Characterization and control of quasi-bound states in the continuous in Si<sub>3</sub>N<sub>4</sub> photonic crystals

Photon localization is of great significance in both basic research and technical applications. Bound states in the continuum (BICs) in photonic crystal provide a new mechanism for effective photon localization. However, the imperfections and defects are inevitable in the process of fabricating photonic crystals. Momentum-space characterization is used as a powerful tool to analyze how such processing variations affect the photonic band structure, providing information for designing and fabricating photonic crystal devices. In this work, a photonic crystal in the visible light band is designed and its band structure is analyzed through FDTD simulation. The high symmetry at the point in momentum space <i>Γ</i> leads to a symmetry mismatch between the internal mode of the photonic crystal and the external propagation mode (radiation continuum), so that bound states with infinite lifetime appear above the light, thereby achieving the localization of photons in the vertical direction. At the same time, the angle-resolved photoluminescence (PL) spectrum of the photonic crystal is measured through the self-built angle-resolved optical path. The weak photoluminescence of the Si<sub>3</sub>N<sub>4</sub> substrate is coupled with the photonic crystal mode for measuring the photonic crystal band. It can be observed that the band structure is consistent with the simulation results. At the same time, the intensity of the TE<sub>1</sub> band near the <i>Γ</i> point is significantly weakened compared with the intensity at the position away from the <i>Γ</i> point, but it is not completely eliminated. This shows that errors and defects caused in fabrication process will destroy the symmetry of the structure, causing the BIC to evolve into the quasi-BIC. The quasi-BIC mode achieves effective localization of photons in the vertical direction near the <i>Γ</i> point. Furthermore, a heterostructure of photonic crystals with different periods is designed to achieve lateral photon localization by utilizing the band nesting between the photonic ctystals with different periods. Through this approach, this study ultimately develops a high-quality microcavity with a ratio of impressive quality factor to mode volume of <inline-formula><tex-math id="M1">\begin{document}$ 6\times {10}^{14} $\end{document}</tex-math></inline-formula> cm<sup>–3</sup>, and achieves characteristic regulation of the momentum space of photonic crystals by adjusting the structural parameters. This research is of great significance for designing photonic crystals and studying the interaction between light and matter.