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Characteristic analysis of orbital angular momentum of vortex beam propagating in atmospheric turbulent
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Abstract
Starting from the expression of Laguerre-Gaussian vortex beam and based on Rayleigh diffraction theory, the variation of rotating coherence function of vortex beam propagating in atmospheric turbulence is studied. The crosstalk between the angular momentum of each orbital angular momentum when the vortex beam propagates in atmospheric turbulence is summarized. The topological charge detection probability is used to describe the crosstalk law, and the analytical expression of the topological charge detection probability is derived. The distribution of topological charge number of vortex beam passing through turbulence is studied, and the results are compared with the numerical simulation results of vortex beam passing through atmospheric random phase screen. The relationship between the detection probability of the theoretical and simulated topological charge numbers with the turbulence intensity and the topological charge number of the initial vortex beam is compared, and the correctness of the analytical expression of the topological charge number detection probability is verified. Through this expression, the interaction between atmospheric turbulence and vortex beam can be further studied, which can affect the essence of angular momentum scattering of vortex beam, and the suitable topological charge number interval can be selected for the space optical communication of vortex beam. It also provides a theoretical basis for selecting the appropriate beam waist size under different turbulence intensities to reduce the bit error rate (BER) caused by crosstalk.-
Keywords:
- atmospheric turbulence /
- vortex beam /
- topological charge /
- orbital angular momentum
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References
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Overview
Overview: In recent years, with the deepening of the study of the propagation characteristics of all kinds of beams, a vortex beam with a new phase structure has been gradually discovered and has become a research focus because of its novel characteristics. The central light intensity of the vortex beam is zero, the phase structure of the wavefront is spiral, and there is a phase singularity in the center of the beam. This spiral phase structure makes the vortex beam have orbital angular momentum, which provides a new channel reuse dimension for space optical communication and improves the channel capacity. However, when the vortex beam passes through the atmospheric turbulence, the intensity and phase distribution of the beam will be affected by the turbulence, which will further cause crosstalk between the angular momentum of each orbit. Finally, the increase of bit error rate (BER) and the decrease of communication capacity are caused by the increase of bit error rate and the decrease of communication capacity. Therefore, the study of the factors affecting the topological charge number scattering of vortex beams and the crosstalk of orbital angular momentum is of great significance for the further study of the interaction between orbital angular momentum and atmospheric turbulence, and is beneficial to improve the capacity of space optical communication system. Starting from the expression of Laguerre-Gaussian vortex beam and based on Rayleigh diffraction theory, the variation of rotating coherence function of vortex beam propagating in atmospheric turbulence is studied. The crosstalk between the angular momentum of each orbital angular momentum when the vortex beam propagates in atmospheric turbulence is summarized. The topological charge detection probability is used to describe the crosstalk law, and the analytical expression of the topological charge detection probability is derived. The distribution of topological charge number of vortex beam passing through turbulence is studied, and the results are compared with the numerical simulation results of vortex beam passing through atmospheric random phase screen. The relationship between the detection probability of the theoretical and simulated topological charge numbers with the turbulence intensity and the topological charge number of the initial vortex beam is compared, and the correctness of the analytical expression of the topological charge number detection probability is verified. Through this expression, the interaction between atmospheric turbulence and vortex beam can be further studied, which can affect the essence of angular momentum scattering of vortex beam, and the suitable topological charge number interval can be selected for the space optical communication of vortex beam. It also provides a theoretical basis for selecting the appropriate beam waist size under different turbulence intensities to reduce the bit error rate caused by crosstalk.
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Figure 1.
Random phase screens simulate the propagation of vortex beams in atmospheric turbulence
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Figure 2.
The topological charge of the vortex beam is 3, the refractive index structure constant of atmospheric turbulence is Cn2=1×10-14 m-2/3. Intensity distribution (a) and the phase (b) of the vortex beam at the source plane; The intensity distribution (c) and the phase (d) on the receiving plane; (e) Probability of detection of each topological charge obtained by numerical calculation; (f) Probability of detection of each topological charge calculated by equation (16)
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Figure 3.
The topological charge of the vortex beam is 1, the average detection probability of each topological charge after 40 times of vortex beam transmission at different turbulence and the comparison between the average detection probability and the theoretical detection probability of the corresponding topological charge. (a~b) The refractive index structure constant of atmospheric turbulence is Cn2=1×10-14 m-2/3; (c~d) The refractive index structure constant of atmospheric turbulence is Cn2=5×10-14 m-2/3; (e~f) The refractive index structure constant of atmospheric turbulence is Cn2=1×10-13 m-2/3
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Figure 4.
The topological charge of the vortex beam is 3, the average detection probability of each topological charge after 40 times of vortex beam transmission at different turbulence and the comparison between the average detection probability and the theoretical detection probability of the corresponding topological charge. (a~b) The refractive index structure constant of atmospheric turbulence is Cn2=1×10-14 m-2/3; (c~d) The refractive index structure constant of atmospheric turbulence is Cn2=5×10-14 m-2/3; (e~f) The refractive index structure constant of atmospheric turbulence is Cn2=1×10-13 m-2/3.
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Figure 5.
The topological charge of the vortex beam is 9, the average detection probability of each topological charge after 40 times of vortex beam transmission at different turbulence and the comparison between the average detection probability and the theoretical detection probability of the corresponding topological charge. (a~b) The refractive index structure constant of atmospheric turbulence is Cn2=1×10-14 m-2/3; (c~d) The refractive index structure constant of atmospheric turbulence is Cn2=5×10-14 m-2/3; (e~f) The refractive index structure constant of atmospheric turbulence is Cn2=1×10-13 m-2/3
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Figure 6.
The detection probability of a vortex beam with different topological charge varies with the atmospheric refractive index structure constant (a) and with coherence parameter ζ (c); Crosstalk between vortex beams with original topological charge 1 and adjacent topological charges when propagating in different turbulent atmosphere (b) and with coherence parameter ζ (d)
