| Vortex beam have attracted extensive attention because of their orbital angular momentum and potential applications in optical communication,optical micromanipulation and optical information processing since 1990s.As far as free space optical communication concerned,vortex beam can greatly expand the channel capacity,however random phase disturbance caused by atmospheric turbulence will lead to a series of negative effects,such as beam expansion,beam wandering,light intensity scintillation,et al.In addition,phase perturbation can give rise to sprial spectrum dispersion of vortex beam,which will lead to a decrease in mode purity and optical communication quality.In order to analyze the influence of atmospheric turbulence on vortex beam,this paper analyzed the propagation of arbitrary order vortex beam in free space/ turbulence with the combination of theoretical methods and numerical methods.Considering the complexity of mathematical model of vortex beam,only the low order(topological charge ±1)cases have been studied in previous studies.In this paper,the GVB(Gaussian vortex beam)is studied through series expansion after utilizing Euler formula.Combined generalized Huygens-Fresnel principle with Rytov approximation,the average intensity expression of arbitrary order GVB can be deduced.This method is also applicable to analytical derivation of GVB-derived beam model,take for instance the symmetric double vortex beam and GVBA(Gaussian vortex beam array),the amplitude/intensity after propagation are derived.Based on this theory,the atmospheric propagation characteristics of GVB,symmetric double vortex beam,GVBA are systematically analyzed,the detailed research contents of this paper are as follows:1.the light intensity expression of arbitrary-order GVB propagated through atmospheric turbulence are derived,based of that,the beam expansion,beam wandering and intensity scintillation are numerically calculated and analyzed,the results indicate that turbulence intensity and topological charge have an evidently stronger effect on beam propagation than other parameters.The mathematical model of multi-vortices beam is briefly introduced,as a special case of that,the propagation characteristics of symmetric double vortex beam are investigated,the amplitude propagated through free space is derived through similar methods mentioned above,compared with previous research,the reliability of these methods is verified.The evolution of Symmetric double vortex beam is studied,the simulation results indicate that the influence of atmospheric turbulence on Symmetric double vortex beam is significantly weaker than GVB beam.2.The mean intensity expression of GVBA propagating through atmospheric turbulence is derived,on this basis,beam width and relative beam width are calculated through numerical integration.Through comparing GVBA and GVB,it can be concluded that GVBA can merge into single vortex beam after propagating through atmospheric turbulence for certain distance whatever the arrangement pattern is,undoubtedly,the single vortex beam will evolve into Gaussian-like beam with the increase of distance.What’s more,with the increase of propagation distance,GVBA and GVB will eventually have an equal beam width,since diffraction will play a leading role in the far field.The beam wander and intensity scintillation of radially distribution GVBA is analyzed with numerical methods.It is found that the beam parameters and turbulence parameters have great influence on the beam wander,and there are certain linear relationships between beam wander and beam number,topological charge.Scintillation index generally rising at first,then decline,and tend to be stable at last.3.The optical field of GVB propagated in atmosphere are obtained through numerical method based on random phase screen,and the spiral spectrum of vortex beam is obtained by spiral harmonic expansion,and then some parameters evaluating the beam communication performance,such as mode purity and channel capacity,are calculated.The scintillation index of GVB beam in the atmosphere is calculated,and the bit error rate of communication system based on OOK modulation is analyzed,it is found that the bit error rate at 1000 m can hardly meet the engineering requirement,even under weak turbulence.The spiral harmonic expansion method is used to analyze the mode purity of the vortex beam obtained through the coherent synthesis of GVBA,and it is found that the larger the number of array elements and the radius of sub-beam beam waist are,the smaller the radius of group beam ring is,that is,the denser the beam array is,the higher the mode purity of the beam will be.In addition,regardless of gaussian beam(radial distribution)array or GVBA(radial distribution),with the increase of propagation distance in free space,mode purity will experience a sharp increase,the difference is that mode purity of GBA will decline slowly,however the mode purity of VBA will decline sharply,finally keeping the same level with single vortex beam in source plane,from this perspective,the synthesis of GBA is better than vortex beam array. |
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