Quasi Phase Matching Based on Aperiodic Hat Monohedral Tiling Superlattice Structure

Quasi-phase matching technology overcomes the limitations of photonic crystal materials and their transmission bands by artificially designing nonlinear photonic structures. Through periodic ferroelectric domain inversion achieved by electric field poling， this approach compensates for phase mismatch while enhancing the efficiency and flexibility of nonlinear frequency conversion. Quasi-periodic structures， with their aperiodic yet ordered arrangements， provide abundant reciprocal lattice vectors. An increasing variety of superlattice structures have been implemented in optical materials to explore their advantages for generating harmonics across diverse wavelengths.In this study， we incorporated the aperiodic hat-tiling monotile structure into nonlinear optical superlattices， successfully designing and fabricating a two-dimensional planar hat-tiling superlattice. The attainable harmonic wavelengths and their characteristics were systematically investigated. Experimental results demonstrate that the reciprocal space of the aperiodic hat-tiling superlattice exhibits pronounced sixfold rotational symmetry while maintaining periodic intense diffraction points. The diffraction pattern of the hat-tiling superlattice structure exhibits not only hexagonal symmetry but also additional bisecting points between every two vertices of the hexagon. Comparative analysis with conventional periodic structures reveals that the hat-tiling pattern demonstrates more pronounced intensity variations among diffraction spots. Furthermore， the reciprocal vectors in this configuration include additional orientations deviated by 30° from the horizontal axis as well as vertical directions. Under collinear conditions， the structure successfully achieved second-harmonic generation at fundamental wavelengths of 858 nm， 895 nm， 932 nm， 1 055 nm， and 1 100 nm， while under non-collinear conditions， the hat-tiling structure enabled efficient SHG at multiple fundamental wavelengths including 892 nm， 971 nm， 1 089 nm， 1 103 nm， and 1 389 nm. Comparative analysis with periodic hexagonal structures confirmed that the aperiodic hat-tiling offers richer reciprocal vectors. Moreover， the periodicity in reciprocal space significantly enhances the conversion efficiency of nonlinear photonic crystals.In conclusion， the hat-tiling structure offers reciprocal vectors of varying magnitudes along multiple directions. While preserving the high conversion efficiency characteristic of regular hexagonal structures， it overcomes the limitation of single reciprocal vectors in hexagonal lattices. The hat-tiling structure can provide reciprocal vectors of varying magnitudes along multiple directions to compensate for phase mismatch， thereby extending the achievable frequency bandwidth of fundamental waves. Based on the experimental results， we propose an optimized design by scaling the hexagonal edge length of the hat-tiling superlattice structure to 32.2 μm. This modification enables the strongest diffraction point to correspond to a reciprocal lattice vector that achieves second-harmonic generation for a fundamental wavelength of 1 550 nm， which is particularly significant for optical communication applications. The experimental data provide crucial references for further optimization to fully exploit the high-efficiency diffraction points. These findings advance the development of multi-channel nonlinear optical devices with enhanced spectral flexibility.