Introduction of a modified anomalous vortex beam with self-focusing properties

This study introduces and experimentally demonstrates the concept of a modified anomalous vortex beam (MAVB), which carries orbital angular momentum (OAM) and exhibits unique self-focusing properties. By utilizing holographic techniques and customizing phase masks, we precisely control the beam's phase and intensity distribution, enhancing self-focusing behavior while preserving traditional anomalous vortex beam features. We derive an analytical formula to describe MAVB propagation within a paraxial ABCD optical system. The self-focusing characteristics are influenced by initial parameters such as beam order, quantum number, beam waist, wavelength, and the modification parameter. Additionally, we simulate MAVB propagation and their OAM spectrum in maritime atmospheric turbulence. Through comprehensive theoretical analysis and experimental validation, we show how MAVBs achieve controlled self-focusing, leading to enhanced beam control and stability. Our study explores the mechanisms, design principles, and practical implications of MAVBs, emphasizing their potential to revolutionize optical applications.