Flexible control of short-depth-of-focus vortex arrays using generalized Snell's spiral zone plates

We propose and experimentally demonstrate a novel phase modulation method based on generalized Snell's spiral zone plates (GSSZP), capable of generating short-depth-of-focus (SDF) vortex arrays. By establishing a phase-coordinate theoretical model, we achieve flexible control of the three-dimensional coordinates of the focal points. Additionally, this paper derives and presents a formula for calculating the depth of focus (DOF) of GSSZP, and experimental measurements validate its accuracy, with the minimum DOF approximately 0.67 mm. Compared to continuous vortex arrays, the SDF vortex arrays exist only within a limited propagation range, overcoming the limitation that continuous vortex beams cannot independently modulate vortex arrays at different propagation planes. Based on the DOF, the SDF vortex array we designed allows the array to independently exist at different propagation planes, enabling optical encryption. Experimental results show that the maximum coordinate error is only 97 μm, demonstrating the stability of this method. Furthermore, we extended the functionality of phase superposition to control light intensity, adding new degrees of freedom to the vortex array. The above techniques show potential applications in fields such as orbital angular momentum (OAM)-multiplexed communications and information encryption.