Higher-Order Airy Patterns and Their Application in Tailoring Orbital Angular Momentum Beams with Fiber Laser Arrays

Airy patterns, formed by the Fraunhofer diffraction of plane waves via circular apertures, have been widely utilized as criterions in areas such as imaging optics and energy transmission. With deeper insights into the spatial structure of light, the use of Airy patterns as criterions today becomes inadequate in many scenarios. Here, a new concept of higher-order Airy patterns is proposed by introducing the orbital angular momentum (OAM) of light, namely the Fraunhofer diffraction pattern of a plane wave via the defined annular aperture with helical wavefront tailoring. For the m-order Airy pattern, the tailored helicity is m, and the scaling factor of the annular aperture and is determined by the m-related equation set, which is derived based on the paraxial diffraction theory. As a potential application of the proposed concept, a coherent fiber laser array system capable of customizing OAM beams is presented and analyzed. Using the higher-order Airy pattern to define the performance metric of combined beam, the fiber laser array system is optimally designed and the properties in energy concentration and high mode purity of the generated OAM beams could be realized. This work could be beneficial to the theoretical study and applications of OAM beams, especially the generation and manipulation of high-power, fast switchable OAM beams with fiber laser arrays.