Caustic beams from unusual powers of the spectral phase

Experimental generation of the polycyclic tornado circular swallowtail beam with self-healing and auto-focusing

In this paper, the polycyclic tornado circular swallowtail beam (PTCSB) with autofocusing and self-healing properties is generated numerically and experimentally and their properties are investigated. Compared with the circular swallowtail beam (CSB), the optical distribution of the PTCSB presents a tornado pattern during the propagation. The number of spiral stripes, as well as the orientation of the rotation, can be adjusted by the number and the sign of the topological charge. The Poynting vectors and the orbital angular momentum are employed to investigate the physical mechanism of beam-rotating. In addition, we also introduce a sector-shaped opaque obstacle to investigate the self-healing property of the PTCSB, passing through it with different center angles and discuss the influence of the scaling factor along the propagation direction. Our results may expand the potential applications in the optical spanner and material processing.

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.

Abruptly autofocusing beams from phase perturbations having forced symmetry

A controllable manipulation of the energy distribution of caustic beams possessing rectangular symmetry is presented. The beams are designed from the spectral phase by adding a linear and/or quadratic perturbation having forced symmetry. This approach breaks the overall caustic structure into branches, allowing a fully controllable displacement of each branch. The caustic breaking leads to peculiar propagation configurations for rectangular beams. Among them, we highlight the abruptly autofocusing beam, which until now was exclusively associated to caustic beams with circular symmetry. Thereby, the abruptly autofocusing effect can be yielded for one-dimensional light sheets, contrary to what happens for circularly symmetric beams. The theoretical predictions are supported by experiments. Besides, the focus width of such rectangular beams can be reduced beyond the standard diffraction limit.

Nonsymmetric curved beams within a symmetric caustic skeleton

Nonsymmetric curved beams having a symmetric caustic skeleton are presented. They arise from a finite jump in the symmetric spectral phase that breaks the symmetry of the beam intensity without altering its associated caustic curve. These nonsymmetric beams can be represented as a superposition of two caustic beams whose wave fields have well-defined even and odd symmetries with weight coefficients dependent on the phase jump. In this approach, the phase jump acts as a measure of the beam asymmetry degree that can be easily controlled in experiments. This scheme is a promising step towards optical cryptography and quantum optics applications.

Accelerating polygon beam with peculiar features

We report on a novel kind of accelerating beams that follow parabolic paths in free space. In fact, this accelerating peculiar polygon beam (APPB) is induced by the spectral phase symmetrization of the regular polygon beam (RPB) with five intensity peaks, and it preserves a peculiar symmetric structure during propagation. Specially, such beam not only exhibits autofocusing property, but also possesses two types of accelerating intensity maxima, i.e., the cusp and spot-like structure, which does not exist in the previously reported accelerating beams with a single kind of lobes. We also provide a detailed insight into the theoretical origin and characteristics of this spatially accelerating beam through catastrophe theory. Moreover, an experimental scheme based on a digital micromirror device (DMD) with the binary spectral hologram is proposed to generate the target beam by precise modulation, and a longitudinal needle-like focus is observed around the focal region. The experimental results confirm the peculiar features presented in the theoretical findings. Further, the APPB is verified to exhibit self-healing property during propagation with either obstructed cusp or spot reconstructing after a certain distance. Hence, we believe that the APPB will facilitate the applications in the areas of particle manipulation, material processing and optofludics.