基于FDTD的等离子体结构逆设计
Inverse Design of Plasmonic Structures with FDTD
摘要：
逆向设计极大地扩展了纳米光子器件，并带来了优化的性能。然而，使用等离子体结构的逆设计一直具有挑战性，由于局部场集中，可以导致梯度计算中的错误时，连续伴随方法被使用。另一方面，用离散伴随方法可以得到精确的梯度。从历史上看，离散版本专门用于有限元模型，并且很少尝试在等离子体结构的逆设计中应用时域差分（FDTD）方法。由于FDTD在等离子体结构模拟中的广泛应用，本文将离散伴随方法与FDTD相结合，提出了一种基于密度拓扑优化的等离子体结构逆设计框架。我们证明了具有不同介电常数的等离子体块结构的梯度计算的准确性。等离子体结构特有的另一个挑战是，由选择不当的材料插值引起的非物理放大可能破坏优化的稳定收敛。为了避免这一点，我们采用了非线性材料插值方案的FDTD求解器。此外，过滤和投影正则化，以确保所设计的结构的可制造性。作为这个框架的一个例子，提出了一个等离子体领结孔径的电场的成功重建。
英文摘要：
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.
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