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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 Γ 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 Si3N4 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 TE1 band near the Γ point is significantly weakened compared with the intensity at the position away from the Γ 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 Γ point. Furthermore, a heterostructure of photonic crystals with different periods is designed to achieve lateral photon localization by utilizing the band nesting between the two]. Through this approach, this study ultimately develops a high-quality microcavity with a ratio of impressive quality factor to mode volume of $ 6\times {10}^{14} $ cm–3, 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.
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Keywords:
- photonic crystals /
- bound states in the continuation domain /
- momentum space /
- visible wavelengths
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图 1 光子晶体的设计和制备 (a) 光子晶体及导致其损耗因素的示意图; (b) 模拟的能带结构, 其中红色圆点代表TE模式, 蓝色圆点代表TM模式, 插图为第一个布里渊区; (c) 制备的光子晶体局部的扫描电子显微镜俯视图, 周期为326 nm, 孔洞结构直径为223 nm; (d) 制备的光子晶体扫描电子显微镜侧视图, 其中孔洞结构的高度为365 nm; (e) 光子晶体的扫描电子显微镜图像
Figure 1. Design and fabrication of photonic crystal: (a) Schematic of a photonic crystal and the factors contributing to loss. (b) Simulated band structure. The TE band is marked with red dots and The TM band is marked with blue dots. Inset: the first Brillouin zone. (c) Scanning electron microscope images of the fabricated photonic crystal from top views. The period is 326 nm and the diameter of the cylindrical holes is 223 nm. (d) Scanning electron microscope images of the fabricated photonic crystal from side views. The height of the cylindrical holes is 365 nm; (e) Scanning electron microscope images of the fabricated photonic crystal.
图 2 光子晶体动量空间表征 (a) 角分辨光路原理示意图, 其中绿色线代表激发光, 浅红色线代表样品光致荧光信号, “BFP”表示后焦面; (b) 沿Γ-X方向和(d)沿Γ-M方向的角分辨光致荧光光谱; (c) 沿Γ-X方向和(e)沿Γ-M方向能带仿真. 光子晶体结构参数如图1(c), (d)所示
Figure 2. Characterization of momentum in photonic crystal: (a) Schematic of angle-resolved optical path. The green lines represent the incident light. The light red region denotes photoluminescence signal. BFP, back focal plane. (b), (d) Measured angle-resolved photoluminescence (PL) spectra along Γ-X (b) and Γ-M (d) directions. (c), (e) Calculated band structure along Γ-X (c) and Γ-M (e) directions. The structure parameters of photonic crystal are shown in Fig. 1 (c) and Fig. 1 (d).
图 3 微腔的模式表征 (a) 微腔SEM图像, A区域光子晶体(周期 a = 325 nm, 直径d = 214 nm, 孔洞数目$ {N}_{a} $ = 13)由不同周期的B区域光子晶体(周期b = 335 nm, 直径d = 214 nm, 孔洞数目$ {N}_{b} $ = 17)包围, 两区域之间的间隔为330 nm; (b) 光子晶体PL光谱; (c) 光子晶体的模式热点位置处的PL光谱; (d) 光子晶体的PL扫描图像; (e) M11模式、(f) M12模式和(g) M21模式的远场模式分布; 白色虚线和蓝色虚线分别表示A区域和B区域光子晶体边界; 黄色虚线表示模式表征的扫描区域
Figure 3. Characterization of micro-cavity modes: (a) SEM image of micro-cavity. Region A photonic crystal (period a = 325 nm, diameter d = 214 nm, the number of holes $ {N}_{\mathrm{a}} $ = 13) are surrounded by region B photonic crystal (period b = 335 nm, diameter d = 214 nm, the number of holes $ {N}_{\mathrm{b}} $ = 17) with different periods, and the interval between the two regions is 330 nm. (b) PL spectral of photonic crystal. (c) PL spectral of mode hot spot in photonic crystal. (d) PL mapping image of photonic crystal. The far-field distribution of (e) M11, (f) M12 and (g) M21 modes. The white dashed and blue dashed represent the photonic crystal boundaries of region A and region B respectively. The yellow dashed represents the scan area of the mode characterization.
图 4 微腔的参数调控 (a) 孔洞直径d为214 nm和(b) 229 nm的光子晶体角分辨PL光谱; (c) 不同孔洞直径的微腔光子晶体A区域PL光谱; (d) 高度h为330 nm, 孔洞直径d为233 nm的光子晶体角分辨PL光谱; (e) 高度h为330 nm不同孔洞直径的微腔光子晶体A区域PL光谱; (f) 高度h为330 nm孔洞直径d为233 nm的光子晶体PL扫描图像, 白色虚线和蓝色虚线分别表示A区域和B区域光子晶体边界; 图4样品的其他结构参数均与图3(a)相同
Figure 4. Parameters tuning of micro-cavity: Measured angle-resolved PL spectra of photonic crystals with hole diameter d of (a) 214 nm and (b) 229 nm; (c) PL spectra of region A of microcavity photonic crystals with different hole diameters; (d) measured angle-resolved PL spectra of photonic crystals with height h of 330 nm and hole diameter d of 233 nm; (e) PL spectra of region A of microcavity photonic crystals with different hole diameters and a height h of 330 nm; (f) PL mapping image of photonic crystals with height h of 330 nm and hole diameter d of 233 nm. The white dashed and blue dashed represent the photonic crystal boundaries of region A and region B respectively. Other structural parameters of the sample in Fig. 4 are the same as those in Fig. 3(a).
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