Highly localized continuous wave optical vortex with controllable orbital angular momentum orientation and topological charge.

We report an approach to simultaneously control orbital angular momentum (OAM) orientation and topological charge in highly localized optical vortices by employing a 4π focusing system. The required continuous wave illumination field in the pupil planes is derived by superimposing the radiation pattern of only one dipole placed at the focal point of the high numerical aperture lens and the corresponding tailored spiral phase factor. The topological charge and OAM orientation of the obtained focused fields are quantitatively evaluated based on the focal field distributions calculated by the Richards-Wolf vector diffraction integration theory. Results show that the OAM of the generated optical vortices can be tailored by changing the oscillation orientation of the mimic dipole and the topological charge of the superimposed spiral phase term. The presented method may find potential applications in optical trapping, optical tweezers, light-matter interaction, etc.

Experimental visualization of various cross sections through a butterfly caustic.

Optical caustics and wavefronts of butterfly beams (BBs) derived by using a catastrophe theory determined by potential functions depending on the state and control variables are reported. Due to the high dimensionality for the control variables, BBs can be manipulated into various optical light structures. It is also demonstrated that these curious beams have relatively simple Fourier spectra that can be described as polynomials, and another way to generate BBs from the Fourier spectrum's perspective is provided. The dynamics for BBs are investigated by potential functions. Our experimental results agree well with the theoretical predictions. In addition to micro-manipulation and machining, these novel, to the best of our knowledge, caustic beams will pave the way for creating waveguide structures since they display high-intensity formations that evolve along curved trajectories.

Swallowtail-type diffraction catastrophe beams.

We demonstrate a universal approach for generating high-order diffraction catastrophe beams, specifically for Swallowtail-type beams (abbreviated as Swallowtail beams), using diffraction catastrophe theory that was defined by potential functions depending on the control and state parameters. The three-dimensional curved caustic surfaces of these Swallowtail catastrophe beams are derived by the potential functions. Such beams are generated by mapping the cross sections of the high-order control parameter space to the corresponding transverse plane. Owing to the flexibility of the high-order diffraction catastrophe, these Swallowtail beams can be tuned to a diverse range of optical light structures. Owing to the similarity in their frequency spectra, we found that the Swallowtail beams change into low-order Pearcey beams under given conditions during propagation. Our experimental results are in close agreement with our simulated results. Such fantastic catastrophe beams that can propagate along curved trajectories are likely to give rise to new applications in micromachining and optical manipulation, furthermore, these diverse caustic beams will pave the way for the tailoring of arbitrarily accelerating caustic beams.

Abruptly autofocusing circular swallowtail beams.

In this Letter, to the best of our knowledge, we report the first experimental demonstration of a new family of autofocusing beams, circular swallowtail beams (CSBs), based on the high-order swallowtail catastrophe, which were determined by potential functions depending on the state and control parameters. The dynamics of the CSBs is discussed here. These types of CSBs tend to automatically focus without external components. Numerical results showed the focal intensity increased significantly, and it was as much as 110 times in the initial plane when the radius of the main ring was 40. Additionally, in contrast to previous circular Pearcey and Airy beams, these CSBs appeared to have more diversity and tunability due to having more propagation trajectories and intensity distribution structures due to high-order diffraction catastrophe. The numerical simulations were verified by our experimental results. These diverse CSBs could have new applications in flexible optical manipulation. These various CSBs could be beneficial for potential applications in optical trapping, medical treatment, or micromachining.