Caustic Interpretation of the Abruptly Autofocusing Vortex beams.

Na Xiao,Erse Jia,Jiaying Li,François Courvoisier,Remo Giust,Minglie Hu,Chen Xie

doi:10.1364/oe.430497

Abstract

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 micromachinings.

Highlights

With the use of radially symmetric Airy beams, abruptly autofocusing (AAF) beams were first introduced theoretically in 2010 [1] and were demonstrated experimentally in 2011 [2]
We further studied the focusing properties of abruptly autofocusing vortex (AAFV) beams of a fixed degree of polynomial (n = 2) with variable topological charges ranging from l = 1 to l = 7
The variations of the axial positions and the inner diameters of the focal rings are shown in Fig. 6, and the analytical values of the above parameters present less than ~4% differences from the simulations of the ideal case

Summary

Introduction

With the use of radially symmetric Airy beams, abruptly autofocusing (AAF) beams were first introduced theoretically in 2010 [1] and were demonstrated experimentally in 2011 [2]. Due to the notable autofocusing property, AAF beams have attracted intense interests and spawned numerous applications like optical trapping and particle micromanipulation [10,11,12,13], material processing [14] and generation of light bullets [15]. Optical vortex beams have acquired considerable interest due to their intriguing features such as the doughnut-shaped spatial profile and the phase singularity With these interesting characteristics, optical vortex beams are useful in quantum information [21], optical communication [22,23], particle micromanipulation [24,25] and material processing [26,27]. By encoding the phase of optical vortices with the AAF beams on the spatial light modulator (SLM), abruptly autofocusing vortex (AAFV) beams are generated. Our analytical results are in excellent agreements with the experimental and numerical results

Phase mask design and Experimental setup

The caustics and the focusing properties of AAFV beams

Experimental results

Manipulation of the focal ring of AAFV beams with a scaling factor

Conclusion