发表机构
Skolkovo Institute of Science and Technology; Moscow Institute of Physics and Technology（斯科尔科沃科学技术研究所; 莫斯科物理技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对光子晶体平板共振计算繁琐的问题，提出将能量与参数平等处理的共振子空间近似，通过往返矩阵投影至小空间，仅需少数点即可快速重建能带与光谱，并在强六角硅光栅上验证了其准确性与高效性。
AI 中文摘要
共振近似对于光子晶体平板的解释和高效建模不可或缺，然而大多数共振近似将本征模式描述为在其余参数固定时复能量平面上的一个极点。跟踪这些极点及其在布里渊区或结构参数变化时的杂化，是劳动密集型的，并严重限制了共振近似在能带结构计算和结构优化中的应用。在此，我们引入一种共振子空间近似，将光子能量与所有其他参数平等对待。考虑一大类可被分为两个非共振部分的光子晶体平板，我们证明其共振完全源于耦合傅里叶谐波在这两部分之间的往返传播，这与法布里-珀罗和波导模式直接类比。我们将标量往返相位推广为往返矩阵和相位矩阵，它们对所有参数的平滑依赖性使我们能够将问题投影到在单一锚点处定义的小型共振子空间上，并将其外推到任意维参数空间的局部区域。因此，仅需在少数几个点进行严格计算，即可在数秒内重建作为能量、波矢、几何尺寸或介电常数函数的能带结构、模态线宽、复杂杂化及光学光谱。我们在强六角硅光栅上展示了该方法的准确性和多功能性，解决了复杂模式杂化、对称性保护特征以及细微的几何控制效应，这些效应对于直接计算而言几乎不可及。该方法快速、准确且易于扩展，为共振光子晶体平板的探索、设计和优化提供了一条实用途径。
英文摘要
Resonant approximations are indispensable for the interpretation and efficient modeling of photonic crystal slabs, yet most of them describe an eigenmode as a pole in the complex energy plane at a fixed set of the remaining parameters. Tracking such poles and their hybridization across the Brillouin zone or upon variation of structural parameters is labor-intensive and severely limits the use of resonant approximations in band-structure calculations and structural optimization. Here we introduce a resonant subspace approximation that treats the photon energy and all other parameters on an equal footing. Considering a wide class of photonic crystal slabs that can be split into two non-resonant parts, we show that their resonances arise solely from the round-trip propagation of coupled Fourier harmonics between these parts, in direct analogy with Fabry--Pérot and waveguide modes. We generalize the scalar round-trip phase to round-trip and phase matrices, whose smooth dependence on all parameters allows us to project the problem onto a small resonant subspace defined at a single anchor point and to extrapolate it throughout a local region of parameter space of arbitrary dimensionality. As a result, rigorous computations at only a few points suffice to reconstruct the band structure, modal linewidths, complex hybridization, and optical spectra as functions of energy, wavevector, geometric dimensions, or permittivity within seconds. We demonstrate the accuracy and versatility of the approach on a strong hexagonal silicon grating, resolving intricate mode hybridization, symmetry-protected features, and subtle geometry-controlled effects that are hardly accessible to straightforward computations. The method is fast, accurate, and readily extensible, offering a practical route to the exploration, design, and optimization of resonant photonic crystal slabs.
Comments18 pages, 7 figures
