# Computer Simulation of Multichannel Beam Focusing System in Turbulent Atmosphere

^{*}

## Abstract

**:**

^{®}Math Kernel Library.

## 1. Introduction

^{®}Math Kernel Library.

## 2. Mathematical Statement and Algorithms

_{x}, V

_{y}) in the transverse direction to propagation axis this system of equations is:

_{p}is the specific heat at constant pressure, ρ is the density of air at constant pressure, and T is the ambient temperature.

_{0}, initial radius, a

_{0}and focus length F:

_{m}} are the layer coordinates, m = 1,…, M. The phase perturbations φ

_{m}(

**r**) in each layer were assumed to be statistically independent, homogeneous, and isotropic random two-dimensional fields with a power-law spatial spectral density as the Karman model:

_{n}

^{2}is the structural characteristic of atmospheric turbulence, and k

_{L}and k

_{m}are the wave numbers of the outer and inner scales of turbulence, respectively.

_{n}

^{2}. This behavior in the discrepancy between the results of numerical and analytical solutions is expected and is explained by the fact that the analytical approximation has a limited scope. In particular, it does not describe such distinguishing features of the TB effect as asymmetrical wind shift of the beam as well as the power density saturation effect [15,16].

## 3. Results and Discussion

_{n}

^{2}= 5.10

^{−14}m

^{−2/3}, absorption coefficient α = 0.1 km

^{−1}, ground wind speed V= 3 m/s, transverse wind velocity vector directed horizontal from left to right, trace elevation angles = 25°, 45°. All calculations were performed for the configuration of a six-channel PCBC array. The diameter of each channel beam was set equal to 2a

_{0}= 10 cm, the radiation wavelength λ = 1μm, initial power of each beam channel P

_{0}= 3 kW, initial intensity I

_{0}= P

_{0}/πa

_{0}

^{2}= 38.2 W/cm

^{2}.

#### 3.1. One Six-Channel PCBC Array

^{2}) is indicated at the top. The dotted line on the axis in the center shows a region with a size equal to the diameter of a single aperture.

^{2}.

#### 3.2. Two Six-Channel PCBC Arrays

_{max}= 208.1 W/cm

^{2}. In the second variant (Figure 6d), there is no mutual influence (Figure 6e), the distribution of the average intensity in the focal spot is more compact (Figure 6f), and the value <I>

_{max}= 333.3 W/cm

^{2}increases by 1.6 times compared to the first case.

#### 3.3. Three Six-Channel PCBC Arrays

^{2}in frame upside). The spikes are the result of atmospheric turbulence, thermal blooming, and random interference of channel beam interactions. This effect of amplification of intensity fluctuations due to TB in comparison with ordinary fluctuations in a turbulent atmosphere is rather complicated and requires separate consideration.

_{n}

^{2}= 5.10

^{−14}m

^{−2/3}.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Illustration of beam propagation in a turbulent atmosphere, performed by the simulation program. In the upper left corner is the transverse plane of the emitter (x, y, 0) and in the lower right corner is the focal plane (x, y, L).

**Figure 2.**Initial transverse distribution of intensity and phase of a simulated 6-channel beam array: (

**a**) intensity; (

**b**) coherent phase (CBC); (

**c**) partial coherent phase (PCBC).

**Figure 3.**Diffraction patterns of intensity in focal plane of a focused 6-channel array at distance L = 5km: (

**a**) CBC in vacuum; (

**b**) PCBC in vacuum; (

**c**) PCBC in turbulent atmosphere.

**Figure 4.**Initial power optimization graphs for one 6-channel PCBC system on the atmospheric paths with elevation angle of 25°.

**Figure 5.**Transverse phase distribution of PCBC, focused on path L = 1km in a turbulent atmosphere with TB at various distances from the initial plane z = 0: (

**a**) z = 0.05 L; (

**b**) z = 0.3 L; (

**c**) z = 0.6 L; (

**d**) z = 0.9 L.

**Figure 6.**Influence of the mutual orientation of two 6-channel PCBC relative to the transverse wind direction–longitudinal (above) and transverse (below): (

**a**,

**d**) Initial PCBC intensity distributions;(

**b**,

**e**) phase distortion tails caused by TB; (

**c**,

**f**)Average intensity distributionsin the focal plane L = 5 km.

**Figure 7.**A three 6-channel PCBC array system focusing on atmospheric paths of length L = 5 km in the presence of turbulence–TB interaction: (

**a**) Initial intensity distribution; (

**b**) instant intensity distribution in the focal plane; (

**c**) average intensity distribution <I(x,y)> in focal plane, <I>

_{max}= 280.9 W/cm

^{2}.

**Figure 8.**Initial power optimization graphs for three 6-channel PCBC systems on the atmospheric paths.

**Figure 9.**Maximum average intensity in the focal plane of a multichannel PCBC system as a function of propagation path length.

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**MDPI and ACS Style**

Konyaev, P.; Lukin, V.
Computer Simulation of Multichannel Beam Focusing System in Turbulent Atmosphere. *Photonics* **2023**, *10*, 431.
https://doi.org/10.3390/photonics10040431

**AMA Style**

Konyaev P, Lukin V.
Computer Simulation of Multichannel Beam Focusing System in Turbulent Atmosphere. *Photonics*. 2023; 10(4):431.
https://doi.org/10.3390/photonics10040431

**Chicago/Turabian Style**

Konyaev, Petr, and Vladimir Lukin.
2023. "Computer Simulation of Multichannel Beam Focusing System in Turbulent Atmosphere" *Photonics* 10, no. 4: 431.
https://doi.org/10.3390/photonics10040431