Study on the vortex structure of orbital angular momentum beams and high-resolution recognition of fractional orbital angular momentum modes

Abstract

Since the discovery of vortex beams carrying orbital angular momentum (OAM), the application of OAM beams has been widely studied in various fields, such as classical and quantum communication, optical manipulation, laser processing, and super-resolution microscopy. Light OAM, one of the spatial degrees of freedom, originates from a helical wavefront. The so-called “twisted” light with these structured phases has three unique properties: OAM, phase singularity, and doughnut-shaped intensity distribution. Unlike spin angular momentum with only two possible states, left- and right-circular polarization, the OAM is theoretically unlimited, providing high degrees of freedom. For this reason, the use of OAM modes as an additional degree of freedom for information transfer has been a popular topic in optical communications. However, increasing the number of available OAM modes is a challenging problem. The range of OAM modes is theoretically unbounded, but the large beam size of higher-order modes and limited aperture size physically restrict available OAM modes. Hence, the utilization of fractional OAM modes has been presented, but the realization of such systems still remains a challenge due to the lack of a high-resolution detection technique. In this thesis, we aim to introduce the characteristics of vortex beams having fractional OAM and an efficient detecting method for the practical application of fractional OAM beams. We first studied a beam shaping method for generating fractional OAM modes and tailoring the field amplitude. The shaping of laser field distribution was implemented by a spatial light modulator (SLM) which consists of pixelated-liquid crystal. The amount of phase modulation that incident light experiences was controlled electrically by a phase hologram loaded into the SLM. Holograms with a helical phase structure were used to generate vortex beams. The OAM mode of the generated beam is determined by a topological charge corresponding to the phase gradient with respect to the azimuth angle. In addition, we developed an amplitude modulation technique based on the combination of an amplitude mask and a phase grating and proposed a method for generating top-hat line-shaped beams. The experimental results showed that the proposed method could generate a top-hat line-shaped focus with steep edges and a high aspect ratio. In Chapter 4, we investigated the characteristics of vortex beams possessing fractional OAM modes. An axicon phase was added to a helical phase to generate fractional Bessel-Gaussian (BG) beams, and the structural change according to the mode indices was observed. The fractional BG beams showed the shape-invariant property within a finite distance. This phenomenon was due to the Gouy phase of Bessel beams independent of the OAM mode. We proposed the application of a deep-learning method to achieve high-resolution recognition of fractional laser spatial modes. We designed a deep-learning model for recognizing 256 fractional BG modes and used the intensity profile of each spatial mode as input data. We tested the recognition accuracy of the deep-learning model and then conducted image transmission experiments assuming an optical link employing 256 fractional BG beams as data carriers. The trained model identified two independent spatial modes without any optical mode sorter, and the recognition accuracy was nearly 100%. In addition, to develop an optical system with stable performance regardless of distorting factors such as atmospheric turbulence, we designed an atmospheric turbulence adaptive neural network. We analyzed the effects of OAM mode spacing and turbulence strength on the recognition performance. The propagation of laser beams through a turbulence channel was modeled with the angular spectrum method and random phase screens emulating turbulence effects. Despite the strong turbulence and the consequent collapse of field structure, transmitted OAM modes were well identified. In particular, the results demonstrated that a model trained in high levels of turbulence strength accommodates a wide range of turbulence environments.