AI 中文总结
该研究在光子学时域逆设计中引入加权长滞后自相关能量的时域度量，融入FDTD拓扑优化框架，用于抑制光学器件宽带响应的带内波纹等缺陷。
AI 中文摘要
光子学中的时域逆设计适用于最大化光学器件在宽频率范围内的效率。该场景下常用的目标包括由坡印廷定理推导的时域积分场量，如能量、通量或耗散功率，这些量可通过帕塞瓦尔定理直接与频域积分响应关联。这类目标计算效率高，但仅测量目标带宽内的总响应，无法捕捉不期望的带内波纹、窄光谱特征或旁瓣。我们通过引入一种基于光学响应的加权长滞后自相关能量、量化此类光谱变化的时域度量来克服这一局限。我们将该度量融入基于FDTD的拓扑优化框架，并通过时域伴随方法逆设计一维介质布拉格镜的实例，展示其有益效果。
英文摘要
Time-domain inverse design in photonics is known to be suitable for maximizing the efficiency of optical devices over broad frequency ranges. Objectives commonly used in this context include time-integrated field quantities derived from Poynting's theorem, such as energy, flux, or dissipated power, which can be directly linked to integrated frequency-domain responses via Parseval's theorem. While computationally efficient, these objectives measure only the total response over the targeted bandwidth and, as we demonstrate, are insufficient to capture undesired in-band ripple, narrow spectral features, or sidelobes. We overcome this limitation by introducing a time-domain metric quantifying such spectral variations based on the weighted long-lag autocorrelation energy of the optical response. We incorporate this metric into an FDTD-based topology-optimization framework and demonstrate its beneficial effect on the example of inverse designing one-dimensional dielectric Bragg mirrors via the time-domain adjoint method.
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