In this Letter, a new, to the best of our knowledge, type of autofocusing and symmetric beam arisen from two quartic spectral phases is introduced in theory and experiment. The symmetric Pearcey Gaussian beam (SPGB), formed with a Gaussian term and two multiplying Pearcey integrals, processes a focusing intensity approximately 1.32 times stronger than the intensity of the symmetric Airy beam. Its four off-axis main lobes split into four bending trajectories symmetrically after focusing. The rectangular intensity distribution and the focal length of the SPGB can be adjusted by two kinds of distribution factors. Additionally, the vortex-guiding property of the beam is demonstrated by embedding an off-axis vortex into the SPGB, which can be applied in particle guiding.

In this study, a new, to the best of our knowledge, form of odd-Pearcey Gauss beams with peculiar characteristics is presented. Compared with the Pearcey beam, the odd-Pearcey Gauss beam is symmetrical about the origin. At the initial stages, the odd-Pearcey Gauss beam propagates with a main central lobe and some residual spots that autofocus to the center, and then splits into two off-axis parabolic lobes after the autofocus finishes. Furthermore, we also introduce the soft well function to investigate the propagation profiles of the odd-Pearcey Gauss beams passing through it with different calibers and discuss the influence of the Gaussian waist width towards the focal distance and the propagation form of the odd-Pearcey Gauss beam. We also enumerate some potential and possible applications based on its peculiar characteristics.

We derive analytical solutions that describe the one-dimensional displaced and chirped symmetric Pearcey Gaussian beam in a uniformly moving parabolic potential. The multiple effective manipulations of the beam, which are originated from the diverse configurations of the dynamic parabolic potential, are demonstrated. On the whole, the accelerating trajectory can transform into a linear superposition form of the oblique straight line and the simple harmonic motion. Meanwhile, we discuss the further modulation of the accelerating trajectory characteristics such as slope, amplitude and phase shift. Additionally, the extension into a two-dimensional scenario is also proposed. Our results theoretically improve the practical value of the Pearcey beam, and lead to potential applications in trajectory manipulation and particle manipulation.

In this paper, an analytical expression with a triple sum of the Hermite–Gaussian vortex beam (HGVB) propagating in a medium with a parabolic transverse spatial distribution of the refractive index is carried out. The intensity, phase, Poynting vector, and angular momentum of the HGVB are demonstrated analytically. The parabolic parameter, orders of the HGVB, and vortex topological charge affect the propagation properties, respectively. Also, the Poynting vector and angular momentum of the HGVB are shown so that we can further discover the properties. Furthermore, radiation forces are used to demonstrate the optical trapping ability of the HGVB, and several trapping positions are formed by the beam during propagation.

We introduce numerically a new polycyclic tornado ring Airy beam (PTRAB) induced by annular spiral zone phases with the second order chirped factor. The PTRAB has such properties of controllable multi focuses, the multi optical bottles and rotation. By choosing appropriate parameters, we can control the times of the multi autofocus and the autofocusing distance, the size and the number of the OBs, the quantity of the spots and the location where the rotary direction changes from counterclockwise to clockwise. We believe our results have potential applications in laser energy focusing, optical tweezers, optical spanners and manufacturing tunable chiral meta-materials.