In recent years, underwater laser communication system has attracted more and more attentions. Oceanic turbulence is one of the main concerns for research of laser beams propagating through the ocean[
Infrared and Laser Engineering, Volume. 49, Issue 7, 20190452(2020)
Validity of beam propagation characteristics through oceanic turbulence simulated by phase screen method
Oceanic turbulence is an important factor to restrict the application of underwater optical communication. Phase screen method is a simple and effective way to simulate the propagation process of complex beams through turbulence. The constraints of parameter setting for phase screen simulated oceanic turbulence based on the sampling principle and turbulence effects were firstly discussed here. Furthermore, the theoretical expressions of propagation characteristics of Gaussian beam through oceanic turbulence from weak to strong fluctuation regime were derived. Our goal in this research was to testify the validity of phase screen method in oceanic turbulence by comparison of major statistical characteristics of Gaussian beam propagating in oceanic turbulence simulated by phase screen method and the theoretical expressions derived. Results show good match between simulation results and theory formulas for long exposure beam radius and centroid displacement under different turbulence conditions, as well as the scintillation index under weak fluctuation regime. However, results show significant mismatch between numerically estimated and theoretically predicted values for the on-axis scintillation index in strong fluctuation regime.
0 Introduction
In recent years, underwater laser communication system has attracted more and more attentions. Oceanic turbulence is one of the main concerns for research of laser beams propagating through the ocean[
In this paper, the equation of beam spreading, beam wander and scintillation of Gaussian beam propagating through oceanic turbulence are derived follow the theory of beam propagation through random media[
1 Theory of propagation characteristics
The spatial power spectrum of the refractive-index fluctuations for the oceanic turbulence can be described as[
Here,
Ref.[
Here,
Large-scale filter function HLS is
The on-axis scintillation of Gaussian beam through turbulence is
Following the approach derived in Ref.[
Collimated Gaussian beam with
Since oceanic turbulence could achieve strong fluctuation in a short distance, the theory formula should apply to from weak to strong fluctuation conditions. The method of effective beam parameters maybe used to extend these following formulas into the strong regime by replacing Λ and Θ by their effective beam parameters
Substituting Eq.(1) into Eq.(2)−(6), the long-exposure beam radius
2 Phase screen method for oceanic turbulence
2.1 Introduction of phase screen method
The principle of phase screen method [
Figure 1.Diagram of phase screen simulation method
Here,
Here,
2.2 Principle of parameter setting
The parameter of phase screen mainly include the grid size
Here,
Meanwhile, the description of beam should also be considered. For Gaussian beam, the beam width
The number of phase screen along the path is decided by the turbulence strength. According to Ref.[
Rytov variance
The example of parameter settings is as follows:
(1) Consider about the strongest turbulence condition as an example, L=50 m,
(2) Use Eq.(15) to calculate the phase screen number, and the distance between adjacent phase screens are should meet
2.3 Statistical properties calculation formula
Assuming that the long exposure intensity distribution is Gaussian, the statistical properties calculation could be expressed as [
Standard deviation of the fluctuation of the instantaneous center of the beam:
On-axis scintillation index:
Here, < > represents the average and
3 Comparison of results and analysis
The following values of parameters are used in the calculations unless the statement of other values: wavelength
The results presented in
Figure 2.Propagation characteristics versus different propagation distance, (a) long-exposure beam radius
Figure 3.Propagation characteristics versus different
,(a) long-exposure beam radius
Figure 4.Propagation characteristics versus different
,(a) long-exposure beam radius
Figure 5.Propagation characteristics versus different
, (a) long-exposure beam radius
Similar to the results in
4 Conclusions
In this paper, the analytical formulas of beam spreading, beam wander and scintillation of Gaussian beam through oceanic turbulence are derived. The principle of parameter setting for phase screen simulated oceanic turbulence is mainly discussed and the steps are given in Sec.2.2. Furthermore, the comparison of the simulation results and theory calculation under different parameter settings and different turbulence conditions are shown in figures.
Results show that beam spreading and beam wander characteristics simulated by phase screen method are in good accordance with the theory formula under different turbulence conditions while the scintillation index has large deviation under strong fluctuation turbulence conditions. In summary, based on appropriate parameter setting, phase screen method can be a simple and effective way to calculate the statistical characteristics depend on the first moment of intensity, such as beam spreading and beam wander. The statistical characteristics depend on the second moment of intensity calculated by numerical simulation achieve good correspondence with theory in weak fluctuation regime and big mismatch in strong fluctuation regime, which should be further researched in the future.
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Chaojun Niu, Xiaobin Wang, Fang Lu, Xiang’e Han. Validity of beam propagation characteristics through oceanic turbulence simulated by phase screen method[J]. Infrared and Laser Engineering, 2020, 49(7): 20190452
Category: Optical communication and sensing
Received: Dec. 5, 2019
Accepted: --
Published Online: Aug. 19, 2020
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