Study Of The Propagation Properties Of Vortex Beams In Optical Mediums

Laser optics is a discipline that studies the transmission characteristics of lasers through various transmission media and the transformation of lasers in optical resonators.In actual production and life,it is often necessary to deal with the transmission and transformation characteristics of lasers in optical media materials,controlling and shaping of laser transmission and the beam quality evaluation.As a result,it is necessary to conduct in-depth research on the transmission characteristics of laser beams in optical media materials.Vortex beams have been widely studied in the field of laser communications due to their unique characteristics,and the optical media materials represented by uniaxial crystals and gradient-index medium have also been widely used in optical devices,imaging equipment,optical fibers and other equipment.Therefore,it is necessary to study the propagation characteristics of vortex beams in uniaxial crystals and gradient index medium.The main work of this article includes the following four parts:Based on the paraxial propagation theory of beams traveling in uniaxial crystals orthogonal to the optical axis,the analytical expression of the Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis has been derived,and the intensity,the phase distribution and optical vortex of Gaussian vortex beams are demonstrated to investigate the propagation properties of Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis.The results show that the initial circular symmetry of intensity distribution cannot remain during propagation due to effect of anisotropic crystals.The intensity distribution changes from circular symmetry to elliptic symmetric distribution,and the stronger the anisotropy is,the more obvious the effect is.The phase distributions are also affected by the anisotropy in the same way.Optical vortex splits into symmetrical optical vortices during propagation.The odevity of topological charge determines the rule of symmetry of optical vortex splitting,and the anisotropy affects the splitting of optical vortices.The analytical expression for Gaussian vortex beams propagating through a gradient-index medium is obtained.The propagation trajectory,the intensity distributions,and the phase distributions of Gaussian vortex beams propagating in the gradient-index medium are demonstrated,and the effects of gradient-index parameter ? and topological charge m on these propagation properties are analyzed in detail.It is found that the propagation trajectory and intensity distributions change on periodically with the increasing of propagation distance,and the periodicities are determined by the gradient-index parameters.As the increasing of the gradient-index parameters,the periodic variations on the propagation trajectory and intensity distributions are slowed down.Interestingly,the phase always circulates about the central null in the medium,but the rotation direction will change.The phase distributions also change on periodically in the medium,but the periodicities are different when the topological charge is odd or even.Furthermore,increasing the topological charge will increase the size of the beam spot and the circular dark hollow in the medium.The analytical expression of the cross-spectral density function for the propagation of partially coherent Gaussian vortex beams in a gradient-index fiber is derived.By numerical analysis,the propagation trajectories,the variations of the phase distributions are showed to illustrate the propagation properties of the partially coherent Gaussian vortex beams.The effects of the topological charge and the initial coherence width of the beam on the propagation properties are analyzed in detail.Research shows that the phase distributions of partially coherent Gaussian vortex beams during propagation are affected by the topological charge m and the initial coherence width,when the initial coherence width is small,a coherent vortex with topological charge of m will split into m coherent vortexes with topological charge of“+1”,and m coherent vortexes with topological charge of“-1”appear.High initial coherence will be more conducive to maintaining the phase singularities in the propagation.In addition,the topological charge and the initial coherence width have similar effects on the intensity distribution at one-half period:when the value is small,the light intensity distribution at one-half period is flat-topped distribution,and the larger the value,the closer the intensity distribution is to the hollow distribution.The analytical expression of the cross-spectral density matrix element for the propagation of random electromagnetic Gaussian vortex beams in a gradient-index fiber is derived.The changes in degree of polarization and degree of coherence of the random electromagnetic Gaussian vortex beams as they propagate through the fiber are numerically simulated.Studies have shown that the degree of polarization and coherence of random electromagnetic Gaussian vortex beams are periodic when beams propagate in a gradient-index fiber,and the period is determined by the gradient-index parameter.In a propagation period,the value of the polarization degree will rise and fall many times,and the value of the topological charge m will affect the magnitude of the extreme value of the polarization degree rise and fall.The greater the initial coherence width ?_0xx is,the greater the degree of initial coherence of the beam is.The value of coherence will rise and fall multiple times during propagation.The value of m will affect the number of rises and falls,and m and ?_0xx will affect the magnitude of the extreme value of the rise and fall of the degree of coherence.