[论文解读] Hyperuniform Disorder in Photonic Crystal Slabs with Intrinsic non-Hermiticity

Zeyu Zhang, Koorosh Sadri+2 more|arXiv (Cornell University)|Mar 4, 2026

Quantum Mechanics and Non-Hermitian Physics被引用 0

一句话总结

论文为具有辐射损耗的非厄米光子晶体薄膜中的超均匀无序建立了理论框架，显示厄米情形下 Im(Σk) ~ k^α，而非厄米情形产生一个主导常数项加一个次主导的 k^β2 项，通过 TB 和 FDTD 模拟得到验证。

ABSTRACT

Hyperuniform disorder is a type of correlated disorder characterized by vanishing spectral density at small wavevectors, making the configuration effectively homogeneous on long length scales. In photonics, hyperuniform disorder is promising for generating isotropic photonic pseudogaps and engineering photonic crystal waveguides. However, these studies are largely restricted to idealized lossless settings, although all photonic systems necessarily have loss. In this work, light propagation in photonic crystal slabs with imposed hyperuniform disorder is investigated theoretically and numerically. The system is intrinsically non-Hermitian due to radiative loss, with non-Hermiticity appearing as a complex effective mass of a quadratic photonic band. A theoretical framework for disorder scattering is analytically derived in Hermitian and non-Hermitian quadratic bands with real and complex effective mass, respectively. In contrast to the power law behavior $|\mathbf{k}|^α$ observed in the Hermitian case (where $α$ is the hyperuniformity exponent), the scattering loss in the non-Hermitian band is given by $C_0+C_{β_2}\cdot|\mathbf{k}|^{β_2}$, where $C_0$ is a finite constant and the exponent $β_2\leq 2$. Our theoretical predictions are verified with tight-binding and Finite-Difference Time-Domain simulations with realistic photonic crystal parameters, based on recent experiments.

研究动机与目标

• 在具有内在辐射损耗（非厄米性）的光子晶体薄膜中激发并建模超均匀无序。
• 为具有实部和虚部有效质量的厄米和非厄米二次能带导出无序-散射框架。
• 预测不同超均匀性指数 α 下散射损失随动量 k 的标度。
• 使用现实参数的紧束缚模型和有限差分时域（FDTD）模拟来验证理论预测。

提出的方法

• 将无序表示为从局部能带尖端能量偏移定标的空间势 V'i,j。
• 通过傅里叶滤波实现超均匀无序，使谱密度 ρ̃(q) ∝ qα 在小 q 时成立。
• 使用微扰（Born）自能 Σk 计算 Im(Σk) 及其对 α 和 k 的依赖。
• 将非厄米带扩展为复杂 m，得到 Im(Σk) 以有限的 C0 为主导，及下一项 Cβ2·kβ2。
• 引入自一致Born近似（SCBA）以在 α 较小时考虑多重散射。
• 用现实光子晶体参数的紧束缚模拟和FDTD模拟来验证预测。

Figure 1: The non-Hermitian nature of photonic crystal slabs. (a) An illustration of the photonic crystal slab. The in-plane geometry contains circular air holes in a square lattice. (b) The simulated reflection spectrum of the structure in (a) along $k_{y}=0$ . (c) The resonance frequency of the ba

实验结果

研究问题

• RQ1 超均匀无序如何改变厄米二次能带中的散射损耗？
• RQ2 在具有复有效质量的非厄米二次能带中，散射损耗随动量 k 的标度为何？
• RQ3 α 对 Im(Σk) 的主导和次主导项在厄米与非厄米情形分别有何影响？
• RQ4 相对于 TB 和 FDTD 结果，多重散射效应（SCBA）在理论预测中的影响程度如何？

主要发现

• 在厄米二次能带中，Im(Σk) ∝ k^α，体现超均匀无序的特征。
• 在非厄米二次能带中，Im(Σk) 具有有限的主导常数 C0 ∝ Im(m)，以及与 k^β2 成比例的次主导项，β2 ≤ 2。
• 非厄米情形的主导散射损耗随 α 的影响为 (α+2)/α 乘以 w^2 a^2 再除以 6π α，乘以 Im(m)。
• 对于 α > 2，第二主导指数 β2 等于 2；β2 在 α 约为 (2/π) arctan(Re(m)/Im(m)) + 1 时出现跃变，原因是在 k^α 项的系数消失。
• SCBA 计算与 TB 和 FDTD 结果吻合良好，尤其在较大 α 时；在较小 α 时的偏差归因于高阶多重散射效应。
• 该工作为非厄米系统中的超均匀无序提供基准，并在现实损耗下为器件设计提供指南。

Figure 2: Hyperuniform disorder in photonic crystal slabs. (a) Local potential configuration with uncorrelated disorder. The color and the size of the holes represent the local potential change at each site with respect to the periodic (without disorder) case. Only an area of $30\times 30$ unit cell