Topological state transitions of skyrmionic beams under focusing configurations.

The recent emerging appearance of optical analogs of magnetic quasiparticles, i.e., optical skyrmions constructed via spin, field, and Stokes vectors, has garnered substantial interest from deep-subwavelength imaging and quantum entanglement. Here, we investigate systematically the topological state transitions of skyrmionic beams constructed by the Stokes vectors in the focusing configuration. We theoretically demonstrated that in the weak focusing, the skyrmion topological number is protected. Whereas, in the tight focusing, a unique topological transformation with skyrmion number variation is exhibited for the optical skyrmion, anti-skyrmion, and 2nd-order skyrmion structures. The significant difference between the topological state transitions of these two cases originates from the transformation from the paraxial optical system to the nonparaxial optical system, and the approximate two-dimensional polarization structure to the three-dimensional polarization structure. The results provide new insights into the topological state transitions in topological structures, which promote applications in information processing, data storage, and free-space optical communications.

Gamma-ray burst data strongly favour the three-parameter fundamental plane (Dainotti) correlation over the two-parameter one.

Gamma-ray bursts (GRBs), observed to redshift z = 9.4, are potential probes of the largely unexplored z ∼ 2.7-9.4 part of the early Universe. Thus, finding relevant relations among GRB physical properties is crucial. We find that the Platinum GRB data compilation, with 50 long GRBs (with relatively flat plateaus and no flares) in the redshift range 0.553 ≤ z ≤ 5.0, and the LGRB95 data compilation, with 95 long GRBs in 0.297 ≤ z ≤ 9.4, as well as the 145 GRB combination of the two, strongly favour the 3D Fundamental Plane (Dainotti) correlation (between the peak prompt luminosity, the luminosity at the end of the plateau emission, and its rest-frame duration) over the 2D one (between the luminosity at the end of the plateau emission and its duration). The 3D Dainotti correlations in the three data sets are standardizable. We find that while LGRB95 data have ∼50 per cent larger intrinsic scatter parameter values than the better-quality Platinum data, they provide somewhat tighter constraints on cosmological-model and GRB-correlation parameters, perhaps solely due to the larger number of data points, 95 versus 50. This suggests that when compiling GRB data for the purpose of constraining cosmological parameters, given the quality of current GRB data, intrinsic scatter parameter reduction must be balanced against reduced sample size.

Standardizing Platinum Dainotti-correlated gamma-ray bursts, and using them with standardized Amati-correlated gamma-ray bursts to constrain cosmological model parameters.

We show that the Platinum gamma-ray burst (GRB) data compilation, probing the redshift range 0.553 ≤ z ≤ 5.0, obeys a cosmological-model-independent three-parameter Fundamental Plane (Dainotti) correlation and so is standardizable. While they probe the largely unexplored z ∼ 2.3-5 part of cosmological redshift space, the GRB cosmological parameter constraints are consistent with, but less precise than, those from a combination of baryon acoustic oscillation (BAO) and Hubble parameter [H(z)] data. In order to increase the precision of GRB-only cosmological constraints, we exclude common GRBs from the larger Amati-correlated A118 data set composed of 118 GRBs and jointly analyse the remaining 101 Amati-correlated GRBs with the 50 Platinum GRBs. This joint 151 GRB data set probes the largely unexplored z ∼ 2.3-8.2 region; the resulting GRB-only cosmological constraints are more restrictive, and consistent with, but less precise than, those from H(z)  + BAO data.

Multipole gap solitons in fractional Schrödinger equation with parity-time-symmetric optical lattices.

We investigate the existence and stability of in-phase three-pole and four-pole gap solitons in the fractional Schrödinger equation supported by one-dimensional parity-time-symmetric periodic potentials (optical lattices) with defocusing Kerr nonlinearity. These solitons exist in the first finite gap and are stable in the moderate power region. When the Lévy index decreases, the stable regions of these in-phase multipole gap solitons shrink. Below a Lévy index threshold, the effective multipole soliton widths decrease as the Lévy index increases. Above the threshold, these solitons become less localized as the Lévy index increases. The Lévy index cannot change the phase transition point of the PT-symmetric optical lattices. We also study transverse power flow in these multipole gap solitons.