[论文解读] Multiple backscattering in trivial and non-trivial topological photonic crystal edge states with controlled disorder

Sonakshi Arora, Thomas Bauer+3 more|arXiv (Cornell University)|Oct 4, 2023

Random lasers and scattering media被引用 4

一句话总结

本研究通过相位分辨近场显微镜对拓扑与平凡光子晶体边缘态中的多重反向散射进行实验研究，以测绘胡须状界面处光的传播。结果表明，在中等群速度下，非平凡拓扑边缘态的反向散射平均自由程（BMFP）比平凡态高出一个数量级，但随着无序度增加，这一优势迅速减弱，挑战了关于拓扑体系中减速与反向散射的传统预期。

ABSTRACT

We present an experimental investigation of multiple scattering in photonic-crystal-based topological edge states with and without engineered random disorder. We map the spatial distribution of light as it propagates along a so-called bearded interface between two valley photonic crystals which supports both trivial and non-trivial edge states. As the light slows down and/or the disorder increases, we observe the photonic manifestation of Anderson localization, illustrated by the appearance of localized high-intensity field distributions. We extract the backscattering mean free path (BMFP) as a function of frequency, and thereby group velocity, for a range of geometrically engineered random disorders of different types. For relatively high group velocities (with $n_g < 15$), we observe that the BMFP is an order of magnitude higher for the non-trivial edge state than for the trivial. However, the BMFP for the non-trivial mode decreases rapidly with increasing disorder. As the light slows down the BMFP for the trivial state decreases as expected, but the BMFP for the topological state exhibits a non-conventional dependence on the group velocity. Due to the particular dispersion of the topologically non-trivial mode, a range of frequencies exist where two distinct states can have the same group index but exhibit a different BMFP. While the topological mode is not immune to backscattering at disorder that breaks the protecting crystalline symmetry, it displays a larger robustness than the trivial mode for a specific range of parameters in the same structure. Intriguingly, the topologically non-trivial edge state appears to break the conventional relationship between slowdown and the amount of backscattering.

研究动机与目标

• 在受控无序条件下，实验量化拓扑与平凡光子晶体边缘态对多重反向散射的鲁棒性。
• 研究群速度与无序强度如何影响平凡与非平凡边缘态中的反向散射平均自由程（BMFP）。
• 确定在破坏晶格对称性的工程化随机无序存在下，拓扑保护是否依然有效。
• 利用相位分辨近场扫描光学显微镜测绘空间电场分布，以直接观察安德森局域化与散射动力学。
• 通过在同一结构中同步测量BMFP与群速度，解决先前关于拓扑鲁棒性的相互矛盾报告。

提出的方法

• 采用170 nm孔径探针的相位分辨近场扫描光学显微镜（NSOM），测量硅基绝缘体光子晶体膜上边缘态的复振幅与相位。
• 制备了两个谷光子晶体（VPC）之间的胡须状界面，以在同一器件中支持平凡与非平凡边缘态，并在相同制造无序条件下运行。
• 引入具有可控幅度的工程化随机无序（孔位与尺寸的波动），以探究其对反向散射的影响。
• 基于多重散射理论的通用度量，从空间场分布图中提取反向散射平均自由程（BMFP），作为频率与群速度的函数。
• 使用MIT Photonic-Bands进行数值模拟，采用60 nm圆角半径建模拐角倒角，并设定硅的折射率为n=3.48以匹配实验色散特性。
• 从测量的色散关系中确定群速度，从而实现在不同慢光区域之间直接比较BMFP。

Figure 1: (a) Scanning electron micrograph (SEM) of the bearded interface in the fabricated sample with the color-coded regions depicting the two mirror-inverted lattices with glide symmetry (blue and green). The lattice periodicity is $a=$510\text{\,}\mathrm{n}\mathrm{m}$$ . (b) Schematic represent

实验结果

研究问题

• RQ1 在相同群速度与受控无序条件下，平凡与非平凡边缘态的反向散射平均自由程（BMFP）如何比较？
• RQ2 在工程化无序存在下，拓扑保护是否显著降低反向散射，相比平凡边缘态？
• RQ3 随着无序度增加与群速度降低，特别是处于慢光区域时，拓扑边缘态的BMFP如何演化？
• RQ4 是否存在某个频率范围，使得两个具有相同群速度指数的模式表现出不同的BMFP，这归因于拓扑保护？
• RQ5 光速减慢在平凡与非平凡边缘态中在多大程度上增强反向散射？其行为是否符合传统标度定律？

主要发现

• 当群速度满足$n_g < 15$时，非平凡拓扑边缘态的反向散射平均自由程（BMFP）比平凡边缘态高出一个数量级。
• 非平凡模式的BMFP随无序度增加而迅速下降，表明在强对称性破缺无序下，拓扑保护是脆弱的。
• 相比之下，平凡模式的BMFP随无序度增加与群速度降低而单调下降，符合传统预期。
• 对于拓扑模式，观察到非传统的群速度依赖关系：在某些频率下，两个群速度指数相同的模式表现出不同的BMFP，表明拓扑保护并非仅由群速度决定。
• 在最慢群速度与高无序条件下，平凡与非平凡边缘态均表现出局域化的高强度场分布，表明安德森局域化已开始出现。
• 尽管存在多重反向散射与局域化，非平凡边缘态在相同条件下仍保持可测量的鲁棒性优势，尽管该优势不足一个数量级。

Figure 2: Real and reciprocal space of electromagnetic field of an ensemble-averaged realization of a bearded interface without the intentional disorder. (a) Near-field spatial-spectral amplitude map normalized to the incoupling region collected as a function of frequency and position along the inte