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.

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Abstract. We construct a continuous model of Gödel's system T and its logic HA ω in which all functions from the Cantor space 2 N to the natural numbers are uniformly continuous. Our development is constructive, and has been carried out in intensional type theory in Agda notation, so that, in particular, we can compute moduli of uniform continuity of T-definable functions 2 N → N. Moreover, the model has a continuous Fan functional of type (2 N → N) → N that calculates moduli of uniform continuity. We work with sheaves, and with a full subcategory of concrete sheaves that can be presented as sets with structure, which can be regarded as spaces, and whose natural transformations can be regarded as continuous maps.

In this Letter, we introduce a new, to the best of our knowledge, structure of multioptical bottles formed by second-order chirped symmetric Airy vortex beams (CSAVBs). The numbers and the locations of the optical bottles embedded in the CSAVBs depend on the numbers and the locations of the vortices. Besides, the lengths and the sizes of the optical bottles could be adjusted by changing the chirp parameter and the topological charges of the vortices, respectively. We believe that our results can diversify the optical tweezers system for multiparticle manipulation.