Numerical experiments are carried out for a plane wave propagating in the
 atmospheric turbulence for a weak to strong fluctuation condition, i.e., the Rytov index
 being in a large range of 2×10−3 to 20. Mainly two categories of propagation
 events are explored for the same range of Rytov index. In one category the propagation
 distance and also the Fresnel length are kept fixed with the turbulence strength
 changing. In the other the turbulence strength is kept fixed with the distance changing.
 The statistical characteristics of the scintillation index, the maximum and minimum of
 the intensity, the fractal dimension of the intensity image, and the number density of
 the phase singularity are analyzed. The behaviors of the fractal dimension and the
 density of the phase singularity present obvious differences for the two categories of
 propagation. The fractal dimension depends both on the Rytov index and the Fresnel
 length. In both weak and strong fluctuation conditions the dimension generally increases
 with the Rytov index, but is at minimum at the onset region. The phase singularity
 density is coincident with the theoretical results under a weak fluctuation condition,
 and has a slowly increasing manner with the Rytov index in the strong fluctuation
 condition. The dependence on the Fresnel size is confident and there is no saturation
 for the phase singularity.

Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence

The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a function of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a f...

The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory

We investigate the atmospheric turbulence effects on the propagation of vortex modes carried by Lommel beam. The analytic expression of the received signal and crosstalk mode intensity is derived based on the weak-to-strong non-Kolmogorov turbulence theory. The simulation results show that turbulence with small non-Kolmogorov spectrum parameter, small inner-scale factor and large outer-scale factor is more likely to induce modal crosstalk. With the increment of turbulence strength, the crosstalk spreads from adjacent modes to peripheral modes. The received signal intensity can be improved by use of Lommel beam with small asymmetry parameter, low orbital angular momentum quantum number and long wavelength. The results are helpful to the design of orbital angular momentum based free-space optical communication link.

Intensity of vortex modes carried by Lommel beam in weak-to-strong non-Kolmogorov turbulence

A concise expression of the scintillation index is proposed for a plane optical wave and a spherical optical wave both propagating in a turbulent atmosphere with a zero inner scale and a finite inner scale under an arbitrary fluctuation condition. The expression is based on both the results in the Rytov approximation under a weak fluctuation condition and the numerical results in a strong fluctuation regime. The maximum value of the scintillation index and its corresponding Rytov index are evaluated. These quantities are affected by the ratio of the turbulence inner scale to the Fresnel size.

https://iopscience.iop.org/article/10.1088/1674-1056/18/2/032/pdf

Scintillation index of optical wave propagating in turbulent atmosphere

The capability to detect an optical target using laser illumination is typically assessed using an equation commonly referred to as the laser range equation. In practice, however, the laser range equation often produces unreliable predictions when compared to actual results under field conditions. The lack of accuracy is due in large part to the failure of the range equation to account for the effects of atmospheric turbulence on the illuminating laser beam. Retrodirective reflections from a corner cube and a simple lens-mirror system, used as a surrogate for a lens-detector optical system, were studied using near-infrared laser illumination. Each optic was tested under a variety of atmospheric conditions in order to assess the effect of atmospheric turbulence on the returned power. Using established theory, a corrective term for use in the laser range equation that accounts for turbulence-induced beam spreading is developed and compared to experimental results. Additionally, a method for correcting the lab-measured optical cross section of a focused optical system in order to account for the defocusing effects of turbulence is developed. With these corrective terms, the laser range equation was modified to provide accurate return-power predictions under varied atmospheric conditions.

Atmospheric-turbulence-effects correction factors for the laser range equation

Recently, new theory governing laser beam scintillation was developed for all regimes of optical turbulence. This theory is based on the Rytov approximation but modified with a filter function that eliminates intermediate scale sizes that do not contribute to the refractive and diffractive effects of propagation. This modification extends the validity of the Rytov approximation into moderate to strong regimes as evidenced by the agreement with simulations and experimental data. In this paper we apply this theory to the phase covariance and new expressions governing phase fluctuations are presented. The phase structure function is then compared with previous experimental data.

Phase fluctuations in moderate to strong turbulence

Recently, a heuristic model for scintillation in moderate to strong turbulence was developed. It is based on the idea of filter functions that eliminate scale sizes that lose their ability to affect a laser beam as it propagates. This approach allows the validity of the Rytov approximation to be extended into moderate to strong turbulence. In this paper, we investigate applying this theory to second order statistics.

Moderately strong theory applied to second-order statistics

Scintillation is one of the most common statistics in the literature of mathematical modeling of laser propagation through random media. One approach to estimating scintillation is through the Rytov approximation, which is limited to weak atmospheric turbulence with the standard Kolmogorov spectrum. Recently, a modification to the Rytov approximation was developed. Through a filter function approach, the new results for scintillation are valid for moderate to strong fluctuations along a horizontal path. To date, expressions governing scintillation for plane, spherical, and Gaussian beam waves has been developed for horizontal propagation paths. For the special cases of plane and spherical waves, expressions have been developed for slant paths. In this paper, an expression governing scintillation of a Gaussian beam along an uplink slant path valid in all regimes of turbulence is presented.

Fredrick E. Thomas

Papers

The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory

Phase fluctuations in moderate to strong turbulence

Moderately strong theory applied to second-order statistics

Scintillation in moderate to strong optical turbulence along a slant path