We numerically study the nonlocal solitons in dual-periodic parity-time ($\mathcal{PT}$) symmetric optical lattices built into a nonlocal self-focusing medium. We state the existence, stability, and propagation dynamics of such $\mathcal{PT}$-gap solitons in detail. Simulated results show that there exist stable gap solitons. The energy flow density and the stable region of the $\mathcal{PT}$-gap solitons in both the propagation constant and the degree of nonlocality are also examined.

We investigate numerically the interaction between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss that the beams with different intensities and phases launch into the different lattice structures but accelerate in opposite directions. During interactions, the interference fringe, breathers, and soliton pairs are observed. 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 in the self-defocusing media, the appropriate AiG beam amplitude and lattice depth may lead to the formation of soliton pairs, On the contrary, the interaction of two Gaussian beams is diffraction.

We propose a method for generation of tunable three-dimensional (3D) helical lattices with varying helix pitch. In order to change only the lattice helix pitch, a periodically varying phase along the propagation direction is added to the central beam – one of the interference beams for lattice construction. The phase periodicity determines the helix pitch, which can be reconfigured at ease. Furthermore, a helical lattice structure with an interface (domain wall) is also achieved by changing the phase structure of the lateral beams, leading to opposite rotating direction (helicity) on different sides of the interface. When a Gaussian beam is used to probe the bulk lattice, it can evolve into a spiral beam with its helicity varying in accordance with that of the lattice. Probing along the interface with two dipole-like optical beams leads to unusual propagation dynamics, depending on the phase and size of the two beams. This approach could be further explored for studies of nonlinear interface solitons and topological interface states. In addition, the helical lattices may find applications in dynamical multi-beam optical tweezers.

We design a framework based on the spatial-domain copropagation of two light beams with mutually orthogonal polarizations and opposite transverse components of carrier wave vectors in a nonlinear waveguide with randomly varying birefringence, the averaging with respect to which introduces an effective Manakov nonlinearity in the system. The corresponding two-component system of nonlinear Schrödinger equations is derived, being similar to the system of coupled one-dimensional Gross-Pitaevskii equations for a binary spin-orbit-coupled Bose-Einstein condensate. The system may also include an effective Rabi coupling (direct linear mixing of the components) and a periodic potential, representing a photonic-crystal structure in the underlying waveguide. For self-focusing and self-defocusing signs of nonlinearity, soliton solutions of several symmetry types are obtained by means of numerical methods, and their stability is investigated, including gap solitons in the case when the periodic potential is present.

The structured light projection (SLP) method occupies a crucial position in three-dimensional (3D) imaging technology. Different working wavelengths of structured light can be employed depending on the situation. However, there are few structured lights that can be modulated based on wavelength at present. Therefore, we have comprehensively investigated and designed a Dammann grating (DG) based on metasurface, which can be controlled through multi-beam interference (MBI) to achieve a change of the working wavelength. In this work, we can convert the straight waveguide to the helical waveguide by fine-tuning the related parameters of the incident lights and generate 5 × 5 diffraction spot arrays in the wavelength range of 480–510 nm and 950–1020 nm, respectively. Furthermore, the metasurfaces exhibit good performance. For example, their spread angles can be up to 44° × 44° and they can reach a conversion efficiency of over ≥50% while maintaining a contrast ratio of roughly 40%. Compared with traditional structured light, it can be used in different working wavelengths and has a broader application range in 3D sensing systems.