We use a tight-binding method to investigate the Floquet-modulated Lieb-Kagome lattices through theoretical and numerical band-structure analyses. We realize a photonic topological insulator by applying a helical Floquet modulation to break time-reversal symmetry. The resulting topological properties, characterized by Chern numbers, reveal robust edge states that enable unidirectional light propagation without backscattering. Notably, edge states at different momenta support forward and backward propagation along the same boundary. Unidirectional propagation and robustness against defects confirm the preservation of topological protection under specific conditions. These findings highlight the potential of Lieb-Kagome lattices for photonic applications and offer insights into the interplay between topology and lattice geometry in photonic systems.

Optical vortices (OVs) with controllable orbital angular momentum (OAM) distributions have potential applications in optical communication and optical manipulation. However, the source of optical vortices with segmented phase gradients generated by existing methods can be used only at a short distance because of their low power. In this study, based on coherent combining technology, we proposed a method to generate a controlled-phase optical vortex (COV). Compared with traditional OVs, the magnitude and direction of the local OAM of the COV are controllable. The transmission characteristics of the COV in free space were numerically examined using a split-step Fourier transform algorithm. We theoretically and experimentally proved the feasibility of the coherent combining technology to generate an COV and proved that it has the properties of non-diffraction and self-healing.

The systematic and comprehensive research on the single-pass second harmonic generation (SHG) of the perfect vortex beam (PVB) under low fundamental wave depletion is reported. Based on Fourier transformation of the Bessel-Gaussian vortex beam (BGVB) generated through the combination of the spiral phase plate and the axicon, the perfect vortex beam (PVB) at 1064 nm with topological charge (TC) up to 6 is created. By single-pass SHG of these PVBs through the MgO-doped, periodically poled congruent LiNbO₃ crystal, PVBs at green wavelength (532 nm) with TCs up to 12 are generated. The TC of the PVB is identified by the interferogram between the PVB and the reference TEM₀₀ Gaussian beam. The SH power (efficiency) of the PVB is measured to be independent of the TC. Furthermore, the impacts of beam parameters, including the ring radius (ρ) and the ring half-width (Δ), on the SH efficiency of the PVB, are also investigated. The SH efficiency is inversely proportional to both the ring radius ρ and ring half-width Δ. Experimental results agree well with those theoretical ones. The SH PVB transforms to the BGVB at the far-field. The paper also indicates that by transforming the Laguerre–Gaussian vortex beam (LGVB) into the PVB, the detrimental impact that the SH efficiency of LGVB decreases with the increase of TC value can be effectively mitigated, and high SH efficiency can be maintained even at high TC value.