Near Field Propagation of Flat-Top Gaussian Beam: Analysis in ‎Weak Atmospheric Turbulence

1. Introduction

The beam of Flat-top (also called top-hat) laser beams was characterized by having a homogeneous distribution of beam intensity in the center with nearly sharp beams at two edges [1,3]. These kinds of beams are very helpful for diverse applications including laser engraving, selected laser melting, laser micro-fabrication, laser radar, and optical metrology [4,5]. By using an optical beam shaper the Gaussian ray laser can be turned into a flat-top laser beam [6] such as holograms [7], Binary Phase Plate [4], and hybrid grating [8] for example but not limited. The atmospheric effects on laser beam propagation can be categorized as attenuation of the laser power and fluctuation caused by beam distortion. The photons of laser light can be attenuated by absorption and scattering due to interaction with aerosols and gaseous molecules in the atmosphere. On the other hand, Small-scale dynamic variations in the atmosphere's index of refraction cause laser beam distortion. As a result, the laser beam wanders, spreads, and distorts the wave front or exhibits scintillation. For short-range propagation ns, the laser beam undergoes fewer fluctuations is and less distorted. The deformation of a beam using a method of small perturbing actions is often referred to as the Rytov Method and laser applications [9,10,11,12,13]. As a laser beam travels across several kilometers, it experiences strong fluctuations causing the deformity cross-sections section of that beam into a speckled pattern. The investigations of this work aimed at modeling A flat-top Gaussian beam, the field as it propagates via atmospheric turbulence, causes to producing beam scintillation and wander are established in order to make a comparison with experimental results.

2. Effect of Flat-Topped Gaussian Beamwidth on Average Intensity

The intensity diffusion of the proportional FTG beam at the sender plane (U_T) is found in z = 0, and the parataxis presented by [14] can be used as given by Eq. 1

$$U_T\left(s,0\right)=Aexp\left(-\frac{\left(N+1\right)s^2}{w_0^2}\right){{\displaystyle \sum }}_{m=0}^N\frac{1}{m!}{\left(\frac{\sqrt{N+1} s}{w_0}\right)}^{2m}$$

(1)

Here U_T is Intensity spread at the source plane, A is the field scattering amplitude, s is the cross vector at the sender plane, w₀ are middle of the spectrum and the N integer number represents superficies ranking. Density spreading at the receiver level U_R They will be able to choose to use the Huygens - Fresnel integral as beneath [15].

$$U_R\left(r,\mathrm{z}\right)=\frac{-ik}{2\pi z}exp\left(ikz\right){{\displaystyle \iint }}_{-\infty }^{\infty }{U}_T\left(s,0\right)\exp (\frac{ik}{2z}\left|\mathit{s}-\left.\mathit{r}\right|\right.)d{s}^2$$

(2)

Wherever the parameters of the equation above, z are defined as the space amidst the planes T (transmitter) and R (receiver), r is the slope vector in the R plane, and wave number k. Moreover, the outdo spread of the FTG beam, and convolution of Eq. (2) and Eq. (3) without turbulent plenty enlargement function is required as given by [16].

$$U_R\left(r,\mathrm{z}\right)=U_T\left(s,0\right)\ast \left(\frac{-ik}{2\pi z}exp\left(ikz+\frac{ik}{2z}\left|\mathit{s}-\left.\mathit{r}\right|\right.\right)\right)$$

(3)

Turbulence affects laser radiation, causing temporal and spatial changes in irradiance that are visible at the receiving plane. the scintillation index of the phase is related to beam fluctuation and is usually measured in space.

$${\sigma }_I^2=\frac{\langle I^2\rangle }{\langle I^2\rangle }-1$$

(4)

where ${\sigma }_I$ is denoted scintillation index and I refer to the light intensity. The Rytov variance can be used to characterize scintillation ${\sigma }_I$ when a model of an unobstructed flat wave or circular wave is utilized.

$${\sigma }_I^2=K{C}_n^2{k}^{7/6}{L}^{11/6}$$

(5)

The refractive index fluctuations and the Kolmogorov power-law spectrum only occur among inertia-band vortices K (rad m^-1). It is isotropic and limited to homogeneous.

$${\Phi }_n\left(\kappa \right)=0.033C_n^2{K}^{-11/3} 2\pi /L_0 \ll K\ll 2\pi /l_0$$

(6)

The parameter C_n acts as a deflective index of structure constant (m^−2/3) and the l₀, L₀ is the inner and outer turbulence measure, correspondingly. The direction along which light propagates depends on whether its medium is homogeneous or not and heterogeneous. Moreover, the degree of refractive index structure constant governs to that the refractive index of a medium vacillates. In the fact of the values order of 10^-17 m^−2/3 is accompanying occurred in weak turbulence to up it, consequently, the section of reasonable turbulence is ${10}^{-17}<C_n^2<{10}^{-17}$ . The grade of turbulence is advanced at minor elevations as mentioned above. Additionally, the higher values of $C_n^2$ results are nearer to the ground level. Eq.7 is defined the refractive index of structure constant as below.

$$C_n^2={\left[79.0\ast {10}^{-6}\left(\frac{P}{T^2}\right)C_T\right]}^2$$

(7)

Somewhere the factors C_T, P, and T, are delighted with the temperature (K) of structure constant, the pressure (m bar) indoors of the turbulence model.

3. Results and Analysis

In this Sector, we are using some numerical examples of the different intensity developments of FTG for dissimilar distances in a turbulence atmosphere accomplished according to Eqs. (1&2). Furthermore, to explain the outcomes of several figures like intensity, scintillation index, contour, and so on, moreover, to apply these parameters, for example, the wavelength λ= 1550 nm, source size ${\omega }_{gx}={\omega }_{gy}=1.0 cm$ , and structure constant parameter ${\complement }_n^2=0.5\times$ 10⁻¹³ m^−2/3 of the Gaussian beam, additionally, to added other factors have been displayed in all figures.

Figure 1. the contour for flat top Gaussian ray of the basic field, we observed the lines in the center are dissimilar on the other line that’s back to equality of source size (x&y) axis, conclusively, Figure 2. source intensity of flat top Gaussian beam in the oblique coordinate structure, thereby like the previous figure but applied color and referring to values of boundary lines. Similarly, Figure 3 and Figure 4 are illustrated the average intensity of FTG Beam in 2-D and 3-D Transverse Coordinate System Interetingly for different distances. Besides, Figure 5 refers to the 3D of average Intensity for the FTG beam in the transmitter plan, in addition to besides, spreads in atmospheric space with distribution as propagation distance rises. On the other hand, the intensity shape will adopt a bright center core comparable to the flat-top Gaussian profile.

In this perspective, Figure 2 provides the source intensity of the flat-top Gaussian ray in the slanting coordinate system dependent on the parameters mentioned earlier, intensity contour loops describe the constant distance between two circles. so, the constant construction stricture, wavelength, is usage. In addition, Figure 3 and Figure 4 show the variation of source intensity with different propagation distances L= (0.5, 1.5, 2.5, 3.5) km in the oblique coordinate classification of two and three dimensions respectively

As a matter of fact, Figure 4. Illustrate the receiver field, indicating a reduction in receiver intensity in comparison with the amplitude of the source as the beam diffusion is passing the far distance of 3.5 km from the source to the receiver plane. Similarly, representative simulated results concerning the variation of source amplitude at different propagation distances and contour rings at the receiver plane are displayed in Figure 6 and Figure 7. Specifically, Figure 8 focuses on the variation of the scintillation index with fixed wavelength FTG beam versus propagation distance which shows the scintillation increases linearly to the far 2.5 km and for up that’s raised high scintillation. As the initial wave front of the laser beam propagates via turbulence zones it would undergo variance in irradiance causing temporal and spatial changes in irradiance that are visible at the receiver. The on-axis scintillation index calculated by Eq. 3 is commonly used to assess the degree of variation in the received signal.

4. Conclusions

In this paper, the near-field proliferation of the FTG beam through a puny atmosphere is mathematically simulated. The analysis was performed with the help of the fragmented beam propagation technique. It is shown that the propagation of an FTG beam with a high uniformity parameter can be analyzed as the deflection of a plane wave occurrence on a spherical gap with an extent equivalent to that of the FTG beam at the T plane. The two and three-dimension intensity possessions were accurately held. The rising scintillation index proportion constant produced a larger distortion in receiver intensity. In fact, the finding is valuable for applications in not only optical communication systems but also in laser material interaction applications.