Caustic Interpretation of the Abruptly Autofocusing Vortex beams
We propose an effective scheme to interpret the abruptly autofocusing vortex beam. In our scheme, a set of analytical formulae are deduced to well predict not only the global caustic, before and after the focal plane, but also the focusing properties of the abruptly autofocusing vortex beam, including the axial position as well as the diameter of focal ring. Our analytical results are in excellent agreement with both numerical simulation and experimental results. Besides, we apply our analytical technique to the fine manipulation of the focusing properties with a scaling factor. This set of methods would be beneficial to a broad range of applications such as particle trapping and micromachi…
Scaling the abruptly autofocusing beams in the direct-space
International audience; We propose a simple technique to scale the abruptly autofocusing beams in the direct space by introducing a scaling factor in the phase. Analytical formulas are deduced based on optical caustics, explicitly revealing how the scaling factor controls location, peak intensity, and size of the focal spot. We demonstrate that the multiplication of a scaling factor on the phase is equivalent to the axial-scaling transformation under the paraxial approximation. Further numerical and experimental results confirm theoretical predictions. In addition, amplitude modulation using phase-only holograms is used to maintain the peak intensity level of the focal spots.