On The Generation, Diffractive Properties, And Mearsurement Of Optical Vortices

The special helical phase structure of an optical vortex leads to an intriguing study in modern singular optics. Due to the dynamics properties, unique topological structure, and orbital angular momentum carrying of photos, opitcal vorties have get more and more attentions in the study of optical micromanipulation, speckle field and quantum communications.Firstly, opitcal vortex has orbital anglure momentum that can be transered to the trapped particles and rotate them. Optical vortex trap has axial gradient force times of the focus Gauss beam under same laser parameters. When focused strongly enough, such helical modes form toroidal optical traps known as optical vortices, whose properties present novel opportunities for scientific research and technological applications. For example, optical vortices can dynamically trap and modulate mesoscopic particles in 2D and 3D, and optical vortex array trapping systems have shown a promising ability to assemble colloidal particles into mesoscopic pumps for microfluidic systems, and offered new applications in nanotechnology, and manufacturing.Secondly, the optical vortex with spiral phase possesses series of unique properties, such as ring distribution of the intensity, small size of the dark spot, no heating effect, and so on. It can trap and manipulate biologic cells in lower power of laser for decreasing the destructive fatalness. Recently, it has been widely used in the area such as laser optics, micro particle waveguiding, biomedicine, atom optics and molecule optics. The manipulation of the Doppler cooling atoms by the hollow intensity configurations of optical vortex potential trap was accomplished.Thirdly, the topological structure of the optical vortices and phase singularities is an important research area in astronomy, superfluid, spekle field and topological arithmetics. The orbital angular momentum of the photos and its quantum entanglement brings widespread applications ranging from carrying more information in quantum information processing, quantum calculation, to optical infromation processing, optoelectronics, and cryptography, and so on.The studies on optical vortices become an intriguing research area which has tremendous potencial application, though the history of the studies is only several decades. Following the further research of the optical vortex, the content and the technology would be more meaningful and rewarding. The further studies need the profound understanding and acknowledgement of the distributions of the optical vortex and the angular momentum properties. The diffractive properties, generation, and the methods for examining the properties of optical vortices need developing theoretically and experimentally, too.We systematically analysized the history and development of the optical vortices in the dissertation, including the fundamental mathematically description, the properties of spin and orbital angular momentum of the photos, the dynamics properties of intensity gradient force and phase gradient force, and the quantum entanglement of the photo carrying orbital angular momentum. Further, we summarized the different methods of generation of optical vortex, such as using mode convertion, by computer generation holography, spiral phase plate and liquid crystal spatial light modulator. The studies above found the experimental and theoretical base for our further research in these areas. Furthermore, we introduced the methods of multi-beams interference and helical phase spatial filtering for generation of optical vortex array.Based on the studies above, we discussed the focus ring structure and the diffractive properties of the optical vortices in linear meadium, presented the method for generating optical vortex array based on fractional Talbot effection, and developped the examing technology for measuring the orbital angular momentum and three-dimensional reconstuction of the wavefront of an optical vortex. The main innovative researches and conclusion are demonstrated as follows:1. We analysed the propagation of the optical vortex solitions in the linear medium based on two of the principal equations in hydromechanics: the Bernoulli and the continuity equations.We found contrasting differences between the trajectories for r vortices that have globally distributed core functions and tanh vortices that have localized core functions when the beam propagates through a linear medium. In particular, we discussed the propogation of the optical vortex array. We found the localized optical vortices enlarging their own field, overlapping with the adjacent vortices, and forming new enlarged local area which can be regarded as a new optical vortex. At last, they degenerated to a new array of optical vortex. Moreover, in comparison with the reconstructed vortex array at the fractional Talbot distance, we found the vortex cells focused into a sharp ringed structure with higher contrast at a defocusing Talbot plane. The phase contrast phenomenon can be useful in optical micromanipulations.2. We presented the method for generating optical vortex array based on the reciprocal vector theory for the fractional Talbot effection. We studied the reciprocal vector theory detailedly, and introdued the method for designing phase-only diffractive element named optical vortex Talbot array illumination (OVTAI) An array of optical vortex with high compress ratio is generated by the wave division multiplex. As our method need not use splitters and reflectors, the optical system is simple and with high practicability. We discussed the fundamental principle and design parameters analytically for OVTAI of rectangular array, centered-square array, and hexagonal array. As an example, an OVTAI for generating a hexagonal array of optical vortices is designed and demonstrated through displaying the OVTAI on a programmable liquid crystal spatial light modulator. The vortex array generated by the OVTAI are observed and analyzed.3. We studied the methods of interferometer for measuring the orbital angular momentum (OAM) detailedly, and introduced the method by a spherical reference wave. We found the total topological charge of the optical vortex in an area can be defined by the recognization of the closed interference pattern or the number of the spiral stripes. Digital simulations prove the feasibility of the method. Furthermore, we used another reference optical vortex wave and studied the procedure forming the interference pattern, and found that it also defined the location and the topological charge of the phase dislocation.4. We presented the arithmetics for retrieval the complex amplitude passing through a multi-pinhole interferometer (MPI), and demonstrated the method for measurement of the OAM of an optical vortex in a background beam. We found the far-field diffraction pattern involves imformation sampled by the multi-pinhole (MP) plate, which can be extracted by inverse Fourier transform of the far-field pattern with a properly arithmetics. We can further use the extracted phase to determine the OAM of the illuminated optical vortex. We have deduced the principle of the method analytically, and demonstrated by digital simulations and experimental result. The error of the systerm was also discussed.5. We introduced a method for three dimensional reconstruction of the wavefront of optical vortex by a line scanning multi-pinhole interferometer (LS-MPI). The reconstruction of the wavefront requires the precise measurement of the phase passing through the MP plate. The method we presented can be resolved by the principle of MPI. If scan the whole wavefront by such a MP plate, we can extracted the sampled complex amplitude of the whole wavefront and further reconstruct the wavefront. We deduced the principle of the method, and found it can be descibed simpler, the inverse Fourier transform pattern can be distinguished more clearly, the sampled data is more precise, and the unwrap operation is easier. The digital simulations demonstrate the feasibility of the mothod.