Inverse Design of Plasmonic Structures with FDTD
Inverse Design of Plasmonic Structures with FDTD
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DOI：
10.1021/acsphotonics.1c00260
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Z. Zeng;Prabhu K. Venuthurumilli;Xianfan Xu
中科院分区：
文献类型：
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作者：
Z. Zeng;Prabhu K. Venuthurumilli;Xianfan Xu
逆设计极大地扩展了纳米光子器件，带来了优化的性能。然而，在等离子体结构中使用逆设计一直具有挑战性，因为当使用连续统伴随方法时，局部场浓度可能导致梯度计算误差。另一方面，用离散伴随法可以得到精确的梯度。历史上，离散版本仅与有限元模型一起使用，并且将时域有限差分（FDTD）方法应用于等离子体结构的反设计很少尝试。鉴于时域有限差分法在等离子体结构模拟中的广泛应用，本文将离散伴随法与时域有限差分法相结合，提出了一种基于密度拓扑优化的等离子体结构反设计框架。我们证明了梯度计算对于具有变介电常数的等离子体块结构的准确性。等离子体结构的另一个独特的挑战是，由选择不当的材料插值引起的非物理放大可能会破坏优化的稳定收敛。为了避免这种情况，我们在FDTD求解器中采用了非线性材料插值方案。此外，为了保证结构的可制造性，还采用了滤波-投影正则化方法。作为该框架的一个例子，成功地重建了等离子体领结孔径的电场。
Inverse design has greatly expanded nanophotonic devices and brought optimized performance. However, the use of inverse design for plasmonic structures has been challenging due to local field concentrations that can lead to errors in gradient calculation when the continuum adjoint method is used. On the other hand, with the discrete adjoint method one can achieve the exact gradient. Historically the discrete version is exclusively used with a Finite Element model, and applying the Finite-Difference Time-Domain (FDTD) method in inverse design of plasmonic structures is rarely attempted. Due to the popularity of using FDTD in simulating plasmonic structures, we integrate the discrete adjoint method with FDTD and present a framework to carry out inverse design of plasmonic structures using density-based topology optimization. We demonstrate the exactness of the gradient calculation for a plasmonic block structure with varying permittivity. Another challenge that is unique with plasmonic structures is that non-physical amplification caused by poorly chosen material interpolation can destroy a stable convergence of the optimization. To avoid this, we adopt a non-linear material interpolation scheme in the FDTD solver. In addition, filtering-and-projection regularization is incorporated to ensure manufacturability of the designed structures. As an example of this framework, successful reconstruction of electric fields of a plasmonic bowtie aperture is presented.