The study of moiré patterns in twisted bilayer two-dimensional van der Waals materials has revealed fascinating electronic properties, including moiré excitons, fractional Chern insulators, and Mott insulators. This research extends the concept of moiré physics to photonics, focusing on the unique properties of twisted bilayer photonic crystals (TBPCs). Optical vortices, light beams with a spiral phase front carrying orbital angular momentum (OAM), have shown promise in various fields, including super-resolution imaging, optical communication, micromanipulation, and quantum information processing. Efficient and robust generation of optical vortices is crucial for these applications. This paper investigates a novel approach to generating optical vortices using the inherent chirality introduced by twisting two layers of photonic crystals. The central hypothesis is that the twist-enabled coupling between BIC modes in the two layers facilitates the generation of robust optical vortices, insensitive to variations in incident angle or illumination position. This approach offers a potential solution for creating stable and highly controlled optical vortices for advanced applications.

Previous research has explored moiré patterns in photonics, demonstrating twist-induced flat bands, energy localization, and optical solitons. The breaking of mirror symmetry by twisting photonic structures has also been shown to enable chiral optical properties. Existing methods for optical vortex generation often rely on complex setups or are sensitive to experimental parameters. While methods using bound states in the continuum (BICs) have shown promise, they often lack the robustness required for practical applications. This research builds upon the understanding of BICs and moiré physics to develop a novel and robust method for generating optical vortices.

The study employs a theoretical model based on coupled-mode theory to analyze the interlayer coupling in TBPCs. The model considers two planar photonic crystal slabs with a small twist angle, each consisting of a honeycomb array of silicon nanodisks. The theory focuses on the coupling between BIC modes in one layer and guided resonances in the other, facilitated by the moiré structure. Equation (1) describes the crosstalk between eigenmodes in closely placed disks, while Equation (2) quantifies the coupling intensity between the BIC in one layer and modes in the other. The analysis reveals that the twist breaks the short-range periodicity, enabling the coupling between BIC modes and guided resonances, creating a "moiré channel" for energy transfer. Equation (3) describes the temporal coupled-mode theory (TCMT) used to analyze the energy transfer between the BIC and guided resonance modes. Equation (4) defines the orientation of the state of polarization (SOP), and Equation (5) formulates the radiated field, showing the emergence of Pancharatnam-Berry (PB) phases. The theoretical findings are validated through full-wave numerical simulations using COMSOL Multiphysics and Lumerical FDTD solutions. The simulations involve exciting the TBPC system with a pulsed Gaussian beam and analyzing the resulting electric field profiles in the far field. The impact of varying interlayer separation and twist angle on vortex generation is also investigated.

The research demonstrates the generation of optical vortices with both even and odd topological orders in TBPCs. The "doughnut" intensity distribution and vortex phase distribution are confirmed through numerical simulations. The topological order of the generated vortices is consistent with the theoretical predictions based on SOPs around the BIC mode. The study shows that the optical vortex generation is robust against variations in interlayer separation and twist angle, confirming the insensitivity to geometric disturbances. The time evolution analysis reveals that the optical vortex radiation emerges from the BIC modes, dominating over other transient modes. The vortex emission is independent of incident beam position and angle, eliminating the need for precise alignment in applications. This is further supported by supplementary figures showcasing the robustness of the vortex generation process even with imperfections.

The findings demonstrate a novel and robust method for generating optical vortices based on the unique properties of TBPCs. The twist-enabled coupling mechanism provides a tunable interlayer channel to connect BIC modes to free space, opening new avenues for manipulating the angular momentum of photons. The robustness of this method against geometric imperfections offers a significant advantage over existing techniques. This work bridges the gap between moiré physics and photonics, offering a versatile platform for generating well-defined and controlled optical vortices. The inherent similarities between photonic systems and condensed matter systems suggest potential applications of this mechanism in other materials.

This research successfully demonstrates the generation of robust optical vortices using twisted bilayer photonic crystals. The key innovation lies in exploiting the twist-enabled coupling between BIC modes and guided resonances. The robustness of the generated vortices against geometric imperfections makes this approach promising for various applications requiring controlled OAM beams. Future research could explore the integration of TBPCs with micro/nanoelectromechanical systems (MEMS/NEMS) to create tunable vortex beams with adjustable parameters, and the development of tunable OAM lasers.

The current study primarily focuses on theoretical and numerical analysis. Experimental validation of the findings is needed to fully confirm the robustness and efficiency of the proposed method in a real-world setting. The analysis is limited to a specific type of photonic crystal structure; the generalizability of the findings to other structures requires further investigation.