Propagation dynamics and auto-focusing properties of a ring compensated Airy beams array

This study introduces a ring compensated Airy beams (RCAB) array, incorporating a compensation factor <i>b</i> to precisely regulate the auto-focusing limitations of conventional ring Airy beam arrays. The compensation factor <i>b</i> acts as a powerful regulatory parameter, enabling simultaneous and predictable control over the array's focusing dynamics. An Airy term governs the spatial oscillation, while an exponential term controls the longitudinal energy gain and sets the focal position. Systematic analysis shows that a negative <i>b</i> significantly enhances auto-focusing capability. The focal length has a stable, negative linear relationship with <i>b</i>; it extends further as <i>b</i> becomes more negative. The number of sub-beams needed for saturated focusing also depends on <i>b</i>, increasing from 22 to 60 as <i>b</i> decreases from -0.2 to -0.8. Crucially, a critical threshold is identified at <i>b</i> = -0.8 under the chosen parameters. Beyond this value, energy detrimentally transfers from the main lobe to the surrounding secondary lobes. This degradation is severe. At <i>b</i> = -4.0, the number of secondary lobes surges to 442, and their intensity can exceed the main lobe by several hundred times, defeating the focusing effectiveness. This work establishes <i>b</i> as a core parameter for precisely regulating RCAB arrays. The findings provide a robust basis for advanced beam manipulation, with potential applications in laser processing, optical trapping, and bio-imaging.