| Due to its unique spatial structure,vortex beams have attracted much attention in the field of structured light.Because the vortex mode itself is an eigensolution in the fiber,and the fiber has many advantages,it will be more advantageous to synthesize the vortex beam in the fiber system than other methods,but the research on the vortex mode in the fiber is mostly It stays within the second order,so it is necessary to study the high-order vortex modes in optical fibers.The main research content of this dissertation is as follows:First,the characteristic equations of the four vector modes in the fiber are deduced in detail,the light intensity and polarization distribution of the four vector modes in the fiber are modeled and simulated,and the influence of different parameters on the light intensity distribution of the mixed vector polarized beam is explored.The corresponding relationship between the root value of the Bessel equation and the mode is studied,and the cut-off conditions of each mode in the optical fiber are explored according to the change curve of the effective refractive index with the normalized frequency.Through the mathematical expression between the four vector polarization modes and the linear polarization mode and the vortex mode,the relationship between different input wavelengths,the relative refractive index difference of the fiber,the core radius and the effective refractive index of the mixed polarization mode is explored,and the synthetic Higher-order linear polarization modes and orbital angular momentum modes are possible.Secondly,without considering the fiber parameters,the low-order linear polarization mode is formed by superposition of four vector polarization modes,and the influence of different parameters on the light field distribution of the linear polarization mode is explored.By analyzing the influence of the normalized frequency on the linear polarization mode,an interval search method is proposed to solve the precise value of the fiber parameters,and the physical field distribution of the first-order to fifth-order linear polarization modes is modeled and simulated.Through mutual verification with the transverse and longitudinal parameters,Prove the correctness of the interval search method.In addition,the electric field contour diagrams and gradient force vector diagrams of the circumferential mode order and radial mode order from the two order to the fifth order are simulated,which provide the basis for the formation of subsequent high-order orbital angular momentum modes.Finally,the linear polarization mode formed by the interval search method is superimposed in the fiber to synthesize the first-order to fourth-order orbital angular momentum modes.By analyzing the light intensity distribution,the influence of different parameters on the diameter and annular distribution of the spot is explored.At the same time,when m =1,l >0 or l <0,the phase distribution and phase step of the superposition-synthesized orbital angular momentum mode are verified,which proves the validity of the superposition synthesis.Using the RichardsWolf diffraction integral formula,the energy flow distribution of the vector radial polarization modes of different polarization topological charges and the orbital angular momentum modes of different vortex topological charges superimposed and synthesized under tight focusing was discovered in the vortex topological charge l =3,the reverse energy flux density distribution appears,which proves that the orbital angular momentum beam synthesized under tight focusing can be used for optical manipulation similar to other traditional vortex beams.In addition,after simulating the orbital angular momentum mode generated by the multimode fiber,the vortex beam carrying different topological charges passes through the Mach-Zehnder interferometer to interfere with the plane wave and spherical wave of the same matrix dimension,and detect the orbit of the synthesized mode through the interference distribution pattern angular momentum state. |
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