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In the current technological landscape, structured light technology holds a critically important position. However, traditional structured light optical components often require complex systems and extensive resources for application, and they function in a fixed manner. This study takes this challenge as an opportunity to design a novel dynamically tunable double-layer Dammann grating (DG) metasurface. During the research, we developed a double-layer DG metasurface structure using silica as the substrate and lithium niobate (LiNbO3, LN) as the nanocolumn material. By specifically introducing parity-time (PT) symmetry, we designed three distinct states, combined with rotational transformations leveraging the Moir\'e effect. Further investigations revealed that for metasurfaces with different radius combinations, changes in rotation and PT symmetry states resulted in significant variations in the shape, position, and intensity of the diffraction spots, alongside changes in conversion efficiency and contrast ratio. This study thoroughly and comprehensively unveils the significant impacts of rotational transformations, PT symmetry, and radius combination on the optical characteristics of double-layer DG metasurfaces, providing a new method for the design of dynamic tunable optical components with structured light.

We report experimental observation and theoretical explanation of novel propagation regimes for optical beams in an artificial nonlinear material with outstanding photorefractive properties. Nondiffractive beams, which keep their shapes invariant in the free space, feature self-splitting from the middle in two separating secondary beams, due to the light-matter interaction. The splitting degree is controlled by means of a phase-pre-modulation method. We propose applications of the self-splitting to the creation of an effectively chiral waveguide and the generation of even-order vortices.

Photonic Floquet lattices provide an excellent platform for manipulating different topologically protect-ed edge states. However, anti-chiral edge states have not been discussed much in Floquet lattices. Here, we propose a waveguide structure by combining two honeycomb Floquet photonic lattices with oppo-site rotation directions. In this structure, we find that the anti-chiral edge states have the same trans-mission direction on two parallel body edges. With an increasing modulation phase difference between the two sublattices in one direction, the width of the band gap becomes smaller and the robustness of the edge states becomes weaker. Interestingly, the transmission speed is also controlled by the phase difference. In addition to their relevance for the topological properties of the Floquet lattice system, these results may be applied to multi-channel optical switches, optical functional devices, and in other fields.

We investigate Airy-soliton interactions in self-defocusing media with PT potentials in one transverse dimension. We discuss different potentials in which the interacting beams with different phases are launched into the media at different separation distances. During interactions, there exist a primary collision region and a relaxation region accompanied by continuous interaction with the dispersed Airy tail. In the relaxation region, the beams exist soliton-like and breathers-like propagation. The beam width and mean power are influenced by initial separation, phase shift and modulation depth of PT potentials. Especially, the collision distance decreases with the spatial beam separation and the mean power possesses sinusoidal dependence on the phase shift., Comment: 16 pages, 5 figures

We investigate interactions by means of direct numerical simulations between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss different lattice structures in which the beams with different intensities and phases are launched into the medium, but accelerate in opposite directions. During interactions we see the interference fringe, breathers and soliton pairs generated that are not accelerating. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift and the beam interval. For a certain lattice period, the periodic interference fringe can form. A constructive or destructive interference can vary with the defect depth and phase shift. While the nonlinearity is introduced, the breathers is generated. Especially, the appropriate beam amplitude and lattice depth may lead to the formation of soliton pairs., Comment: 18 pages, 9 figures

We investigate numerically that a finite Airy-Gaussian (AiG) beam varies its trajectory and shape in the defected photonic lattices. The propagation properties and beam self-bending are controlled with modulation depth and period of the photonic lattices, positive and negative defects, beam distribution factor and nonlinearity change. For positive defects, the pseudo-period oscillation and localization of the AiG beam may be formed under a certain condition, while the beam is diffused for negative defects. Moreover, the solitons may appear during the propagation process when the self-focusing nonlinearity is introduced., Comment: 15 pages, 8 figures

We demonstrate that in-bulk vortex localized modes, and their surface half-vortex ("horseshoe") counterparts self-trap in two-dimensional (2D) nonlinear optical systems with $\mathcal{PT}$-symmetric photonic lattices (PLs). The respective stability regions are identified in the underlying parameter space. The in-bulk states are related to truncated nonlinear Bloch waves in gaps of the PL-induced spectrum. The basic vortex and horseshoe modes are built, severally, of four and three beams with appropriate phase shifts between them. Their stable complex counterparts, built of up to 12 beams, are reported too., Comment: 5 pages, 4 figures

We investigate light beam propagation along the interface between linear and nonlinear media with parity-time PT symmetry, and derive an equation governing the beam propagation. A novel class of two-dimensional PT surface solitons are found analytically and numerically, and checked to be stable over a wide range of PT potential structures and parameters. These surface solitons do not require a power threshold. The transverse power flow across beam is examined within the solitons and found to be caused by the nontrivial phase structure of the solitons. PT surface solitons are possibly observed experimentally in photorefractive crystals., Comment: 5 figures

We investigate one-dimensional Helmholtz solitons with nonlocal nonlinearity. We show an exact analytical solution to the nonlocal nonlinear nonparaxial propagation equation in the cases of high and weak nonlocality. We also numerically find that the degree of nonlocality can affect the width of nonlocal Helmholtz soliton beams, but have no effect on their stability. Contrarily, nonparaxiality can affect their stability, but have no effect on their width., Comment: 5 pages, 3 figures

It is studied the bright spatial solitons in nonlocal defocusing Kerr media with parity-time (PT) symmetric potentials. We find that these solitons can exist and be stable over a different range of potential parameters. The influence of the degree of nonlocality on the solitons and the transverse energy flow within the stable solitons are also examined., Comment: 4 pages

We numerically study the nonlocal gap solitons in parity-time (PT) symmetric optical lattices built into a nonlocal self-focusing medium. We state the existence, stability, and propagation dynamics of such PT gap solitons in detail. Simulated results show that there exist stable gap soltions. The influences of the degree of nonlocality on the soliton power, the energy flow density and the stable region of the PT gap solitons are also examined., Comment: 4 pages

We address (2+1)D surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium whose nonlinear contribution to the refractive index has a initial value at the interface. We find that there exist stable single and dipole surface solitons which do not exhibit a power threshold. The properties of the surface solitons can be affected by the initial value and the degree of nonlocality. When a laser beam is launched away from the interface, the beam will be periodic oscillations., Comment: 16 pages, 6 figures

We address the properties of surface-wave solitons on the interface between a semi-infinite homogeneous linear medium and a semi-infinite homogeneous nonlinear nonlocal medium. The stability, energy flow and FWHM of the surface wave solitons can be affected by the degree of nonlocality of the nonlinear medium. We find that the refractive index difference affects the power distribution of the surface solitons in two media. We show that the different boundary values at the interface can lead to the different peak position of the surface solitons, but it can not influence the solitons stability with a certain degree of nonlocality., Comment: 8 pages, 14 figures, 15 references, and so on