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Based on the theory of coherence, the model of multi-Gaussian Schell-model (MGSM) beams carrying an edge dislocation generated by the MGSM source is introduced. The analytical cross-spectral density of MGSM beams carrying an edge dislocation propagating in oceanic turbulence is derived, and used to study the evolution properties of the MGSM beams carrying an edge dislocation. The results indicate that the MGSM beam carrying an edge dislocation propagating in oceanic turbulence will evolve from the profile with two intensity peaks into a flat-topped beam caused by the MGSM source, and the beam will evolve into the Gaussian-like beam due to the influences of oceanic turbulence in the far field. As the propagation distance increases, the MGSM beam carrying an edge dislocation propagating in oceanic turbulence with the larger rate of dissipation of mean-squared temperature (
The properties of laser beams propagating in underwater oceanic turbulence were widely investigated due to their applications in wireless optical communications and laser sensing. So far, the power spectrums of oceanic turbulence have been introduced by many researchers.[1, 2] Until now, a variety of laser beams propagating in turbulent ocean have been studied based on the power spectrum of oceanic turbulence. The evolution properties of coherent laser beams propagating in oceanic turbulence have been studied, such as higher order mode laser beam,[3] Lorentz beam,[4] Lorentz Gauss beam,[5] Lommel–Gaussian beam,[6] Gaussian beam,[7] Gaussian pulsed X wave,[8] radially polarized beam,[9] vector beam,[10] rotating elliptical chirped Gaussian vortex beam,[11] ultra-short pulse,[12] Gaussian array,[13, 14] and chirped Gaussian pulsed beam.[15] On the other hand, it can be found that partially coherent beams have advantage over fully coherent beams for mitigating the effect of turbulence.[16] The evolution properties of various partially coherent beams propagating in oceanic turbulent were discussed, such as partially coherent flat-topped vortex hollow beam,[17] partially coherent Lorentz–Gauss beam,[18] partially coherent Lorentz–Gauss vortex beam,[19] stochastic beams,[20] astigmatic stochastic electromagnetic beam,[21] partially coherent four-petal Gaussian beam,[22] partially coherent four-petal Gaussian vortex beam,[23] partially coherent Hermite–Gaussian linear array beam,[24] radial phase-locked partially coherent Lorentz–Gauss array beam,[25] radial phase-locked partially coherent standard Hermite–Gaussian beam,[26] phase-locked partially coherent radial flat-topped array laser beam,[27] Gaussian Schell-model vortex beam,[28] stochastic electromagnetic vortex beam,[29] partially coherent anomalous hollow vortex beam,[30] multi-Gaussian Schell-model beam,[31] rectangular multi-Gaussian Schell-model beam,[32] electromagnetic multi-Gaussian Schell-model beams with astigmatic aberration,[33] stochastic electromagnetic higher-order Bessel–Gaussian beam,[34] optical wave and short-term beam,[35] and random electromagnetic multi-Gaussian Schell-model vortex beam.[36] The beams generated by the multi-Gaussian Schell-model (MGSM) source can evolve into the flat-topped beam as the propagation distance increases.[37] It is very interesting to ask what will happen if the MGSM beam carries an edge dislocation. Thus, we will firstly introduce the model of multi-Gaussian Schell-model (MGSM) beams carrying an edge dislocation, and then discuss the evolution properties of the MGSM carrying an edge dislocation propagating through oceanic turbulence in this paper.
In the Cartesian coordinate system, the electric field of a Gaussian beam with an edge dislocation at the plane z = 0 takes the form[38]
Considering the multi-Gaussian Schell-model source,[37] the cross-spectral density (CSD) of the MGSM beams carrying an edge dislocation can be expressed as
Based on the extended Huygens–Fresnel principle, the CSD of the partially coherent beam propagating in oceanic turbulence can be expressed as[17–30]
In Eq. (
Here the propagation properties of the MGSM beam carrying an edge dislocation in free space and oceanic turbulence are investigated by using the derived analytical equations in the above section. In the numerical calculations, the parameters are selected as
During the coherence length
The cross sections of the MGSM beams carrying an edge dislocation propagating in free space for different M and σ are plotted in Figs.
Figure
The cross sections of the MGSM beams carrying an edge dislocation propagating in oceanic turbulence are given in Figs.
To obtain the influences of oceanic turbulence on the spreading properties of the MGSM beam, we illustrate in Figs.
The spectral degrees of coherence of the MGSM beams carrying an edge dislocation propagating in oceanic turbulence for different p, d, and M are given in Figs.
The model of MGSM beams carrying an edge dislocation has been introduced, and the evolution properties of MGSM beams carrying an edge dislocation propagating in oceanic turbulence have been investigated using the numerical examples. It is shown that the MGSM beam carrying an edge dislocation propagating in oceanic turbulence will evolve from the profile with two intensity peaks into a flat-topped beam caused by the MGSM source, and the beam will evolve into the flat-topped beam with smaller beam spot or the Gaussian-like beam due to the influences of the oceanic turbulence in the far field, and the MGSM beams carrying an edge dislocation propagating in oceanic turbulence with the larger
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[6] | |
[7] | |
[8] | |
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[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] | |
[31] | |
[32] | |
[33] | |
[34] | |
[35] | |
[36] | |
[37] | |
[38] | |
[39] | |
[40] | |
[41] |