The two-dimensional photonic Moiré superlattice (PMS) possesses some properties that conventional photonic crystals do not have, such as flat-band features and optical localization phenomena different from Anderson localization. We construct the two-dimensional photonic Moiré superlattice by multiple-beam interference and investigate its band structure and optical field properties via the finite element method. By optimizing the effects of square photonic Moiré superlattice flims (SPMSs) thickness and air-hole radius on its flat-band and localization properties, the structure of SPMSs with high localization properties is obtained. The square lattice is found to have an optical localization effect of quasi-Dirac cone different from that of the hexagonal lattice. Our study provides reference significance for the development of high-performance micro- and nanostructured devices.

We adopt MATLAB software to simulate the multiple-beam interference for preparing SPMSs, and add the threshold processing part in the algorithm to optimize the blurring phenomenon in the interferogram due to the uneven distribution of interfering light intensity. Then, square lattice photonic crystals and SPMSs with clearer structures can be obtained, and the sublattice air-hole radius r of the SPMSs can be controlled by changing the threshold value. The SPMSs model prepared uses perfectly matched layers and periodic boundary conditions. The eigenmodes and band structures are calculated using the finite element method. Comparative simulations are carried out by varying r and film thickness h to test whether these two parameters affect the local and flat band properties of SPMSs.

Optical localization and flat-band properties exist in SPMSs as in HPMSs, while quasi-Dirac cone localization phenomena exist in SPMSs differently from HPMSs. The sublattice air-hole radius of SPMSs r and the film thickness h affect the localization and flat-band properties of SPMSs. Specifically, smaller values deform localized modes and reduce flat-band properties, and larger ones decrease the strength and flat-band properties of the localized central electric field, both of which have optimal values. Generally, SPMSs with γ of 4.98°, r of 127.5 nm, and h of 700 nm have higher-quality optical and flat-band properties.