Generation of a controllable multi-spiral beam by using the modulated helico-conical phases

In this Letter, we propose a kind of controllable multi-spiral beam that can be generated using the modulated helico-conical phases with an axicon. The focal-field intensity distributions of the multi-spiral beams were investigated theoretically and experimentally. The relative distance between the two adjacent sub-beams of the multi-spiral beams was discussed based on the approximate mapping of the local spatial frequency. The result demonstrated that the relative distance between the two adjacent sub-beams was linearly dependent on the radial factor gradient Delta alpha of the two sub-beams. When the radial factor gradient Delta alpha is equal to a critical value (i.e., Delta alpha(c)), the multi-spiral beam can be changed into an Archimedean spiral-shaped beam (the sub-beams of multi-spiral beams will be connected with each other). In addition, the dependence of the topological charge l on the critical radial factor gradient Delta alpha(c) is also discussed. The result demonstrates that the critical radial factor gradient Delta alpha(c) has a linear dependence on the topological charge l. The experimental results are in good agreement with the numerical simulation results. The controllable multi-spiral beams are potentially applied in three-dimensional optical micro-manipulation and information transmission.