian beam--thus plane and spherical wave scintillation indices--and also correctly yields the existing weak turbulence annular beam scintillations. Compared to collimated Gaussian beam, plane, and spherical wave scintillations, collimated annular beams seem to be advantageous in the weak regime but lose this advantage in strongly turbulent atmosphere. It is observed that the contribution of annular beam scintillations comes mainly from the small-scale effects. At a fixed primary beam size, the scintillations of thinner collimated annular beams compared to thicker collimated annular beams are smaller in moderate turbulence but larger in strong turbulence; however, thinner annular beams of finite focal length have a smaller scintillation index than the thicker annular beams in strong turbulence. Decrease in the focal length decreases the annular beam scintillations in strong turbulence. Examining constant area annular beams, smaller primary sized annular structures have larger scintillations in moderate but smaller scintillations in strong turbulence.
Depth variations of the power spectrum of underwater turbulence are obtained. Considered specific medium is the Atlantic Ocean at mid and low latitudes. Associated temperature and salinity changes at low latitude, mid latitude–summer and mid latitude-winter are found for the Nikishovs’ spectrum model. By employing the equations for the temperature and salinity changes, figures for the rate of dissipation of the mean squared refractive index fluctuation, rate of dissipation of turbulent kinetic energy per unit mass of fluid and the relative strength of temperature and salinity fluctuations against the depth in underwater are provided. Additionally, plots of the power spectra of underwater turbulence are presented against the changes in the depth.
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