Study On Propagation Properties Of Vortex Beam In Gradient Index Fiber

In conventional communications,frequency division multiplexing,code division multiplexing,time division multiplexing,and space division multiplexing are used to enhance communication capacity.With the increasing demand for modern communication capacity and rate,there is an inevitable need to explore higher-capacity and higher-rate communication systems.Because of the infinite and orthogonal of orbital angular momentum of vortex beam,it can exponentially raise the channel capacity,spectrum utilization and enhance confidentiality in communication.In addition,the radial gradient-index（GRIN）fiber has low dispersion,low bending loss,and self-focusing characteristics,which can greatly expand the transmission capacity of the fiber and is an ideal transmission medium for laser communication.Therefore,it is necessary to study the propagation characteristics of vortex beams in radial GRIN fibers.In this paper,the background and overview of the research on vortex beams and the progress of the research on the coherent polarization properties of light are presented firstly.Secondly,the transmission theory of beams and the radial GRIN fiber is introduced.And based on this,the following aspects are accomplished:The analytical expression of a random electromagnetic Gaussian vortex beam transmitted in an ABCD optical system is built and used to simulate and analyze the effects of the initial beam parameters on the distribution properties of beam coherence and polarization.The numerical simulation conclusions show that the distribution of spectral degree of coherence（SDOC）,spectral degree of polarization（SDOP）,and state of polarization（SOP）is periodic and the distribution will return to the initial distribution state after one transmission period.The period is determined by the GRIN coefficient of the fiber.The topological charge,spatial self-correlation length,and wavelength change the SDOC distribution,and spatial mutual-correlation length does not affect the SDOC distribution.For SDOP and SOP,the topological charge does not change the distribution law,but whether spatial self-correlation lengthσ_xx andσ_yy of the beam are the same has a major influence on the SDOP and SOP.The field distribution expression of a partially coherent cylindrical vector vortex beam transmitted in an ABCD optical system is built and used to numerically simulate and analyze the distribution of SDOC and SOP for beam propagating in radially GRIN fiber.The results show that the dark rings number of the SDOC distribution increases gradually with the decrease of coherence length at the focal plane of the radially GRIN fiber,and the change of the SDOC distribution is more obvious with the increase of topological charge.The distribution law of the SDOC with different wavelengths is the same when the coherence length takes a fixed value and the topological charge is the same.The simulation results for the SOP show that the polarization distribution of the cylindrical vector vortex beam changes from the original nonuniform linear polarization to nonuniform elliptical polarization after focusing by the radial GRIN fiber,and the SOP distribution changes more obvious as the topological charge increases.In addition,the coherence length has a partial effect on the SOP distribution at the focal plane of the fiber,but it is very small compared with the effect of the topological charge on the SOP distribution.The field distribution expression of a fully coherent cylindrical vector vortex beam transmitted in the radial GRIN fiber are derived and used to simulate and analyze the spin angular momentum distribution of the fully coherent cylindrical vector vortex beam at the focal plane of the radial GRIN fiber.The spin angular momentum calculation method of partially coherent light is derived based on the spin angular momentum calculation method of fully coherent light,based on which the changes of the spin angular momentum distribution of partially coherent cylindrical vector vortex beams are numerically simulated.The results show that the orbital angular momentum and spin angular momentum of both fully coherent and partially coherent cylindrical vector vortex beams can be converted periodically.spin angular momentum showing the opposite distribution when the beam carries opposite topological charges.