Research On The Tightly Focusing Property Of Vortex Beam Arrays

In recent years,vortex beam draws more and more attention due to its orbital angular momentum(OAM).The intrinsic orthogonality of OAM can provide a new dimension for optical communication,so its application in free space and optical fibers becomes the research focus.Affected by atmospheric turbulence,effective transmission in free space is difficult for vortex beam over long distance.In optical fiber transmission of vortex beam,there are two main ways: one is exciting OAM modes in the optical fiber,the other is coupling vortex beams into the optical fiber to transmit.Under the condition of tight focus,the radii of focus are small,so vortex beams can more easily couple into the fiber.Multiplexing technology can greatly increase the transmission capacity of OAM communication.In this paper,the problem of focusing and coupling vortex beam arrays into optical fiber is studied.The main of our research work has been summarized as follows:Firstly,we have proposed a method to generate OAM multifocal arrays with controllable focus numbers,three dimensional positions and OAM modes under tight focus conditions.This array is generated by a specially designed multizone phase plane,which is placed at back aperture of high numerical aperture lens.By using Debye diffraction integral,the focusing field could be rewritten as a fast Fourier transform.According to the shifting theorem of Fourier transform,we can attain a pure-phase three-dimensional displacement formula.By using this displacement formula in different areas in the phase plane,and adding a spiral phase,the multizone phase plane is accomplished.Since each focus is generated by an independent region of the multizone phase plane,OAM multiplexing technology can be achieved by focusing two or more foci to the same location.This practical and flexible technology can dynamically control the number,3D position and OAM modes of foci in the array to adapt to different application environment,such as optical storage,hollow fiber couplers,and parallel optical manipulation.Secondly,we have proposed a brand new pixel checkboard method to generate multifocal perfect vortex array.The perfect vortex overcomes the limitation that the diameter of vortex beam increases with the rise of topological charges.It is of great significance for solving the problems like trapping and manipulation of particles and coupling multiple OAM beams into optical fibers.By adjusting the parameters of axicon,the diameter of the perfect vortexes can be controlled.The multizone phase plane cannot allocate pixels completely in the central region.Nevertheless,our pixel checkerboard method can overcome this defect.So it can improve the imaging quality of the multifocal spots array.Combining the pure phase displacement formula and the pixel checkerboard method,a hybrid phase plate is fabricated to produce a perfect vortex array with controllable focus numbers,3D positions,OAM modes,and focal diameters.The problem of higher order OAM modes coupling into optical fibers is solved.Thirdly,we have proposed opening perfect vortexes.The phase plate for generating an opening perfect vortex is produced by superimposing two axially stacked conjugated diffractive optical elements phase and an axicon phase.The opening angle of the opening perfect vortex is free to control.This opening angle can be considered as a new dimension in optical communications,and can be multiplexed with OAM to greatly increase the capacity of optical communication channels.By pixel checkerboard method,an opening perfect vortex array with controllable focus numbers,3D positions,OAM modes,radii and opening angles is constructed under tight focus system.