Orbital Angular Momentum And Its Measurement Of Optical Vortices

Optical vortices have special helical wave fronts, which have attracted great attention to their well-defined orbital angular momentum property. This kind of special optical field has been applied in many fields including optical micromanipulation, atomic optics, biomedicine, nonlinear optics, and quantum information processing. In this thesis, we explored the methods to determine the angular momentum of optical vortices. The major content and result are as follows:1. The properties of optical vortices are introduced concisely. The history and the main developments of the optical vortices are reviewed, and their main applications are also summarized.2. The angular momentum of the optical vortices under paraxial condition and non-paraxial condition are analyzed respectively, and it is demonstrated that optical vortices really have a well-defined orbital angular momentum.3. Different methods for determining the angular momentum of optical vortices are summarized , including the method based on computer-generated hologram , the interferometric method analyzing the interferogram between an optical vortex and a plane wave or its mirror image, the method based on Young's double-slit interference experiment setup or Mach-Zehnder interferometer. Finally, the method based on a multi-pinhole interferometer is introduced, which lays a basis for our newly proposed methods to determine the angular momentum of optical vortices.4. A method for measuring the orbital angular momentum of optical vortices through extracting the phase values sampled by a multi-pinhole plate is presented. It is demonstrated that the phase of an optical vortex passing through a multipinhole plate can be directly extracted from the Fourier transform of a single diffraction intensity pattern according to a simple algorithm and thus the l state or the OAM of the photons can be measured quantitatively.5. The spatial frequency properties of the far-field diffraction intensity pattern of an optical vortex after passing through an annular aperture are analyzed. The theoretical analysis reveals that this spatial spectrum (or the Fourier transform) consists of some bright and dark rings and the number of the rings is just equal to the absolute value of the topological charge. Based on this property, a simple method to measure the topological charge of the optical vortex through its diffraction intensity pattern after an annular aperture is demonstrated.